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11 non-alternating
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all knots up to 12 crossings maybe slow
discussion of unknown values
statistics of invariants
introduction and help
Download KNOTORIOUS (32 bit version)
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Shorthands denote
u_a algebraic unknotting number
Nak Nakanishi index
det determinant
sign signature
max LT maximum absolute value of
Levine-Tristram signatures
Hidden features
Click on to see
algebraic unknotting number how it has been detected
Alexander polynomial a Seifert matrix
(nondegenerate representative in the S-equivalence class)
Nakanishi index generator of the Alexander module,
if Nakanishi index is 1
Determinant H_1 of the double branched cover


Welcome to the
KNOTORIOUS
world wide web page!
set up by Maciej Borodzik mcboro'at'mimuw;edu;pl
and Stefan Friedl sfriedl'at'gmail;com
last update of the webpage 19 Feb 2012
last update of the knotorious data 01 Dec 2011
You may freely contact the authors in case of any questions.

Knot u_a Alexander
polynomial 		Nak.
index 		det. sign max LT.
3_1
1

detected by
an unknotting move
1-t+t^2
Seifert matrix of 3_1
-1 0
-1 -1
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
1
3
First homology
of the double branched cover of 3_1
Z/3
-2 2
4_1
1

detected by
an unknotting move
-1+3t-t^2
Seifert matrix of 4_1
1 0
-1 -1
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
1
5
First homology
of the double branched cover of 4_1
Z/5
0 0
5_1
2

detected by
the signature
1-t+t^2-t^3+t^4
Seifert matrix of 5_1
-1 -1 0 -1
0 -1 0 0
-1 -1 -1 -1
0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-1-1+t
5
First homology
of the double branched cover of 5_1
Z/5
-4 4
5_2
1

detected by
an unknotting move
2-3t+2t^2
Seifert matrix of 5_2
-1 -1
0 -2
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
1
7
First homology
of the double branched cover of 5_2
Z/7
-2 2
6_1
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 6_1
1 0
1 -2
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
t^-1-2+t
9
First homology
of the double branched cover of 6_1
Z/9
0 0
6_2
1

detected by
an unknotting move
-1+3t-3t^2+3t^3-t^4
Seifert matrix of 6_2
1 0 0 0
-1 -1 -1 -1
-1 0 -1 0
-1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-1+3-t
11
First homology
of the double branched cover of 6_2
Z/11
-2 2
6_3
1

detected by
an unknotting move
1-3t+5t^2-3t^3+t^4
Seifert matrix of 6_3
-1 0 0 0
-1 -1 0 0
-1 -1 1 1
0 0 0 1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-1
13
First homology
of the double branched cover of 6_3
Z/13
0 0
7_1
3

detected by
the signature
1-t+t^2-t^3+t^4-t^5+t^6
Seifert matrix of 7_1
-1 -1 -1 0 -1 -1
0 -1 -1 0 0 -1
0 0 -1 0 0 0
-1 -1 -1 -1 -1 -1
0 -1 -1 0 -1 -1
0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
7
First homology
of the double branched cover of 7_1
Z/7
-6 6
7_2
1

detected by
an unknotting move
3-5t+3t^2
Seifert matrix of 7_2
-1 1
0 -3
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
1
11
First homology
of the double branched cover of 7_2
Z/11
-2 2
7_3
2

detected by
the signature
2-3t+3t^2-3t^3+2t^4
Seifert matrix of 7_3
-1 -1 -1 -1
0 -1 0 -1
0 -1 -1 -1
0 0 0 -2
1
Generator of the Alexander module
(2t^3,0,t^3,1)
the Blanchfield form on it
-5t^-2+18t^-1-24+18t-5t^2
13
First homology
of the double branched cover of 7_3
Z/13
-4 4
7_4
2

detected by
the Lickorish test
4-7t+4t^2
Seifert matrix of 7_4
-2 0
-1 -2
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
-2t^-1+4-2t
15
First homology
of the double branched cover of 7_4
Z/15
-2 2
7_5
2

detected by
the signature
2-4t+5t^2-4t^3+2t^4
Seifert matrix of 7_5
-1 0 -1 0
0 -1 -1 0
0 0 -2 0
0 -1 -1 -1
1
Generator of the Alexander module
(-t,0,1,1)
the Blanchfield form on it
2t^-1-2+2t
17
First homology
of the double branched cover of 7_5
Z/17
-4 4
7_6
1

detected by
an unknotting move
-1+5t-7t^2+5t^3-t^4
Seifert matrix of 7_6
-1 0 0 0
-1 -1 0 0
-1 -1 1 -1
0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-2t^-1+3-2t
19
First homology
of the double branched cover of 7_6
Z/19
-2 2
7_7
1

detected by
an unknotting move
1-5t+9t^2-5t^3+t^4
Seifert matrix of 7_7
1 0 0 0
-1 -1 0 -1
0 0 1 0
-1 0 -1 -1
1
Generator of the Alexander module
(0,0,-1,1)
the Blanchfield form on it
t^-1-3+t
21
First homology
of the double branched cover of 7_7
Z/21
0 0
8_1
1

detected by
an unknotting move
-3+7t-3t^2
Seifert matrix of 8_1
1 0
-1 -3
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
t^-1-2+t
13
First homology
of the double branched cover of 8_1
Z/13
0 0
8_2
2

detected by
the signature
-1+3t-3t^2+3t^3-3t^4+3t^5-t^6
Seifert matrix of 8_2
1 0 0 0 0 0
-1 -1 -1 -1 -1 -1
-1 0 -1 -1 0 -1
-1 0 0 -1 0 0
-1 0 -1 -1 -1 -1
-1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
17
First homology
of the double branched cover of 8_2
Z/17
-4 4
8_3
1

detected by
an unknotting move
-4+9t-4t^2
Seifert matrix of 8_3
2 0
-1 -2
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
2t^-1-4+2t
17
First homology
of the double branched cover of 8_3
Z/17
0 0
8_4
1

detected by
an unknotting move
-2+5t-5t^2+5t^3-2t^4
Seifert matrix of 8_4
1 0 0 0
1 1 1 0
1 0 1 0
1 1 1 -2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
19
First homology
of the double branched cover of 8_4
Z/19
2 2
8_5
2

detected by
the signature
-1+3t-4t^2+5t^3-4t^4+3t^5-t^6
Seifert matrix of 8_5
-1 0 0 -1 -1 -1
0 1 0 0 0 0
-1 0 -1 -1 -1 -1
0 -1 0 -1 -1 -1
0 -1 0 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
21
First homology
of the double branched cover of 8_5
Z/21
-4 4
8_6
1

detected by
an unknotting move
-2+6t-7t^2+6t^3-2t^4
Seifert matrix of 8_6
1 0 0 0
0 -1 0 -1
1 -1 -2 -1
0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
23
First homology
of the double branched cover of 8_6
Z/23
-2 2
8_7
1

detected by
an unknotting move
1-3t+5t^2-5t^3+5t^4-3t^5+t^6
Seifert matrix of 8_7
-1 0 0 0 0 0
0 1 0 0 1 0
-1 0 -1 0 0 0
-1 1 -1 1 1 1
0 0 0 0 1 0
0 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-1
23
First homology
of the double branched cover of 8_7
Z/23
2 2
8_8
2

detected by
the Lickorish test
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 8_8
-1 0 0 0
-1 -1 0 0
0 0 1 0
1 1 -1 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
25
First homology
of the double branched cover of 8_8
Z/25
0 0
8_9
1

detected by
an unknotting move
-1+3t-5t^2+7t^3-5t^4+3t^5-t^6
Seifert matrix of 8_9
1 0 0 0 0 0
1 1 0 0 1 0
-1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 0
1 0 0 0 1 0
-1 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,-1)
the Blanchfield form on it
-t^-1+2-t
25
First homology
of the double branched cover of 8_9
Z/25
0 0
8_10
1

detected by
an unknotting move
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 8_10
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 1 0
-1 -1 1 1 1 1
0 0 0 0 1 0
-1 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
27
First homology
of the double branched cover of 8_10
Z/27
2 2
8_11
1

detected by
an unknotting move
-2+7t-9t^2+7t^3-2t^4
Seifert matrix of 8_11
1 0 0 0
-1 -1 1 -1
1 0 -2 1
-1 0 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
27
First homology
of the double branched cover of 8_11
Z/27
-2 2
8_12
1

detected by
an unknotting move
1-7t+13t^2-7t^3+t^4
Seifert matrix of 8_12
-1 -1 0 0
0 1 0 0
-1 0 1 -1
0 0 0 -1
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
-t^-1+3-t
29
First homology
of the double branched cover of 8_12
Z/29
0 0
8_13
1

detected by
an unknotting move
2-7t+11t^2-7t^3+2t^4
Seifert matrix of 8_13
-1 0 0 0
0 2 0 0
-1 0 -1 0
-1 -1 -1 1
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
1
29
First homology
of the double branched cover of 8_13
Z/29
0 0
8_14
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 8_14
1 0 0 0
-1 -1 0 1
0 0 -1 -1
1 0 0 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
1
31
First homology
of the double branched cover of 8_14
Z/31
-2 2
8_15
2

detected by
the signature
3-8t+11t^2-8t^3+3t^4
Seifert matrix of 8_15
-1 -1 -1 -1
0 -2 -1 -2
0 -1 -2 -1
0 -1 -1 -2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
33
First homology
of the double branched cover of 8_15
Z/33
-4 4
8_16
2

detected by
the Lickorish test
1-4t+8t^2-9t^3+8t^4-4t^5+t^6
Seifert matrix of 8_16
1 0 0 0 -1 0
0 -1 0 0 0 0
1 0 1 0 -1 0
1 -1 1 1 -1 1
0 -1 0 0 -1 0
1 -1 1 0 -1 1
1
Generator of the Alexander module
(0,1,-t,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
35
First homology
of the double branched cover of 8_16
Z/35
2 2
8_17
1

detected by
an unknotting move
-1+4t-8t^2+11t^3-8t^4+4t^5-t^6
Seifert matrix of 8_17
1 0 0 0 0 0
1 1 0 1 0 0
-1 -1 -1 -1 -1 -1
1 0 0 1 0 0
0 -1 0 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
1
37
First homology
of the double branched cover of 8_17
Z/37
0 0
8_18
2

detected by
the Nakanishi index
-1+5t-10t^2+13t^3-10t^4+5t^5-t^6
Seifert matrix of 8_18
1 0 0 0 -1 0
0 -1 0 0 0 0
0 -1 -1 0 0 0
1 -1 -1 1 -1 1
0 -1 -1 0 -1 0
1 0 -1 0 -1 1
2
45
First homology
of the double branched cover of 8_18
Z/15+Z/3
0 0
8_19
3

detected by
the signature
1-t+t^3-t^5+t^6
Seifert matrix of 8_19
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 -1
-1 -1 0 -1 0 0
0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
3
First homology
of the double branched cover of 8_19
Z/3
-6 6
8_20
1

detected by
an unknotting move
1-2t+3t^2-2t^3+t^4
Seifert matrix of 8_20
-1 -1 -1 -1
0 0 -1 -1
0 -1 0 -1
0 0 -1 0
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
9
First homology
of the double branched cover of 8_20
Z/9
0 0
8_21
1

detected by
an unknotting move
-1+4t-5t^2+4t^3-t^4
Seifert matrix of 8_21
-1 -1 -1 -1
0 -2 -1 -2
0 -1 0 -1
0 -1 -1 -2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
1
15
First homology
of the double branched cover of 8_21
Z/15
-2 2
9_1
4

detected by
the signature
1-t+t^2-t^3+t^4-t^5+t^6-t^7+t^8
Seifert matrix of 9_1
-1 -1 -1 -1 0 -1 -1 -1
0 -1 -1 -1 0 0 -1 -1
0 0 -1 -1 0 0 0 -1
0 0 0 -1 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -1 0 -1 -1 -1
0 0 -1 -1 0 0 -1 -1
0 0 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-t^-2+t^-1-1+t-t^2+t^3
9
First homology
of the double branched cover of 9_1
Z/9
-8 8
9_2
1

detected by
an unknotting move
4-7t+4t^2
Seifert matrix of 9_2
-1 -1
0 -4
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
1
15
First homology
of the double branched cover of 9_2
Z/15
-2 2
9_3
3

detected by
the signature
2-3t+3t^2-3t^3+3t^4-3t^5+2t^6
Seifert matrix of 9_3
-1 -1 -1 -1 -1 -1
0 -1 -1 0 -1 -1
0 0 -1 0 0 -1
0 -1 -1 -1 -1 -1
0 0 -1 0 -1 -1
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-3t^-1+3-3t+2t^2
19
First homology
of the double branched cover of 9_3
Z/19
-6 6
9_4
2

detected by
the signature
3-5t+5t^2-5t^3+3t^4
Seifert matrix of 9_4
-1 -1 1 -1
0 -1 1 0
0 0 -3 0
0 -1 1 -1
1
Generator of the Alexander module
(t+t^3-t^4,0,1+t-t^3,0)
the Blanchfield form on it
3t^-1-5+3t
21
First homology
of the double branched cover of 9_4
Z/21
-4 4
9_5
1

detected by
an unknotting move
6-11t+6t^2
Seifert matrix of 9_5
-3 1
0 -2
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
-2t^-1+4-2t
23
First homology
of the double branched cover of 9_5
Z/23
-2 2
9_6
3

detected by
the signature
2-4t+5t^2-5t^3+5t^4-4t^5+2t^6
Seifert matrix of 9_6
-1 0 0 -1 0 0
0 -1 -1 -1 0 -1
0 0 -1 -1 0 0
0 0 0 -2 0 0
0 -1 -1 -1 -1 -1
0 0 -1 -1 0 -1
1
Generator of the Alexander module
(t+t^2-t^3,0,-t^2,-1-t,-1+t^3,-t)
the Blanchfield form on it
2t^-2-2t^-1+3-2t+2t^2
27
First homology
of the double branched cover of 9_6
Z/27
-6 6
9_7
2

detected by
the signature
3-7t+9t^2-7t^3+3t^4
Seifert matrix of 9_7
-1 0 1 0
0 -1 1 0
0 0 -3 0
0 -1 1 -1
1
Generator of the Alexander module
(-1,0,0,1)
the Blanchfield form on it
3t^-1-4+3t
29
First homology
of the double branched cover of 9_7
Z/29
-4 4
9_8
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 9_8
-1 0 0 0
-1 -1 0 0
0 0 -1 0
1 1 1 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-t^-2+3t^-1-4+3t-t^2
31
First homology
of the double branched cover of 9_8
Z/31
-2 2
9_9
3

detected by
the signature
2-4t+6t^2-7t^3+6t^4-4t^5+2t^6
Seifert matrix of 9_9
-1 -1 0 -1 -1 0
0 -1 0 0 -1 0
0 0 -1 0 -1 0
0 -1 0 -1 -1 0
0 0 0 0 -2 0
0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-3t^-1+3-3t+2t^2
31
First homology
of the double branched cover of 9_9
Z/31
-6 6
9_10
2

detected by
the signature
4-8t+9t^2-8t^3+4t^4
Seifert matrix of 9_10
-1 1 -1 -1
0 -2 1 1
0 0 -1 -1
0 0 0 -2
1 or 2
33
First homology
of the double branched cover of 9_10
Z/33
-4 4
9_11
2

detected by
the signature
-1+5t-7t^2+7t^3-7t^4+5t^5-t^6
Seifert matrix of 9_11
1 0 0 0 1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
1 -1 0 1 1 1
0 0 0 0 1 0
1 0 0 0 1 1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
2t^-2-3t^-1+3-3t+2t^2
33
First homology
of the double branched cover of 9_11
Z/33
4 4
9_12
1

detected by
an unknotting move
-2+9t-13t^2+9t^3-2t^4
Seifert matrix of 9_12
-1 0 0 0
0 -2 0 0
-1 0 -1 0
-1 1 -1 1
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
1
35
First homology
of the double branched cover of 9_12
Z/35
-2 2
9_13
2

detected by
the signature
4-9t+11t^2-9t^3+4t^4
Seifert matrix of 9_13
-1 0 -1 0
0 -2 0 0
0 -1 -2 0
-1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,1-t)
the Blanchfield form on it
4t^-1-7+4t
37
First homology
of the double branched cover of 9_13
Z/37
-4 4
9_14
1

detected by
an unknotting move
2-9t+15t^2-9t^3+2t^4
Seifert matrix of 9_14
1 0 0 0
-1 -1 -1 0
-1 0 -1 1
0 0 0 2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
2t^-1-3+2t
37
First homology
of the double branched cover of 9_14
Z/37
0 0
9_15
2

detected by
the Lickorish test
-2+10t-15t^2+10t^3-2t^4
Seifert matrix of 9_15
-1 -1 0 0
0 1 0 0
0 0 1 0
1 0 -1 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-t^-2+5t^-1-8+5t-t^2
39
First homology
of the double branched cover of 9_15
Z/39
2 2
9_16
3

detected by
the signature
2-5t+8t^2-9t^3+8t^4-5t^5+2t^6
Seifert matrix of 9_16
-1 0 -1 -1 -1 0
0 -1 -1 -1 -1 0
0 0 -2 -1 -2 0
0 0 -2 -2 -2 0
0 0 -1 -1 -2 0
0 -1 -1 -1 -1 -1
1
Generator of the Alexander module
(-1,0,0,0,0,1)
the Blanchfield form on it
2t^-2-3t^-1+4-3t+2t^2
39
First homology
of the double branched cover of 9_16
Z/39
-6 6
9_17
2

detected by
the Lickorish test
1-5t+9t^2-9t^3+9t^4-5t^5+t^6
Seifert matrix of 9_17
1 0 0 0 0 0
-1 -1 -1 0 -1 -1
-1 0 -1 0 0 -1
0 0 0 1 0 0
-1 0 -1 0 -1 -1
-1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,-1)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
39
First homology
of the double branched cover of 9_17
Z/39
-2 2
9_18
2

detected by
the signature
4-10t+13t^2-10t^3+4t^4
Seifert matrix of 9_18
-1 0 0 -1
0 -2 1 1
0 0 -1 -1
0 0 0 -2
1 or 2
41
First homology
of the double branched cover of 9_18
Z/41
-4 4
9_19
1

detected by
an unknotting move
2-10t+17t^2-10t^3+2t^4
Seifert matrix of 9_19
1 0 0 0
-1 -1 0 1
0 0 1 0
1 0 1 -2
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
t^-1-3+t
41
First homology
of the double branched cover of 9_19
Z/41
0 0
9_20
2

detected by
the signature
-1+5t-9t^2+11t^3-9t^4+5t^5-t^6
Seifert matrix of 9_20
-1 0 0 0 0 0
0 -1 0 0 -1 0
-1 0 -1 0 0 0
-1 0 -1 1 -1 0
0 0 0 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+4t^-1-5+4t-2t^2
41
First homology
of the double branched cover of 9_20
Z/41
-4 4
9_21
1

detected by
an unknotting move
-2+11t-17t^2+11t^3-2t^4
Seifert matrix of 9_21
2 0 0 0
0 -1 -1 0
0 0 1 0
-1 -1 0 1
1 or 2
43
First homology
of the double branched cover of 9_21
Z/43
2 2
9_22
1

detected by
an unknotting move
1-5t+10t^2-11t^3+10t^4-5t^5+t^6
Seifert matrix of 9_22
1 0 0 0 0 0
-1 -1 0 -1 -1 -1
0 0 1 0 0 0
-1 0 -1 -1 -1 -1
-1 0 -1 0 -1 0
-1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-2-5t^-1+9-5t+t^2
43
First homology
of the double branched cover of 9_22
Z/43
-2 2
9_23
2

detected by
the signature
4-11t+15t^2-11t^3+4t^4
Seifert matrix of 9_23
-1 0 -1 0
0 -1 0 -1
0 0 -2 0
0 0 1 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
2t^-1-3+2t
45
First homology
of the double branched cover of 9_23
Z/45
-4 4
9_24
1

detected by
an unknotting move
-1+5t-10t^2+13t^3-10t^4+5t^5-t^6
Seifert matrix of 9_24
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 -1 0
-1 -1 1 1 -1 1
0 0 0 0 -1 0
-1 -1 1 0 -1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
t^-2-5t^-1+7-5t+t^2
45
First homology
of the double branched cover of 9_24
Z/45
0 0
9_25
1

detected by
an unknotting move
-3+12t-17t^2+12t^3-3t^4
Seifert matrix of 9_25
-1 -1 0 -1
0 -2 0 -1
0 0 1 -1
0 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
-2t^-1+5-2t
47
First homology
of the double branched cover of 9_25
Z/47
-2 2
9_26
1

detected by
an unknotting move
1-5t+11t^2-13t^3+11t^4-5t^5+t^6
Seifert matrix of 9_26
1 0 0 0 0 0
-1 -1 0 0 -1 0
0 0 1 0 0 0
0 0 1 1 0 1
-1 0 -1 -1 -1 -1
0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,-1,1,0)
the Blanchfield form on it
-1
47
First homology
of the double branched cover of 9_26
Z/47
2 2
9_27
1

detected by
an unknotting move
-1+5t-11t^2+15t^3-11t^4+5t^5-t^6
Seifert matrix of 9_27
-1 0 0 0 0 0
0 -1 0 0 -1 0
-1 0 -1 0 0 0
-1 0 -1 1 1 1
0 0 0 0 1 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
49
First homology
of the double branched cover of 9_27
Z/49
0 0
9_28
1

detected by
an unknotting move
1-5t+12t^2-15t^3+12t^4-5t^5+t^6
Seifert matrix of 9_28
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 1 1 0
0 0 0 1 0 0
0 0 0 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
51
First homology
of the double branched cover of 9_28
Z/51
-2 2
9_29
1

detected by
an unknotting move
1-5t+12t^2-15t^3+12t^4-5t^5+t^6
Seifert matrix of 9_29
1 0 0 1 1 1
-1 -1 0 0 -1 0
0 0 -1 0 0 0
0 0 -1 1 0 0
0 0 -1 1 1 1
0 0 -1 1 0 1
1
Generator of the Alexander module
(0,-1,-1,0,-t,0)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
51
First homology
of the double branched cover of 9_29
Z/51
2 2
9_30
1

detected by
an unknotting move
-1+5t-12t^2+17t^3-12t^4+5t^5-t^6
Seifert matrix of 9_30
-1 -1 -1 -1 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 -1 -1 0 0
0 -1 0 -1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-1-5+2t
53
First homology
of the double branched cover of 9_30
Z/53
0 0
9_31
2

detected by
the Lickorish test
1-5t+13t^2-17t^3+13t^4-5t^5+t^6
Seifert matrix of 9_31
-1 0 0 0 0 0
0 -1 0 0 -1 0
-1 0 -1 0 0 0
-1 0 -1 1 0 1
0 0 0 0 -1 0
0 1 0 0 1 1
1
Generator of the Alexander module
(0,0,t,1+t,0,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
55
First homology
of the double branched cover of 9_31
Z/55
-2 2
9_32
1

detected by
an unknotting move
1-6t+14t^2-17t^3+14t^4-6t^5+t^6
Seifert matrix of 9_32
1 0 0 0 0 0
-1 -1 -1 0 -1 -1
0 0 1 1 0 1
0 0 0 1 0 0
-1 0 -1 0 -1 0
0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-1-1+t
59
First homology
of the double branched cover of 9_32
Z/59
2 2
9_33
1

detected by
an unknotting move
-1+6t-14t^2+19t^3-14t^4+6t^5-t^6
Seifert matrix of 9_33
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 -1 -1 0 0 0
-1 0 -1 1 -1 1
-1 -1 -1 0 -1 0
0 0 -1 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-1+1-t
61
First homology
of the double branched cover of 9_33
Z/61
0 0
9_34
1

detected by
an unknotting move
-1+6t-16t^2+23t^3-16t^4+6t^5-t^6
Seifert matrix of 9_34
-1 0 -1 -1 0 0
-1 -1 -1 -1 0 0
0 0 -1 -1 -1 0
0 0 0 1 0 0
0 0 0 1 1 0
-1 0 -1 0 0 1
1
Generator of the Alexander module
(0,1,1,0,-1,1)
the Blanchfield form on it
-t^-2+4t^-1-7+4t-t^2
69
First homology
of the double branched cover of 9_34
Z/69
0 0
9_35
2

detected by
the Nakanishi index
7-13t+7t^2
Seifert matrix of 9_35
-3 -1
-2 -3
2
27
First homology
of the double branched cover of 9_35
Z/3+Z/9
-2 2
9_36
2

detected by
the signature
-1+5t-8t^2+9t^3-8t^4+5t^5-t^6
Seifert matrix of 9_36
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 0 1 0
-1 0 1 1 1 1
0 0 0 0 1 0
-1 0 1 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
t^-2-5t^-1+7-5t+t^2
37
First homology
of the double branched cover of 9_36
Z/37
4 4
9_37
2

detected by
the Nakanishi index
2-11t+19t^2-11t^3+2t^4
Seifert matrix of 9_37
1 0 0 0
0 1 0 0
1 0 -2 1
-1 -1 0 -1
2
45
First homology
of the double branched cover of 9_37
Z/15+Z/3
0 0
9_38
2

detected by
the signature
5-14t+19t^2-14t^3+5t^4
Seifert matrix of 9_38
-2 1 0 1
0 -2 -1 -2
-1 -1 -2 -1
0 -1 -1 -2
1 or 2
57
First homology
of the double branched cover of 9_38
Z/57
-4 4
9_39
1

detected by
an unknotting move
-3+14t-21t^2+14t^3-3t^4
Seifert matrix of 9_39
-1 0 -1 1
0 2 1 1
0 0 1 0
0 1 0 2
1
Generator of the Alexander module
(1,0,0,1)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
55
First homology
of the double branched cover of 9_39
Z/55
2 2
9_40
2

detected by
the Nakanishi index
1-7t+18t^2-23t^3+18t^4-7t^5+t^6
Seifert matrix of 9_40
1 0 0 0 -1 1
-1 -1 0 -1 0 -1
0 0 -1 0 -1 0
-1 0 0 -1 0 0
0 0 0 0 -1 0
0 0 -1 0 -1 1
2
75
First homology
of the double branched cover of 9_40
Z/15+Z/5
-2 2
9_41
2

detected by
the Nakanishi index
3-12t+19t^2-12t^3+3t^4
Seifert matrix of 9_41
-1 1 -1 1
0 2 0 1
0 0 -1 1
0 1 0 2
2
49
First homology
of the double branched cover of 9_41
Z/7+Z/7
0 0
9_42
1

detected by
an unknotting move
-1+2t-t^2+2t^3-t^4
Seifert matrix of 9_42
1 0 0 0
-1 0 1 -1
1 1 -2 1
-1 0 1 0
1
Generator of the Alexander module
(0,t,1,0)
the Blanchfield form on it
t^-1-2+t
7
First homology
of the double branched cover of 9_42
Z/7
2 2
9_43
2

detected by
the signature
-1+3t-2t^2+t^3-2t^4+3t^5-t^6
Seifert matrix of 9_43
-1 -1 -1 -1 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 -1 -1 0 0
0 -1 0 -1 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
13
First homology
of the double branched cover of 9_43
Z/13
-4 4
9_44
1

detected by
an unknotting move
1-4t+7t^2-4t^3+t^4
Seifert matrix of 9_44
-1 -1 0 -1
0 0 0 -1
0 0 1 0
0 -1 1 -2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
1
17
First homology
of the double branched cover of 9_44
Z/17
0 0
9_45
1

detected by
an unknotting move
-1+6t-9t^2+6t^3-t^4
Seifert matrix of 9_45
0 2 -1 -1
1 1 1 0
0 0 1 0
0 1 -1 0
1
Generator of the Alexander module
(-1+t,0,-1,0)
the Blanchfield form on it
-1
23
First homology
of the double branched cover of 9_45
Z/23
2 2
9_46
2

detected by
the Nakanishi index
-2+5t-2t^2
Seifert matrix of 9_46
3 2
1 0
2
9
First homology
of the double branched cover of 9_46
Z/3+Z/3
0 0
9_47
2

detected by
the Nakanishi index
1-4t+6t^2-5t^3+6t^4-4t^5+t^6
Seifert matrix of 9_47
-1 0 -1 -1 0 0
-1 -1 -1 -1 0 0
0 0 -1 -1 -1 0
0 0 0 1 0 0
0 0 0 1 1 0
-1 0 -1 0 0 -1
2
27
First homology
of the double branched cover of 9_47
Z/9+Z/3
-2 2
9_48
2

detected by
the Nakanishi index
-1+7t-11t^2+7t^3-t^4
Seifert matrix of 9_48
1 0 0 0
0 1 0 0
1 0 1 1
-1 -1 0 -1
2
27
First homology
of the double branched cover of 9_48
Z/9+Z/3
2 2
9_49
3

detected by
the Stoimenow criterion
3-6t+7t^2-6t^3+3t^4
Seifert matrix of 9_49
-1 1 -1 1
0 -2 0 -1
0 0 -1 1
0 -1 0 -2
2
25
First homology
of the double branched cover of 9_49
Z/5+Z/5
-4 4
10_1
1

detected by
an unknotting move
-4+9t-4t^2
Seifert matrix of 10_1
1 0
1 -4
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
t^-1-2+t
17
First homology
of the double branched cover of 10_1
Z/17
0 0
10_2
3

detected by
the signature
-1+3t-3t^2+3t^3-3t^4+3t^5-3t^6+3t^7-t^8
Seifert matrix of 10_2
1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1
-1 0 -1 -1 -1 0 -1 -1
-1 0 0 -1 -1 0 0 -1
-1 0 0 0 -1 0 0 0
-1 0 -1 -1 -1 -1 -1 -1
-1 0 0 -1 -1 0 -1 -1
-1 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-3t^-1+3-3t+3t^2-t^3
23
First homology
of the double branched cover of 10_2
Z/23
-6 6
10_3
2

detected by
the Lickorish test
-6+13t-6t^2
Seifert matrix of 10_3
-3 1
0 2
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
2t^-1-4+2t
25
First homology
of the double branched cover of 10_3
Z/25
0 0
10_4
1

detected by
an unknotting move
-3+7t-7t^2+7t^3-3t^4
Seifert matrix of 10_4
1 0 0 0
1 1 0 1
-1 -1 -3 -1
1 0 0 1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
27
First homology
of the double branched cover of 10_4
Z/27
2 2
10_5
2

detected by
the signature
1-3t+5t^2-5t^3+5t^4-5t^5+5t^6-3t^7+t^8
Seifert matrix of 10_5
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
0 1 1 0 0 1 1 0
-1 0 0 -1 0 0 0 0
-1 1 1 -1 1 1 1 1
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
0 1 1 0 0 1 1 1
1
Generator of the Alexander module
(0,0,0,2,2,0,0,-1)
the Blanchfield form on it
t^-3-t^-2+t^-1-1+t-t^2+t^3
33
First homology
of the double branched cover of 10_5
Z/33
4 4
10_6
2

detected by
the signature
-2+6t-7t^2+7t^3-7t^4+6t^5-2t^6
Seifert matrix of 10_6
1 0 0 0 0 0
0 -1 -1 0 -1 -1
0 0 -1 0 0 -1
1 -1 -1 -2 -1 -1
0 0 -1 0 -1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(-2,0,0,1,0,0)
the Blanchfield form on it
-5t^-3+11t^-2-12t^-1+12-12t+11t^2-5t^3
37
First homology
of the double branched cover of 10_6
Z/37
-4 4
10_7
1

detected by
an unknotting move
-3+11t-15t^2+11t^3-3t^4
Seifert matrix of 10_7
1 0 0 0
-1 -1 -1 -1
-1 0 -1 0
-1 0 -1 -3
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
43
First homology
of the double branched cover of 10_7
Z/43
-2 2
10_8
2

detected by
the signature
-2+5t-5t^2+5t^3-5t^4+5t^5-2t^6
Seifert matrix of 10_8
-1 -1 -1 1 -1 -1
0 -1 -1 1 0 -1
0 0 -1 1 0 0
0 0 0 2 0 0
0 -1 -1 1 -1 -1
0 0 -1 1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+2t^-2-2t^-1+2-2t+2t^2-t^3
29
First homology
of the double branched cover of 10_8
Z/29
-4 4
10_9
1

detected by
an unknotting move
-1+3t-5t^2+7t^3-7t^4+7t^5-5t^6+3t^7-t^8
Seifert matrix of 10_9
1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
-1 -1 -1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 -1 0 -1
-1 -1 0 0 -1 -1 0 0
1 0 0 0 0 1 0 0
-1 -1 0 -1 -1 -1 -1 -1
-1 -1 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,2,1,1,t,1,1)
the Blanchfield form on it
1
39
First homology
of the double branched cover of 10_9
Z/39
-2 2
10_10
1

detected by
an unknotting move
3-11t+17t^2-11t^3+3t^4
Seifert matrix of 10_10
-1 0 0 0
-1 -1 0 0
-1 -1 1 1
0 0 0 3
1
Generator of the Alexander module
(0,1,1,0)
the Blanchfield form on it
1
45
First homology
of the double branched cover of 10_10
Z/45
0 0
10_11
1

detected by
an unknotting move
-4+11t-13t^2+11t^3-4t^4
Seifert matrix of 10_11
-1 0 0 -1
0 2 0 0
-1 -1 -2 -1
0 0 0 -1
1 or 2
43
First homology
of the double branched cover of 10_11
Z/43
-2 2
10_12
1

detected by
an unknotting move
2-6t+10t^2-11t^3+10t^4-6t^5+2t^6
Seifert matrix of 10_12
-1 0 0 0 0 0
0 1 0 1 0 0
-1 0 -1 0 0 0
0 0 0 1 0 0
0 1 0 1 1 0
1 -1 1 -1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-6+5t-3t^2+t^3
47
First homology
of the double branched cover of 10_12
Z/47
2 2
10_13
1

detected by
an unknotting move
2-13t+23t^2-13t^3+2t^4
Seifert matrix of 10_13
-2 0 0 0
0 -1 -1 0
0 0 1 0
1 -1 0 1
1
Generator of the Alexander module
(0,-2-27t+99t^2-144t^3+84t^4-16t^5,0,3+35t-167t^2+304t^3-266t^4+108t^5-16t^6)
the Blanchfield form on it
357953t^-2-2326696t^-1+4116466-2326696t+357953t^2
53
First homology
of the double branched cover of 10_13
Z/53
0 0
10_14
2

detected by
the signature
-2+8t-12t^2+13t^3-12t^4+8t^5-2t^6
Seifert matrix of 10_14
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 -1 -1 -1 -1
0 0 0 -1 0 -1
0 0 0 -1 -1 -1
1 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
57
First homology
of the double branched cover of 10_14
Z/57
-4 4
10_15
1

detected by
an unknotting move
2-6t+9t^2-9t^3+9t^4-6t^5+2t^6
Seifert matrix of 10_15
-1 0 -1 0 0 0
0 1 0 0 1 0
0 0 -2 0 0 0
0 1 1 1 1 1
0 0 0 0 1 0
0 1 0 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
43
First homology
of the double branched cover of 10_15
Z/43
2 2
10_16
1

detected by
an unknotting move
-4+12t-15t^2+12t^3-4t^4
Seifert matrix of 10_16
-1 1 -1 1
0 -2 1 -1
0 0 -1 1
0 0 0 2
1 or 2
47
First homology
of the double branched cover of 10_16
Z/47
-2 2
10_17
1

detected by
an unknotting move
1-3t+5t^2-7t^3+9t^4-7t^5+5t^6-3t^7+t^8
Seifert matrix of 10_17
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 1 0
-1 -1 0 -1 -1 0 0 0
0 -1 0 0 -1 0 0 0
-1 -1 1 -1 -1 1 1 1
0 0 0 0 0 0 1 0
0 0 1 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-1
41
First homology
of the double branched cover of 10_17
Z/41
0 0
10_18
1

detected by
an unknotting move
-4+14t-19t^2+14t^3-4t^4
Seifert matrix of 10_18
-1 -1 0 0
0 -2 0 0
0 -1 -1 1
0 0 0 2
1 or 2
55
First homology
of the double branched cover of 10_18
Z/55
-2 2
10_19
2

detected by
the Lickorish test
2-7t+11t^2-11t^3+11t^4-7t^5+2t^6
Seifert matrix of 10_19
-1 -1 0 0 -1 0
0 -1 0 0 0 0
0 0 2 0 0 0
-1 -1 0 -1 -1 0
0 -1 0 0 -1 0
-1 -1 -1 -1 -1 1
1 or 2
51
First homology
of the double branched cover of 10_19
Z/51
-2 2
10_20
2

detected by
the Lickorish test
-3+9t-11t^2+9t^3-3t^4
Seifert matrix of 10_20
1 0 0 0
0 -1 0 -1
-1 1 -3 1
0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
35
First homology
of the double branched cover of 10_20
Z/35
-2 2
10_21
2

detected by
the signature
-2+7t-9t^2+9t^3-9t^4+7t^5-2t^6
Seifert matrix of 10_21
1 0 0 0 0 0
-1 -1 -1 1 -1 -1
-1 0 -1 1 -1 0
1 0 0 -2 1 0
-1 0 0 0 -1 0
-1 0 -1 1 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+6t^-1-6+6t-4t^2+t^3
45
First homology
of the double branched cover of 10_21
Z/45
-4 4
10_22
1

detected by
an unknotting move
-2+6t-10t^2+13t^3-10t^4+6t^5-2t^6
Seifert matrix of 10_22
1 0 0 0 0 0
1 1 0 1 0 0
0 0 -1 0 0 -1
1 0 0 1 0 0
1 1 -1 1 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-6+5t-3t^2+t^3
49
First homology
of the double branched cover of 10_22
Z/49
0 0
10_23
1

detected by
an unknotting move
2-7t+13t^2-15t^3+13t^4-7t^5+2t^6
Seifert matrix of 10_23
-1 0 0 0 0 0
0 1 0 0 0 1
0 -1 2 0 0 -1
-1 0 0 -1 0 0
-1 1 -1 -1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,t,1+t,0)
the Blanchfield form on it
2t^-2-3t^-1+3-3t+2t^2
59
First homology
of the double branched cover of 10_23
Z/59
2 2
10_24
2

detected by
the Lickorish test
-4+14t-19t^2+14t^3-4t^4
Seifert matrix of 10_24
1 0 0 0
0 -1 1 0
0 0 -2 0
1 -1 1 -2
1 or 2
55
First homology
of the double branched cover of 10_24
Z/55
-2 2
10_25
2

detected by
the signature
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 10_25
1 0 0 0 0 0
-1 -1 1 1 -1 1
1 0 -2 -2 1 -2
1 0 -1 -2 1 -1
-1 0 0 0 -1 0
1 0 -1 -2 1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+7t^-1-9+7t-2t^2
65
First homology
of the double branched cover of 10_25
Z/65
-4 4
10_26
1

detected by
an unknotting move
-2+7t-13t^2+17t^3-13t^4+7t^5-2t^6
Seifert matrix of 10_26
1 0 0 0 0 0
1 1 0 0 0 1
-1 -1 -1 1 -1 -1
1 1 0 -2 1 1
-1 -1 0 0 -1 -1
1 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-10+8t-4t^2+t^3
61
First homology
of the double branched cover of 10_26
Z/61
0 0
10_27
1

detected by
an unknotting move
2-8t+16t^2-19t^3+16t^4-8t^5+2t^6
Seifert matrix of 10_27
-1 0 0 0 0 0
0 2 1 0 0 1
0 2 2 0 0 2
-1 0 0 -1 0 0
-1 -1 -1 -1 1 -1
0 2 1 0 0 2
1
Generator of the Alexander module
(0,0,0,t,1+t,0)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
71
First homology
of the double branched cover of 10_27
Z/71
2 2
10_28
1

detected by
an unknotting move
4-13t+19t^2-13t^3+4t^4
Seifert matrix of 10_28
-1 0 0 0
0 2 0 0
-1 0 -1 0
1 1 1 2
1
Generator of the Alexander module
(0,0,-1,1)
the Blanchfield form on it
2t^-1-3+2t
53
First homology
of the double branched cover of 10_28
Z/53
0 0
10_29
2

detected by
the Lickorish test
1-7t+15t^2-17t^3+15t^4-7t^5+t^6
Seifert matrix of 10_29
-1 0 0 0 -1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 0 1 -1 0
0 0 0 0 -1 0
-1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1+t,0,t^2)
the Blanchfield form on it
t^-2-7t^-1+13-7t+t^2
63
First homology
of the double branched cover of 10_29
Z/63
-2 2
10_30
1

detected by
an unknotting move
-4+17t-25t^2+17t^3-4t^4
Seifert matrix of 10_30
1 0 0 0
-1 -1 0 1
0 0 -2 0
1 0 -1 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
1
67
First homology
of the double branched cover of 10_30
Z/67
-2 2
10_31
1

detected by
an unknotting move
4-14t+21t^2-14t^3+4t^4
Seifert matrix of 10_31
-1 0 -1 0
0 2 0 0
0 0 -2 0
0 -1 1 1
1 or 2
57
First homology
of the double branched cover of 10_31
Z/57
0 0
10_32
1

detected by
an unknotting move
-2+8t-15t^2+19t^3-15t^4+8t^5-2t^6
Seifert matrix of 10_32
-1 0 0 -1 0 0
0 1 0 0 0 0
0 1 1 0 0 1
0 0 0 -2 0 0
0 -1 -1 -1 -1 -1
0 1 0 0 0 1
1
Generator of the Alexander module
(-t,0,0,1,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
69
First homology
of the double branched cover of 10_32
Z/69
0 2
10_33
1

detected by
an unknotting move
4-16t+25t^2-16t^3+4t^4
Seifert matrix of 10_33
-2 1 0 0
0 -1 0 0
0 0 2 0
1 -1 -1 1
1 or 2
65
First homology
of the double branched cover of 10_33
Z/65
0 0
10_34
1

detected by
an unknotting move
3-9t+13t^2-9t^3+3t^4
Seifert matrix of 10_34
-1 0 0 0
-1 -1 0 0
-1 -1 3 1
0 0 0 1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
37
First homology
of the double branched cover of 10_34
Z/37
0 0
10_35
1

detected by
an unknotting move
2-12t+21t^2-12t^3+2t^4
Seifert matrix of 10_35
-1 -1 0 0
0 1 0 0
0 0 -1 0
1 0 1 2
1
Generator of the Alexander module
(0,0,1,-1)
the Blanchfield form on it
-t^-1+3-t
49
First homology
of the double branched cover of 10_35
Z/49
0 0
10_36
2

detected by
the Lickorish test
-3+13t-19t^2+13t^3-3t^4
Seifert matrix of 10_36
1 0 0 0
-1 -1 0 -1
0 0 -1 1
-1 0 0 -3
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-1+3-t
51
First homology
of the double branched cover of 10_36
Z/51
-2 2
10_37
1

detected by
an unknotting move
4-13t+19t^2-13t^3+4t^4
Seifert matrix of 10_37
-1 -1 0 0
0 -2 0 0
0 0 1 0
0 -1 -1 2
1
Generator of the Alexander module
(-2t+t^2,0,-2+t,1-4t+2t^2)
the Blanchfield form on it
-4t^-1+7-4t
53
First homology
of the double branched cover of 10_37
Z/53
0 0
10_38
1

detected by
an unknotting move
-4+15t-21t^2+15t^3-4t^4
Seifert matrix of 10_38
-1 0 -1 0
0 1 0 0
0 0 -2 0
0 1 1 -2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
2t^-2-7t^-1+10-7t+2t^2
59
First homology
of the double branched cover of 10_38
Z/59
-2 2
10_39
2

detected by
the signature
-2+8t-13t^2+15t^3-13t^4+8t^5-2t^6
Seifert matrix of 10_39
1 0 0 0 0 0
-1 -1 -1 0 -1 1
-1 0 -1 0 0 1
0 0 0 -1 0 -1
-1 0 -1 0 -1 1
1 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
61
First homology
of the double branched cover of 10_39
Z/61
-4 4
10_40
2

detected by
the Lickorish test
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 10_40
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 1 -1 0
0 0 0 1 0 0
0 0 0 -1 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,1)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
75
First homology
of the double branched cover of 10_40
Z/75
2 2
10_41
1

detected by
an unknotting move
1-7t+17t^2-21t^3+17t^4-7t^5+t^6
Seifert matrix of 10_41
1 0 0 0 0 0
-1 -1 0 -1 -1 0
0 0 -1 0 0 -1
-1 0 0 -1 0 0
-1 0 0 -1 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,1+3t-4t^2+t^3,2-2t,1-2t+3t^2-t^3,0)
the Blanchfield form on it
t^-2-7t^-1+14-7t+t^2
71
First homology
of the double branched cover of 10_41
Z/71
-2 2
10_42
1

detected by
an unknotting move
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 10_42
-1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 1 1 0
0 0 0 0 1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-2-7t^-1+11-7t+2t^2
81
First homology
of the double branched cover of 10_42
Z/81
0 0
10_43
1

detected by
an unknotting move
-1+7t-17t^2+23t^3-17t^4+7t^5-t^6
Seifert matrix of 10_43
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
0 0 0 1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-1+1-t
73
First homology
of the double branched cover of 10_43
Z/73
0 0
10_44
1

detected by
an unknotting move
1-7t+19t^2-25t^3+19t^4-7t^5+t^6
Seifert matrix of 10_44
1 0 0 0 0 0
-1 -1 0 -1 0 0
0 0 1 0 -1 0
-1 0 -1 -1 0 0
0 0 0 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,-1,1,0,-1)
the Blanchfield form on it
t^-2-5t^-1+8-5t+t^2
79
First homology
of the double branched cover of 10_44
Z/79
-2 2
10_45
1

detected by
an unknotting move
-1+7t-21t^2+31t^3-21t^4+7t^5-t^6
Seifert matrix of 10_45
1 0 0 0 0 0
-1 -1 0 0 -1 0
0 0 1 0 0 0
0 0 0 -1 0 1
-1 0 -1 0 -1 -1
0 0 1 0 0 1
1
Generator of the Alexander module
(t^2,-t-2t^2-2t^3+3t^4+4t^5+t^6,1-3t^2-t^3,-1+3t^2+4t^3+t^4,1+t-3t^2-t^3,2+t-6t^2-2t^3)
the Blanchfield form on it
x
89
First homology
of the double branched cover of 10_45
Z/89
0 0
10_46
3

detected by
the signature
-1+3t-4t^2+5t^3-5t^4+5t^5-4t^6+3t^7-t^8
Seifert matrix of 10_46
-1 0 0 -1 -1 -1 -1 -1
0 1 0 0 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1
0 -1 0 -1 -1 -1 -1 -1
0 -1 0 0 -1 -1 0 -1
0 -1 0 0 0 -1 0 0
0 -1 0 0 -1 -1 -1 -1
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,1,-t,0,0,0,0,0)
the Blanchfield form on it
-t^-3+2t^-2-2t^-1+2-2t+2t^2-t^3
31
First homology
of the double branched cover of 10_46
Z/31
-6 6
10_47
2

detected by
the signature
-1+3t-6t^2+7t^3-7t^4+7t^5-6t^6+3t^7-t^8
Seifert matrix of 10_47
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
-1 -1 1 1 0 1 1 0
-1 -1 1 1 1 1 1 1
0 0 0 0 0 1 0 0
-1 -1 1 0 0 1 1 0
-1 -1 1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+6t^-1-7+6t-3t^2+t^3
41
First homology
of the double branched cover of 10_47
Z/41
4 4
10_48
1

detected by
an unknotting move
1-3t+6t^2-9t^3+11t^4-9t^5+6t^6-3t^7+t^8
Seifert matrix of 10_48
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 1 0 0 1 0
0 -1 0 0 -1 0 0 0
0 -1 0 1 -1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(0,0,-t,0,1,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+4t^-1-4+4t-2t^2+t^3
49
First homology
of the double branched cover of 10_48
Z/49
0 0
10_49
3

detected by
the signature
3-8t+12t^2-13t^3+12t^4-8t^5+3t^6
Seifert matrix of 10_49
-1 -1 -1 -1 -1 -1
0 -2 -2 -1 -2 -2
0 -1 -2 -1 -1 -2
0 -1 -1 -2 -1 -1
0 -1 -2 -1 -2 -2
0 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(t,0,0,1,0,0)
the Blanchfield form on it
3t^-2-4t^-1+4-4t+3t^2
59
First homology
of the double branched cover of 10_49
Z/59
-6 6
10_50
2

detected by
the signature
-2+7t-11t^2+13t^3-11t^4+7t^5-2t^6
Seifert matrix of 10_50
-1 0 0 -1 1 -1
0 1 0 0 0 0
-1 0 -1 -1 1 -1
0 -1 0 -1 1 -1
0 1 0 0 -2 1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,-1,0,1,1)
the Blanchfield form on it
-6t^-2+17t^-1-19+17t-6t^2
53
First homology
of the double branched cover of 10_50
Z/53
-4 4
10_51
1

detected by
an unknotting move
2-7t+15t^2-19t^3+15t^4-7t^5+2t^6
Seifert matrix of 10_51
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 0 1
1 1 -1 2 0 -1
-1 -1 1 -1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,-2t,1,0)
the Blanchfield form on it
5t^-3-18t^-2+39t^-1-50+39t-18t^2+5t^3
67
First homology
of the double branched cover of 10_51
Z/67
2 2
10_52
1

detected by
an unknotting move
2-7t+13t^2-15t^3+13t^4-7t^5+2t^6
Seifert matrix of 10_52
-1 -1 0 0 -1 0
0 -1 0 0 0 0
-1 -1 -1 0 -1 0
0 0 0 2 0 0
0 -1 0 0 -1 0
0 -1 0 -1 -1 1
1
Generator of the Alexander module
(0,0,t-t^4,0,0,1+t-t^3)
the Blanchfield form on it
2t^-2-5t^-1+8-5t+2t^2
59
First homology
of the double branched cover of 10_52
Z/59
-2 2
10_53
2

detected by
the signature
6-18t+25t^2-18t^3+6t^4
Seifert matrix of 10_53
-1 -1 1 -1
0 -2 2 -1
0 1 -3 1
0 -1 1 -2
1
Generator of the Alexander module
(0,0,1,-2)
the Blanchfield form on it
-17t^-2+56t^-1-78+56t-17t^2
73
First homology
of the double branched cover of 10_53
Z/73
-4 4
10_54
1

detected by
an unknotting move
2-6t+10t^2-11t^3+10t^4-6t^5+2t^6
Seifert matrix of 10_54
-1 -1 0 0 0 0
0 -2 0 0 0 0
0 1 1 0 1 0
0 1 1 1 1 1
0 0 0 0 1 0
0 1 1 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
47
First homology
of the double branched cover of 10_54
Z/47
2 2
10_55
2

detected by
the signature
5-15t+21t^2-15t^3+5t^4
Seifert matrix of 10_55
-1 -1 1 0
0 -2 1 0
0 1 -3 0
0 0 -1 -1
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
3t^-1-5+3t
61
First homology
of the double branched cover of 10_55
Z/61
-4 4
10_56
2

detected by
the signature
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 10_56
-1 0 -1 0 0 0
0 1 0 0 0 0
0 0 -2 0 0 0
0 -1 -1 -1 -1 -1
0 -1 -1 0 -1 0
0 -1 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
65
First homology
of the double branched cover of 10_56
Z/65
-4 4
10_57
1

detected by
an unknotting move
2-8t+18t^2-23t^3+18t^4-8t^5+2t^6
Seifert matrix of 10_57
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 1 0
0 0 0 1 0 0
0 0 0 0 1 0
1 1 -1 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-5t^-2+12t^-1-16+12t-5t^2+t^3
79
First homology
of the double branched cover of 10_57
Z/79
2 2
10_58
1

detected by
an unknotting move
3-16t+27t^2-16t^3+3t^4
Seifert matrix of 10_58
1 0 0 0
1 -2 0 -1
0 0 1 -1
1 -1 0 -2
1
Generator of the Alexander module
(0,0,t,1)
the Blanchfield form on it
2t^-1-5+2t
65
First homology
of the double branched cover of 10_58
Z/65
0 0
10_59
1

detected by
an unknotting move
1-7t+18t^2-23t^3+18t^4-7t^5+t^6
Seifert matrix of 10_59
-1 -1 -1 -1 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 -1 -1 0 0
0 -1 0 -1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
75
First homology
of the double branched cover of 10_59
Z/75
-2 2
10_60
1

detected by
an unknotting move
-1+7t-20t^2+29t^3-20t^4+7t^5-t^6
Seifert matrix of 10_60
1 0 0 0 0 0
-1 -1 0 -1 0 -1
0 0 1 0 0 0
-1 0 -1 -1 0 -1
0 0 0 0 1 0
-1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
1
85
First homology
of the double branched cover of 10_60
Z/85
0 0
10_61
2

detected by
the signature
-2+5t-6t^2+7t^3-6t^4+5t^5-2t^6
Seifert matrix of 10_61
-1 0 -1 -1 0 -1
-1 -1 -1 -1 0 -1
0 0 -1 -1 1 -1
0 0 0 -1 1 0
0 0 0 0 2 0
0 0 0 -1 1 -1
2
33
First homology
of the double branched cover of 10_61
Z/33
-4 4
10_62
2

detected by
the signature
1-3t+6t^2-8t^3+9t^4-8t^5+6t^6-3t^7+t^8
Seifert matrix of 10_62
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 0 1 1 0
-1 1 -1 1 1 1 1 1
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
-1 1 -1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-5t^-1+5-5t+3t^2-t^3
45
First homology
of the double branched cover of 10_62
Z/45
4 4
10_63
2

detected by
the signature
5-14t+19t^2-14t^3+5t^4
Seifert matrix of 10_63
-1 1 -1 -1
0 -3 1 1
0 1 -2 -2
0 1 -1 -2
2
57
First homology
of the double branched cover of 10_63
Z/57
-4 4
10_64
1

detected by
an unknotting move
-1+3t-6t^2+10t^3-11t^4+10t^5-6t^6+3t^7-t^8
Seifert matrix of 10_64
-1 0 0 0 -1 -1 0 -1
0 1 0 0 0 0 0 0
0 1 1 0 0 0 1 0
-1 0 0 -1 -1 -1 0 -1
0 -1 -1 0 -1 -1 -1 -1
0 -1 -1 0 0 -1 -1 0
0 1 0 0 0 0 1 0
0 -1 -1 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+3t^-2-5t^-1+7-5t+3t^2-t^3
51
First homology
of the double branched cover of 10_64
Z/51
-2 2
10_65
2

detected by
the Lickorish test
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 10_65
-1 0 0 0 0 0
0 2 0 0 0 0
-1 0 -1 0 0 0
-1 -1 -1 1 0 0
-1 -1 -1 1 1 1
-1 -1 -1 1 0 1
2
63
First homology
of the double branched cover of 10_65
Z/63
2 2
10_66
3

detected by
the signature
3-9t+16t^2-19t^3+16t^4-9t^5+3t^6
Seifert matrix of 10_66
-1 0 -1 -1 0 -1
0 -1 0 -1 0 0
0 0 -2 -1 0 -2
0 0 -1 -2 0 -1
0 -1 0 -1 -1 0
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,1,0)
the Blanchfield form on it
6t^-2-15t^-1+20-15t+6t^2
75
First homology
of the double branched cover of 10_66
Z/75
-6 6
10_67
2

detected by
the Lickorish test
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 10_67
1 0 0 0
0 -1 0 -1
1 0 -2 -1
1 0 0 -2
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
2t^-2-8t^-1+12-8t+2t^2
63
First homology
of the double branched cover of 10_67
Z/63
-2 2
10_68
1

detected by
an unknotting move
4-14t+21t^2-14t^3+4t^4
Seifert matrix of 10_68
-1 0 0 0
1 2 1 0
-1 0 -1 0
1 1 1 2
1
Generator of the Alexander module
(0,4-6t+4t^2,0,-3+4t-2t^2)
the Blanchfield form on it
-4t^-1+8-4t
57
First homology
of the double branched cover of 10_68
Z/57
0 0
10_69
2

detected by
the Lickorish test
1-7t+21t^2-29t^3+21t^4-7t^5+t^6
Seifert matrix of 10_69
-1 0 -1 0 0 -1
0 1 0 0 0 0
0 0 1 0 0 0
-1 0 0 1 1 0
0 0 0 0 1 0
0 1 -1 0 0 -1
1 or 2
87
First homology
of the double branched cover of 10_69
Z/87
2 2
10_70
1

detected by
an unknotting move
1-7t+16t^2-19t^3+16t^4-7t^5+t^6
Seifert matrix of 10_70
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 0 -1 0
-1 0 1 1 -1 1
0 0 0 0 -1 0
-1 0 1 0 -1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+7t^-1-13+7t-t^2
67
First homology
of the double branched cover of 10_70
Z/67
2 2
10_71
1

detected by
an unknotting move
-1+7t-18t^2+25t^3-18t^4+7t^5-t^6
Seifert matrix of 10_71
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 1 1 0
0 0 0 1 0 0
0 0 0 0 -1 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
77
First homology
of the double branched cover of 10_71
Z/77
0 0
10_72
2

detected by
the signature
-2+9t-16t^2+19t^3-16t^4+9t^5-2t^6
Seifert matrix of 10_72
1 0 0 0 0 0
-1 -1 0 0 1 0
0 0 -1 0 -1 0
0 0 0 -1 0 -1
1 0 0 -1 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1+t-t^2,1-t,0,0)
the Blanchfield form on it
-2t^-2+7t^-1-8+7t-2t^2
73
First homology
of the double branched cover of 10_72
Z/73
-4 4
10_73
1

detected by
an unknotting move
1-7t+20t^2-27t^3+20t^4-7t^5+t^6
Seifert matrix of 10_73
-1 0 -1 -1 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 1 -1 -1 0 0
0 0 0 -1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-1
83
First homology
of the double branched cover of 10_73
Z/83
2 2
10_74
2

detected by
the Nakanishi index
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 10_74
1 0 0 0
-1 -1 1 1
1 0 -2 -1
1 0 0 -2
2
63
First homology
of the double branched cover of 10_74
Z/21+Z/3
-2 2
10_75
2

detected by
the Nakanishi index
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 10_75
1 0 0 0 0 0
-1 -1 0 0 -1 -1
0 0 1 0 0 0
0 0 0 1 0 0
-1 0 -1 0 -1 -1
-1 0 0 -1 0 -1
2
81
First homology
of the double branched cover of 10_75
Z/27+Z/3
0 0
10_76
2

detected by
the signature
-2+7t-12t^2+15t^3-12t^4+7t^5-2t^6
Seifert matrix of 10_76
1 0 0 0 0 0
0 -1 0 0 0 -1
0 0 -1 0 -1 0
0 0 -1 -1 -1 0
1 -1 0 0 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-2t^-2+6t^-1-7+6t-2t^2
57
First homology
of the double branched cover of 10_76
Z/57
-4 4
10_77
1

detected by
an unknotting move
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 10_77
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 1
0 0 0 1 0 0
1 1 1 -1 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,1,0)
the Blanchfield form on it
-3t^-2+9t^-1-13+9t-3t^2
63
First homology
of the double branched cover of 10_77
Z/63
2 2
10_78
2

detected by
the signature
-1+7t-16t^2+21t^3-16t^4+7t^5-t^6
Seifert matrix of 10_78
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 1 0
0 0 0 -1 0 0
0 0 0 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,1,1,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
69
First homology
of the double branched cover of 10_78
Z/69
-4 4
10_79
1

detected by
an unknotting move
1-3t+7t^2-12t^3+15t^4-12t^5+7t^6-3t^7+t^8
Seifert matrix of 10_79
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 -1 0 -1 0 0 0 0
0 -1 0 -1 1 0 1 0
0 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
0 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,-t,1,0,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+5t^-1-6+5t-2t^2+t^3
61
First homology
of the double branched cover of 10_79
Z/61
0 0
10_80
3

detected by
the signature
3-9t+15t^2-17t^3+15t^4-9t^5+3t^6
Seifert matrix of 10_80
-1 -1 -1 0 -1 0
0 -2 -1 0 -2 0
0 -1 -2 0 -1 0
0 -1 0 -1 -1 0
0 -1 -1 0 -2 0
0 -1 0 -1 -1 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
71
First homology
of the double branched cover of 10_80
Z/71
-6 6
10_81
1

detected by
an unknotting move
-1+8t-20t^2+27t^3-20t^4+8t^5-t^6
Seifert matrix of 10_81
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
-1 -1 0 -1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,t,0,-t,1)
the Blanchfield form on it
t^-2-7t^-1+10-7t+t^2
85
First homology
of the double branched cover of 10_81
Z/85
0 0
10_82
1

detected by
an unknotting move
-1+4t-8t^2+12t^3-13t^4+12t^5-8t^6+4t^7-t^8
Seifert matrix of 10_82
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1
1 0 0 1 0 0 0 0
0 -1 0 0 -1 -1 0 -1
0 -1 0 0 0 -1 0 0
0 -1 0 0 -1 -1 -1 -1
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+11-8t+4t^2-t^3
63
First homology
of the double branched cover of 10_82
Z/63
-2 2
10_83
1

detected by
an unknotting move
2-9t+19t^2-23t^3+19t^4-9t^5+2t^6
Seifert matrix of 10_83
1 0 0 0 0 -1
0 -1 0 0 0 0
1 0 1 0 0 -1
-1 1 -1 2 0 1
1 -1 1 -1 1 -1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-14+11t-5t^2+t^3
83
First homology
of the double branched cover of 10_83
Z/83
2 2
10_84
1

detected by
an unknotting move
2-9t+20t^2-25t^3+20t^4-9t^5+2t^6
Seifert matrix of 10_84
-1 0 -1 0 0 0
0 -1 -1 0 0 0
0 0 -2 0 0 0
0 -1 -1 -1 0 0
0 0 1 0 1 1
0 1 1 0 0 1
1
Generator of the Alexander module
(1-t,0,0,0,2-t,0)
the Blanchfield form on it
2t^-2-7t^-1+10-7t+2t^2
87
First homology
of the double branched cover of 10_84
Z/87
-2 2
10_85
2

detected by
the signature
1-4t+8t^2-10t^3+11t^4-10t^5+8t^6-4t^7+t^8
Seifert matrix of 10_85
1 0 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
1 0 1 0 0 -1 0 0
1 -1 1 1 0 -1 1 0
1 -1 1 1 1 -1 1 1
0 -1 0 0 0 -1 0 0
1 -1 1 0 0 -1 1 0
1 -1 1 1 0 -1 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+9-8t+4t^2-t^3
57
First homology
of the double branched cover of 10_85
Z/57
4 4
10_86
2

detected by
the Lickorish test
-2+9t-19t^2+25t^3-19t^4+9t^5-2t^6
Seifert matrix of 10_86
1 0 0 0 0 0
1 1 0 1 0 0
-1 -1 -1 -1 1 -1
1 0 0 1 0 0
0 1 0 0 -2 1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,-t,t,0,1,0)
the Blanchfield form on it
-t^-2+3t^-1-4+3t-t^2
85
First homology
of the double branched cover of 10_86
Z/85
0 0
10_87
1

detected by
an unknotting move
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 10_87
-1 0 -1 0 0 0
0 1 0 0 0 0
0 0 -2 -1 0 -1
0 1 0 1 0 1
0 -1 -1 -1 -1 -1
0 1 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
81
First homology
of the double branched cover of 10_87
Z/81
0 0
10_88
1

detected by
an unknotting move
-1+8t-24t^2+35t^3-24t^4+8t^5-t^6
Seifert matrix of 10_88
1 0 0 0 0 0
-1 -1 -1 0 -1 -1
0 0 1 0 0 1
0 0 -1 -1 0 -1
-1 0 -1 0 -1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-2-5t^-1+9-5t+t^2
101
First homology
of the double branched cover of 10_88
Z/101
0 0
10_89
2

detected by
the Lickorish test
1-8t+24t^2-33t^3+24t^4-8t^5+t^6
Seifert matrix of 10_89
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
-1 0 0 1 -1 1
-1 -1 1 0 -1 0
0 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-1-3+t
99
First homology
of the double branched cover of 10_89
Z/99
2 2
10_90
1

detected by
an unknotting move
-2+8t-17t^2+23t^3-17t^4+8t^5-2t^6
Seifert matrix of 10_90
-1 -1 0 0 -1 1
0 1 0 1 1 0
-1 0 -1 0 0 1
0 0 0 1 0 0
0 0 0 1 1 0
0 1 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-4t^-2+9t^-1-12+9t-4t^2+t^3
77
First homology
of the double branched cover of 10_90
Z/77
0 0
10_91
1

detected by
an unknotting move
1-4t+9t^2-14t^3+17t^4-14t^5+9t^6-4t^7+t^8
Seifert matrix of 10_91
1 0 1 0 0 1 -1 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 1 0 0
0 -1 0 -1 0 0 0 -1
1 0 1 -1 1 1 -1 -1
0 0 0 0 0 1 0 0
0 -1 0 -1 0 0 -1 -1
0 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,1,0,-t,-t,0,-t-2t^4,0)
the Blanchfield form on it
-9t^-3+30t^-2-64t^-1+85-64t+30t^2-9t^3
73
First homology
of the double branched cover of 10_91
Z/73
0 0
10_92
2

detected by
the signature
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 10_92
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 -1 -2 -2 0 -2
0 0 -1 -2 0 -1
0 -1 -1 -1 -1 -1
0 -1 -1 -2 0 -2
1
Generator of the Alexander module
(t,0,0,0,1,0)
the Blanchfield form on it
3t^-3-17t^-2+38t^-1-48+38t-17t^2+3t^3
89
First homology
of the double branched cover of 10_92
Z/89
-4 4
10_93
1

detected by
an unknotting move
2-8t+15t^2-17t^3+15t^4-8t^5+2t^6
Seifert matrix of 10_93
-1 0 0 0 0 -1
-1 1 1 1 1 -1
0 0 1 0 0 0
-1 0 1 1 1 0
-1 0 1 0 1 0
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,-t,0,0,1+t^2,0)
the Blanchfield form on it
-2t^-2+8t^-1-13+8t-2t^2
67
First homology
of the double branched cover of 10_93
Z/67
2 2
10_94
1

detected by
an unknotting move
-1+4t-9t^2+14t^3-15t^4+14t^5-9t^6+4t^7-t^8
Seifert matrix of 10_94
-1 -1 0 0 -1 -1 -1 -1
0 1 0 1 0 0 1 0
-1 0 -1 0 -1 -1 0 -1
0 0 0 1 0 0 0 0
0 -1 0 0 -1 -1 0 -1
0 -1 0 0 0 -1 0 0
0 0 0 1 0 0 1 0
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+11-8t+4t^2-t^3
71
First homology
of the double branched cover of 10_94
Z/71
-2 2
10_95
1

detected by
an unknotting move
2-9t+21t^2-27t^3+21t^4-9t^5+2t^6
Seifert matrix of 10_95
-1 0 0 0 0 0
0 2 0 1 0 1
-1 0 -1 0 0 0
-1 0 -1 1 0 0
-1 -1 -1 0 1 0
-1 0 -1 1 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-1
91
First homology
of the double branched cover of 10_95
Z/91
2 2
10_96
1

detected by
an unknotting move
-1+7t-22t^2+33t^3-22t^4+7t^5-t^6
Seifert matrix of 10_96
-1 -1 -1 1 0 -1
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 -1 0 0 1 -1
0 -1 -1 1 0 -1
1 or 2
93
First homology
of the double branched cover of 10_96
Z/93
0 0
10_97
2

detected by
the Lickorish test
-5+22t-33t^2+22t^3-5t^4
Seifert matrix of 10_97
1 0 0 0
1 -2 -1 -1
1 -1 -2 -1
1 0 -1 -2
1
Generator of the Alexander module
(0,-1,1,1)
the Blanchfield form on it
-3t^-1+8-3t
87
First homology
of the double branched cover of 10_97
Z/87
-2 2
10_98
2

detected by
the Nakanishi index
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 10_98
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 -1 -1 0 -1 0
0 -1 0 -1 0 0
0 0 0 1 -2 1
0 -1 0 -1 0 -1
2
81
First homology
of the double branched cover of 10_98
Z/27+Z/3
-4 4
10_99
2

detected by
the Nakanishi index
1-4t+10t^2-16t^3+19t^4-16t^5+10t^6-4t^7+t^8
Seifert matrix of 10_99
-1 -1 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 0
-1 0 -1 1 0 1 0 0
-1 -1 -1 1 1 1 -1 1
0 0 0 0 0 1 0 0
0 -1 0 0 0 0 -1 0
-1 -1 -1 1 0 1 -1 1
2
81
First homology
of the double branched cover of 10_99
Z/9+Z/9
0 0
10_100
2

detected by
the signature
1-4t+9t^2-12t^3+13t^4-12t^5+9t^6-4t^7+t^8
Seifert matrix of 10_100
1 0 1 0 0 1 -1 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 1 0 0
1 0 1 1 0 1 -1 0
1 -1 1 1 1 1 -1 1
0 0 0 0 0 1 0 0
0 -1 0 0 0 0 -1 0
1 -1 1 1 0 1 -1 1
1
Generator of the Alexander module
(0,0,0,-1+t,0,0,1,2-t)
the Blanchfield form on it
-t^-3+3t^-2-6t^-1+7-6t+3t^2-t^3
65
First homology
of the double branched cover of 10_100
Z/65
4 4
10_101
2

detected by
the signature
7-21t+29t^2-21t^3+7t^4
Seifert matrix of 10_101
-1 1 -1 0
0 -3 1 -1
0 1 -2 -1
0 -1 0 -2
1 or 2
85
First homology
of the double branched cover of 10_101
Z/85
-4 4
10_102
1

detected by
an unknotting move
-2+8t-16t^2+21t^3-16t^4+8t^5-2t^6
Seifert matrix of 10_102
1 0 0 0 0 0
1 1 1 0 0 0
1 0 1 0 0 0
0 -1 0 -1 0 0
1 1 1 1 -2 1
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-10+8t-4t^2+t^3
73
First homology
of the double branched cover of 10_102
Z/73
0 0
10_103
3

detected by
the new u==2 criterion
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 10_103
-1 0 0 0 0 0
0 2 1 1 1 1
0 0 1 0 0 0
-1 0 1 1 0 1
-1 0 0 0 -1 0
-1 0 1 0 0 1
2
75
First homology
of the double branched cover of 10_103
Z/15+Z/5
2 2
10_104
1

detected by
an unknotting move
1-4t+9t^2-15t^3+19t^4-15t^5+9t^6-4t^7+t^8
Seifert matrix of 10_104
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
-1 0 1 0 0 -1 1 0
0 -1 0 -1 0 0 0 0
-1 -1 1 -1 1 -1 1 1
-1 -1 0 -1 0 -1 0 0
-1 0 0 0 0 -1 1 0
-1 0 1 0 0 -1 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,-1)
the Blanchfield form on it
-t^-2+3t^-1-7+3t-t^2
77
First homology
of the double branched cover of 10_104
Z/77
0 0
10_105
2

detected by
the Lickorish test
1-8t+22t^2-29t^3+22t^4-8t^5+t^6
Seifert matrix of 10_105
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 1 1 -1 0 1
-1 0 0 -1 0 0
-1 1 0 -1 1 0
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
91
First homology
of the double branched cover of 10_105
Z/91
-2 2
10_106
2

detected by
the Lickorish test
-1+4t-9t^2+15t^3-17t^4+15t^5-9t^6+4t^7-t^8
Seifert matrix of 10_106
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 -1 0 -1
1 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 0 -1 -1 -1 -1 -1
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+11-8t+4t^2-t^3
75
First homology
of the double branched cover of 10_106
Z/75
-2 2
10_107
1

detected by
an unknotting move
-1+8t-22t^2+31t^3-22t^4+8t^5-t^6
Seifert matrix of 10_107
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 1 1 -1 0 0
-1 0 0 -1 0 0
-1 0 0 -1 1 1
-1 1 0 -1 0 1
1
Generator of the Alexander module
(0,-6,3,1,-2t^2,-11-t-3t^2)
the Blanchfield form on it
-127t^-2-8t^-1-30-8t-127t^2
93
First homology
of the double branched cover of 10_107
Z/93
0 0
10_108
2

detected by
the Lickorish test
2-8t+14t^2-15t^3+14t^4-8t^5+2t^6
Seifert matrix of 10_108
-1 -1 0 -1 0 0
0 -1 0 0 0 0
1 0 2 0 0 1
0 -1 0 -1 0 0
-1 -1 -1 -1 1 -1
-1 -1 0 -1 0 -1
1
Generator of the Alexander module
(-15+120t-268t^2+162t^3+198t^4-864t^5+1218t^6-1320t^7+768t^8-192t^9,24-186t+84t^2+336t^3-1108t^4+1516t^5-1720t^6+1036t^7-264t^8,5-42t+96t^2-142t^3+154t^4-124t^5+58t^6-12t^7,-9+70t-36t^2-114t^3+394t^4-544t^5+622t^6-376t^7+96t^8,6t-48t^2-72t^3+348t^4-780t^5+960t^6-996t^7+576t^8-144t^9,-10+84t-192t^2+2
the Blanchfield form on it
x
63
First homology
of the double branched cover of 10_108
Z/63
-2 2
10_109
2

detected by
the Lickorish test
1-4t+10t^2-17t^3+21t^4-17t^5+10t^6-4t^7+t^8
Seifert matrix of 10_109
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
-1 0 -1 1 0 0 1 0
0 -1 0 0 -1 0 0 0
-1 -1 -1 1 -1 1 1 1
0 0 0 0 0 0 1 0
-1 0 -1 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-1+1-t
85
First homology
of the double branched cover of 10_109
Z/85
0 0
10_110
1

detected by
an unknotting move
1-8t+20t^2-25t^3+20t^4-8t^5+t^6
Seifert matrix of 10_110
1 0 0 0 0 0
1 -1 0 0 1 0
-1 0 -1 0 -1 0
0 -1 0 -1 1 -1
0 0 0 0 1 0
1 -1 0 0 1 -1
1
Generator of the Alexander module
(0,1-6t+10t^2-12t^3+2t^4+9t^5-14t^6+11t^7-5t^8+t^9,t-2t^2+5t^3-4t^4+3t^5-t^6,1-4t+4t^2+3t^3-18t^4+28t^5-26t^6+16t^7-6t^8+t^9,-4+5t-8t^2-t^3+10t^4-14t^5+11t^6-5t^7+t^8,0)
the Blanchfield form on it
x
83
First homology
of the double branched cover of 10_110
Z/83
-2 2
10_111
2

detected by
the signature
-2+9t-17t^2+21t^3-17t^4+9t^5-2t^6
Seifert matrix of 10_111
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 -1 -1 -1 0 -1
0 0 0 -2 1 0
0 -1 0 0 -1 0
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(-2t+2t^2-2t^3,0,2-2t+2t^2,3-2t+2t^2,0,2-2t+2t^2)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
77
First homology
of the double branched cover of 10_111
Z/77
-4 4
10_112
1

detected by
an unknotting move
-1+5t-11t^2+17t^3-19t^4+17t^5-11t^6+5t^7-t^8
Seifert matrix of 10_112
1 0 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
1 -1 -1 1 0 -1 1 0
1 -1 -1 1 1 -1 1 1
0 -1 -1 0 0 -1 0 0
1 0 -1 0 0 -1 1 0
1 -1 -1 1 0 -1 1 1
1
Generator of the Alexander module
(0,0,1,-t^4,0,-t,0,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
87
First homology
of the double branched cover of 10_112
Z/87
2 2
10_113
1

detected by
an unknotting move
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 10_113
-1 0 -1 0 0 -1
0 1 0 0 0 0
0 -1 -2 -1 0 -2
0 1 0 1 0 0
0 -1 -1 -1 -1 -1
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(3-4t+2t^2,0,2,0,0,0)
the Blanchfield form on it
-69t^-3+380t^-2-899t^-1+1142-899t+380t^2-69t^3
111
First homology
of the double branched cover of 10_113
Z/111
-2 2
10_114
1

detected by
an unknotting move
-2+10t-21t^2+27t^3-21t^4+10t^5-2t^6
Seifert matrix of 10_114
1 0 0 -1 0 0
0 -1 0 0 0 0
0 -1 -1 0 0 0
0 -1 -1 -1 0 0
1 0 -1 -1 1 0
-1 1 1 1 -1 2
1
Generator of the Alexander module
(0,0,1,1,t,1-t)
the Blanchfield form on it
2t^-2-7t^-1+8-7t+2t^2
93
First homology
of the double branched cover of 10_114
Z/93
0 2
10_115
2

detected by
A(F_2)
-1+9t-26t^2+37t^3-26t^4+9t^5-t^6
Seifert matrix of 10_115
-1 0 0 0 0 0
0 -1 0 0 0 0
0 1 1 -1 0 0
-1 0 0 -1 0 0
-1 0 0 -1 1 1
0 1 0 -1 0 1
2
109
First homology
of the double branched cover of 10_115
Z/109
0 0
10_116
2

detected by
the Lickorish test
-1+5t-12t^2+19t^3-21t^4+19t^5-12t^6+5t^7-t^8
Seifert matrix of 10_116
1 0 -1 0 0 1 0 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 -1 0
1 0 -1 1 0 1 -1 0
1 -1 -1 1 1 1 -1 1
0 0 0 0 0 1 0 0
0 -1 0 0 0 0 -1 0
1 -1 -1 1 0 1 -1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-11+8t-4t^2+t^3
95
First homology
of the double branched cover of 10_116
Z/95
2 2
10_117
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 10_117
-1 0 0 0 0 0
0 2 1 0 1 1
0 0 1 0 0 0
-1 -1 0 1 -1 0
-1 0 0 0 -1 0
-1 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-1+1-t
103
First homology
of the double branched cover of 10_117
Z/103
2 2
10_118
1

detected by
an unknotting move
1-5t+12t^2-19t^3+23t^4-19t^5+12t^6-5t^7+t^8
Seifert matrix of 10_118
1 0 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 -1 0
1 0 -1 1 0 -1 -1 0
1 -1 -1 1 1 -1 -1 1
0 -1 -1 0 0 -1 -1 0
0 -1 0 0 0 0 -1 0
1 -1 -1 1 0 -1 -1 1
1
Generator of the Alexander module
(0,-1,0,t,1,0,0,t)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+9-8t+4t^2-t^3
97
First homology
of the double branched cover of 10_118
Z/97
0 0
10_119
1

detected by
an unknotting move
-2+10t-23t^2+31t^3-23t^4+10t^5-2t^6
Seifert matrix of 10_119
1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 -1 1 -1
0 -1 0 -1 0 0
-1 1 0 0 2 0
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,4t-2t^2,t,1,t)
the Blanchfield form on it
-2t^-2+6t^-1-9+6t-2t^2
101
First homology
of the double branched cover of 10_119
Z/101
0 0
10_120
2

detected by
the signature
8-26t+37t^2-26t^3+8t^4
Seifert matrix of 10_120
-2 1 0 0
0 -2 -1 -1
-1 -1 -2 -1
-1 0 -1 -2
1
Generator of the Alexander module
(0,0,1-t,t)
the Blanchfield form on it
-28t^-2+95t^-1-136+95t-28t^2
105
First homology
of the double branched cover of 10_120
Z/105
-4 4
10_121
2

detected by
the Lickorish test
2-11t+27t^2-35t^3+27t^4-11t^5+2t^6
Seifert matrix of 10_121
-1 0 0 -1 0 -1
-1 1 -1 -1 1 0
-1 0 -1 -1 0 -1
0 0 0 -2 0 -2
0 0 -1 0 1 0
0 0 0 -1 0 -2
1
Generator of the Alexander module
(0,1,0,0,1,0)
the Blanchfield form on it
-2t^-1+3-2t
115
First homology
of the double branched cover of 10_121
Z/115
-2 2
10_122
2

detected by
the Lickorish test
-2+11t-24t^2+31t^3-24t^4+11t^5-2t^6
Seifert matrix of 10_122
-1 0 0 0 0 0
0 2 0 0 1 1
-1 0 -1 0 0 0
-1 -1 -1 1 -1 0
-1 0 -1 0 -1 0
0 0 -1 0 0 1
2
105
First homology
of the double branched cover of 10_122
Z/105
0 2
10_123
2

detected by
the Nakanishi index
1-6t+15t^2-24t^3+29t^4-24t^5+15t^6-6t^7+t^8
Seifert matrix of 10_123
1 0 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 -1
1 0 1 0 1 0 0 1
-1 -1 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0
0 0 -1 0 0 -1 0 0
0 -1 -1 0 -1 -1 -1 -1
1 0 0 0 1 0 0 1
2
121
First homology
of the double branched cover of 10_123
Z/11+Z/11
0 0
10_124
4

detected by
the signature
-1+t-t^3+t^4-t^5+t^7-t^8
Seifert matrix of 10_124
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 0 -1 -1
-1 -1 0 -1 -1 0 0 -1
-1 -1 0 0 -1 0 0 0
0 0 -1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 0 -1 -1
-1 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
-t^-3+t^-2-t^-1+1-t+t^2-t^3
1
First homology
of the double branched cover of 10_124
0
-8 8
10_125
1

detected by
an unknotting move
1-2t+2t^2-t^3+2t^4-2t^5+t^6
Seifert matrix of 10_125
-1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 -1
0 0 0 -1 0 -1
0 -1 -1 -2 -1 -1
0 0 -1 -1 0 -1
0 0 0 -1 0 0
1
Generator of the Alexander module
(1,0,0,0,1,0)
the Blanchfield form on it
-t^-2+t^-1+t-t^2
11
First homology
of the double branched cover of 10_125
Z/11
2 2
10_126
1

detected by
an unknotting move
1-2t+4t^2-5t^3+4t^4-2t^5+t^6
Seifert matrix of 10_126
-1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 -1
0 0 0 -1 0 -1
0 -1 -1 0 -1 -1
0 0 -1 -1 0 -1
0 0 0 -1 0 0
1
Generator of the Alexander module
(-t,0,0,1,0,0)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
19
First homology
of the double branched cover of 10_126
Z/19
2 2
10_127
2

detected by
the signature
-1+4t-6t^2+7t^3-6t^4+4t^5-t^6
Seifert matrix of 10_127
-1 -1 -1 -1 -1 -1
0 -2 -2 -1 -2 -2
0 -1 -2 -1 -1 -2
0 -1 -1 0 -1 -1
0 -1 -2 -1 -2 -2
0 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(-t,0,0,1,0,0)
the Blanchfield form on it
-t^-2+2t^-1-2+2t-t^2
29
First homology
of the double branched cover of 10_127
Z/29
-4 4
10_128
3

detected by
the signature
2-3t+t^2+t^3+t^4-3t^5+2t^6
Seifert matrix of 10_128
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 1 -1 0
1 1 0 -2 1 0
-1 -1 0 0 -1 0
0 0 -1 1 -1 -1
1
Generator of the Alexander module
(0,1,0,-1,1,0)
the Blanchfield form on it
2t^-2-5t^-1+7-5t+2t^2
11
First homology
of the double branched cover of 10_128
Z/11
-6 6
10_129
1

detected by
an unknotting move
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 10_129
-1 -1 1 -1
0 0 1 -1
0 0 1 1
0 -1 1 -2
1
Generator of the Alexander module
(t,0,0,1)
the Blanchfield form on it
2t^-1-2+2t
25
First homology
of the double branched cover of 10_129
Z/25
0 0
10_130
1

detected by
an unknotting move
2-4t+5t^2-4t^3+2t^4
Seifert matrix of 10_130
-1 -1 1 -1
0 0 1 -1
0 0 1 1
0 -1 1 0
1
Generator of the Alexander module
(-t,0,0,1)
the Blanchfield form on it
2t^-1-4+2t
17
First homology
of the double branched cover of 10_130
Z/17
0 2
10_131
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 10_131
-1 -1 1 -1
0 -2 2 -1
0 1 -3 1
0 -1 1 0
1
Generator of the Alexander module
(0,0,1,-1)
the Blanchfield form on it
-2t^-1+3-2t
31
First homology
of the double branched cover of 10_131
Z/31
-2 2
10_132
1

detected by
an unknotting move
1-t+t^2-t^3+t^4
Seifert matrix of 10_132
-1 -1 1 0
0 0 1 0
0 1 1 1
0 0 0 1
1
Generator of the Alexander module
(-1,0,1,0)
the Blanchfield form on it
t^-1-2+t
5
First homology
of the double branched cover of 10_132
Z/5
0 2
10_133
1

detected by
an unknotting move
-1+5t-7t^2+5t^3-t^4
Seifert matrix of 10_133
-3 -2 -2 0
-3 -3 -2 0
-2 -2 -1 0
-1 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
1
19
First homology
of the double branched cover of 10_133
Z/19
-2 2
10_134
3

detected by
the signature
2-4t+4t^2-3t^3+4t^4-4t^5+2t^6
Seifert matrix of 10_134
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 0 0 1
0 0 0 -1 0 -1
0 0 -1 0 -1 1
1 1 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
23
First homology
of the double branched cover of 10_134
Z/23
-6 6
10_135
1

detected by
an unknotting move
3-9t+13t^2-9t^3+3t^4
Seifert matrix of 10_135
1 0 -1 1
0 -1 0 0
-1 -1 -2 0
0 0 0 1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-2+3t^-1-4+3t-t^2
37
First homology
of the double branched cover of 10_135
Z/37
0 0
10_136
1

detected by
an unknotting move
-1+4t-5t^2+4t^3-t^4
Seifert matrix of 10_136
0 0 1 1
1 1 1 2
0 0 1 0
2 1 1 4
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-1-2+t
15
First homology
of the double branched cover of 10_136
Z/15
2 2
10_137
1

detected by
an unknotting move
1-6t+11t^2-6t^3+t^4
Seifert matrix of 10_137
1 0 0 0
-1 0 1 -1
1 1 -2 0
0 0 0 -1
1
Generator of the Alexander module
(0,1,-2,0)
the Blanchfield form on it
-t^-1+4-t
25
First homology
of the double branched cover of 10_137
Z/25
0 0
10_138
1

detected by
an unknotting move
1-5t+8t^2-7t^3+8t^4-5t^5+t^6
Seifert matrix of 10_138
1 0 0 0 0 0
-1 -1 0 -1 0 -1
0 0 -1 0 0 0
-1 0 -1 -1 0 -1
0 0 0 0 1 0
-1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-2t^-1+5-2t
35
First homology
of the double branched cover of 10_138
Z/35
-2 2
10_139
3

detected by
the signature
1-t+2t^3-3t^4+2t^5-t^7+t^8
Seifert matrix of 10_139
-1 0 0 0 0 0 0 0
0 -1 0 -1 -1 0 -1 -1
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 -1
-1 0 -1 0 -1 0 0 0
0 -1 0 -1 -1 -1 -1 -1
0 0 0 -1 -1 0 -1 -1
-1 0 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-t^-2+t^-1-1+t-t^2+t^3
3
First homology
of the double branched cover of 10_139
Z/3
-6 6
10_140
2

detected by
A(F_2)
1-2t+3t^2-2t^3+t^4
Seifert matrix of 10_140
1 2 0 2
1 1 0 2
0 0 -1 1
0 0 0 1
2
9
First homology
of the double branched cover of 10_140
Z/9
0 0
10_141
1

detected by
an unknotting move
-1+3t-4t^2+5t^3-4t^4+3t^5-t^6
Seifert matrix of 10_141
-1 0 -1 -1 0 -1
0 1 0 0 1 0
0 0 -2 -1 0 -2
0 1 -1 0 1 -1
0 0 0 0 1 0
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(-t,0,1,1,0,1)
the Blanchfield form on it
1
21
First homology
of the double branched cover of 10_141
Z/21
0 2
10_142
3

detected by
the signature
2-3t+2t^2-t^3+2t^4-3t^5+2t^6
Seifert matrix of 10_142
-1 0 0 0 0 0
0 -2 0 1 1 1
-1 0 -1 0 0 0
-1 0 -1 -1 -1 -1
-1 0 -1 0 -1 0
-1 0 -1 0 -1 -1
2
15
First homology
of the double branched cover of 10_142
Z/15
-6 6
10_143
1

detected by
an unknotting move
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 10_143
-1 0 -1 -1 0 -1
0 1 0 0 1 0
0 0 0 -1 0 -1
0 1 -1 0 1 -1
0 0 0 0 1 0
0 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-1
27
First homology
of the double branched cover of 10_143
Z/27
2 2
10_144
2

detected by
the Lickorish test
-3+10t-13t^2+10t^3-3t^4
Seifert matrix of 10_144
-2 -1 -1 -1
-1 1 -1 -1
-2 -1 -2 -1
0 0 0 -1
2
39
First homology
of the double branched cover of 10_144
Z/39
-2 2
10_145
1

detected by
an unknotting move
1+t-3t^2+t^3+t^4
Seifert matrix of 10_145
1 0 0 0
1 1 0 -1
1 0 1 0
1 0 0 1
1
Generator of the Alexander module
(0,1,t,0)
the Blanchfield form on it
t^-1-2+t
3
First homology
of the double branched cover of 10_145
Z/3
2 2
10_146
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 10_146
1 0 1 0
1 2 1 0
1 1 0 0
0 -1 -1 -1
1
Generator of the Alexander module
(7t+14t^2-21t^3+7t^4,-1-2t+3t^2-t^3,54t+60t^2-162t^3+94t^4-16t^5,2t-2t^2-6t^3+7t^4-2t^5)
the Blanchfield form on it
1425t^-6-12200t^-5+35579t^-4-13578t^-3-171458t^-2+492598t^-1-664732+492598t-171458t^2-13578t^3+35579t^4-12200t^5+1425t^6
33
First homology
of the double branched cover of 10_146
Z/33
0 0
10_147
1

detected by
an unknotting move
-2+7t-9t^2+7t^3-2t^4
Seifert matrix of 10_147
-1 0 -1 0
0 0 0 1
0 0 -1 0
0 2 2 2
1
Generator of the Alexander module
(1+2t-2t^2,-1-2t+t^2,0,-1-4t+2t^2)
the Blanchfield form on it
-2t^-1+3-2t
27
First homology
of the double branched cover of 10_147
Z/27
-2 2
10_148
1

detected by
an unknotting move
1-3t+7t^2-9t^3+7t^4-3t^5+t^6
Seifert matrix of 10_148
-1 -1 -1 0 -1 0
0 0 -1 1 -1 1
0 -1 0 0 -1 0
0 0 0 1 0 1
0 0 -1 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,t,1,-1,1)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
31
First homology
of the double branched cover of 10_148
Z/31
2 2
10_149
2

detected by
the signature
-1+5t-9t^2+11t^3-9t^4+5t^5-t^6
Seifert matrix of 10_149
-1 -1 -1 0 -1 0
0 -2 -1 0 -2 0
0 -1 0 0 -1 0
0 -1 0 -1 -1 0
0 -1 -1 0 -2 0
0 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
41
First homology
of the double branched cover of 10_149
Z/41
-4 4
10_150
2

detected by
the signature
-1+4t-6t^2+7t^3-6t^4+4t^5-t^6
Seifert matrix of 10_150
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 1 0 0
-1 -1 0 -1 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,-t)
the Blanchfield form on it
-t^-2+3t^-1-2+3t-t^2
29
First homology
of the double branched cover of 10_150
Z/29
-4 4
10_151
1

detected by
an unknotting move
1-4t+10t^2-13t^3+10t^4-4t^5+t^6
Seifert matrix of 10_151
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 1 0 0
-1 -1 0 -1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-1+1-t
43
First homology
of the double branched cover of 10_151
Z/43
2 2
10_152
3

detected by
the signature
1-t-t^2+4t^3-5t^4+4t^5-t^6-t^7+t^8
Seifert matrix of 10_152
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 -1 0 -1 0 0 0 0
0 -1 0 -1 -1 -1 0 -1
0 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-3-t^-2+1-t^2+t^3
11
First homology
of the double branched cover of 10_152
Z/11
-6 6
10_153
1

detected by
an unknotting move
1-t-t^2+3t^3-t^4-t^5+t^6
Seifert matrix of 10_153
-1 -1 -1 0 -1 0
0 0 -1 1 -1 1
0 -1 -2 0 -1 0
0 0 0 1 0 1
0 0 -1 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
1
First homology
of the double branched cover of 10_153
0
0 0
10_154
2

detected by
the signature
1-4t^2+7t^3-4t^4+t^6
Seifert matrix of 10_154
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 -1 0 0
-1 -1 0 -1 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,1,0,0,0,t)
the Blanchfield form on it
t^-2+2t^-1-4+2t+t^2
13
First homology
of the double branched cover of 10_154
Z/13
-4 4
10_155
2

detected by
the Nakanishi index
-1+3t-5t^2+7t^3-5t^4+3t^5-t^6
Seifert matrix of 10_155
-1 -1 0 0 0 -1
0 1 0 -1 0 0
-1 -1 -1 0 0 -1
0 -1 0 1 1 -1
0 0 0 0 1 0
0 -1 0 0 0 0
2
25
First homology
of the double branched cover of 10_155
Z/5+Z/5
0 0
10_156
1

detected by
an unknotting move
1-4t+8t^2-9t^3+8t^4-4t^5+t^6
Seifert matrix of 10_156
-1 0 0 0 0 0
0 1 0 0 0 0
-1 1 1 -1 0 0
-1 0 0 -1 0 0
-1 0 0 -1 1 1
-1 1 0 -1 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-1
35
First homology
of the double branched cover of 10_156
Z/35
2 2
10_157
2

detected by
the Nakanishi index
-1+6t-11t^2+13t^3-11t^4+6t^5-t^6
Seifert matrix of 10_157
0 0 0 -1 0 0
0 1 0 0 0 0
-1 0 0 -1 0 0
-1 1 -1 0 0 1
-1 0 -1 0 1 1
0 0 0 0 0 1
2
49
First homology
of the double branched cover of 10_157
Z/7+Z/7
4 4
10_158
1

detected by
an unknotting move
-1+4t-10t^2+15t^3-10t^4+4t^5-t^6
Seifert matrix of 10_158
1 0 0 0 0 0
0 -1 0 0 0 0
1 -1 1 0 0 0
1 0 1 -1 1 1
0 -1 0 0 -1 0
1 -1 1 0 0 1
1
Generator of the Alexander module
(-t^2-t^4-t^5,2t^4+2t^6+t^7-3t^8-2t^9,t^2+t^4+t^5,-1-t+t^2+2t^3-t^4+2t^6-4t^7-4t^8+4t^9+4t^10,-t^5-t^6,-t^2+2t^3+2t^5+2t^6)
the Blanchfield form on it
x
45
First homology
of the double branched cover of 10_158
Z/45
0 0
10_159
1

detected by
an unknotting move
1-4t+9t^2-11t^3+9t^4-4t^5+t^6
Seifert matrix of 10_159
0 -1 -1 -1 0 -1
-1 -2 -1 -1 -1 -1
-1 -2 -2 -1 -1 -1
0 0 0 -1 0 0
-1 -2 -2 -1 -2 -1
0 -1 0 -1 0 0
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
1
39
First homology
of the double branched cover of 10_159
Z/39
-2 2
10_160
2

detected by
the signature
-1+4t-4t^2+3t^3-4t^4+4t^5-t^6
Seifert matrix of 10_160
-1 0 0 0 0 0
0 1 0 0 0 0
-1 1 -1 -1 0 0
-1 0 0 -1 0 0
-1 0 0 -1 -1 0
-1 1 0 -1 -1 -1
1 or 2
21
First homology
of the double branched cover of 10_160
Z/21
-4 4
10_161
2

detected by
the signature
1-2t^2+3t^3-2t^4+t^6
Seifert matrix of 10_161
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 1 -1 -1 0 0
-1 0 0 -1 0 0
-1 0 0 -1 -1 0
-1 1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,t)
the Blanchfield form on it
-t^-2+3t^-1-4+3t-t^2
5
First homology
of the double branched cover of 10_161
Z/5
-4 4
10_162
1

detected by
an unknotting move
-3+9t-11t^2+9t^3-3t^4
Seifert matrix of 10_162
1 -1 0 -1
-1 0 -1 -1
1 -1 1 -1
0 -2 0 -1
1 or 2
35
First homology
of the double branched cover of 10_162
Z/35
2 2
10_163
2

detected by
the Lickorish test
1-5t+12t^2-15t^3+12t^4-5t^5+t^6
Seifert matrix of 10_163
1 0 0 -1 0 0
0 -1 0 0 0 0
0 -1 -1 0 0 0
0 -1 -1 -1 0 0
1 0 -1 -1 1 0
-1 1 1 1 -1 -1
2
51
First homology
of the double branched cover of 10_163
Z/51
-2 2
10_164
1

detected by
an unknotting move
3-11t+17t^2-11t^3+3t^4
Seifert matrix of 10_164
3 0 3 0
-1 -3 0 -2
1 0 2 0
0 -1 1 -1
1
Generator of the Alexander module
(0,4t,2,-1+2t)
the Blanchfield form on it
3t^-1-5+3t
45
First homology
of the double branched cover of 10_164
Z/45
0 0
10_165
2

detected by
the Lickorish test
-2+10t-15t^2+10t^3-2t^4
Seifert matrix of 10_165
2 1 2 0
1 2 2 0
1 2 2 -1
0 1 0 0
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
2t^-1-4+2t
39
First homology
of the double branched cover of 10_165
Z/39
2 2
11a_1
1

detected by
an unknotting move
2-12t+30t^2-39t^3+30t^4-12t^5+2t^6
Seifert matrix of 11a_1
1 0 0 0 0 0
-1 -1 0 -1 0 1
0 0 1 0 0 0
-1 0 -1 -1 0 1
0 0 0 0 -1 -1
1 0 1 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-2-5t^-1+9-5t+t^2
127
First homology
of the double branched cover of 11a_1
Z/127
-2 2
11a_2
2

detected by
the signature
-3+15t-31t^2+39t^3-31t^4+15t^5-3t^6
Seifert matrix of 11a_2
1 0 0 0 0 0
-1 -1 0 1 1 1
0 0 -1 -1 -1 -1
1 0 0 -2 -1 -2
1 0 0 -1 -2 -1
1 0 0 -1 -1 -2
1
Generator of the Alexander module
(0,0,-2+t,0,0,-3+2t)
the Blanchfield form on it
-6t^-2+21t^-1-25+21t-6t^2
137
First homology
of the double branched cover of 11a_2
Z/137
-4 4
11a_3
2

detected by
the Lickorish test
-1+5t-13t^2+24t^3-29t^4+24t^5-13t^6+5t^7-t^8
Seifert matrix of 11a_3
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 1 0 1 0
0 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
0 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+12t^-1-17+12t-5t^2+t^3
115
First homology
of the double branched cover of 11a_3
Z/115
2 2
11a_4
1

detected by
an unknotting move
-2+10t-22t^2+29t^3-22t^4+10t^5-2t^6
Seifert matrix of 11a_4
-1 -1 -1 -1 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 -1 -1 0 0
0 0 0 0 1 0
0 1 0 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
97
First homology
of the double branched cover of 11a_4
Z/97
0 0
11a_5
1

detected by
an unknotting move
-1+9t-30t^2+45t^3-30t^4+9t^5-t^6
Seifert matrix of 11a_5
-1 0 -1 -1 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 1 -1 -1 0 0
0 0 0 -1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,t,2)
the Blanchfield form on it
t^-2-5t^-1+9-5t+t^2
125
First homology
of the double branched cover of 11a_5
Z/125
0 0
11a_6
1

detected by
an unknotting move
2-13t+32t^2-41t^3+32t^4-13t^5+2t^6
Seifert matrix of 11a_6
1 0 0 0 0 0
-1 -1 0 0 1 0
0 0 -1 0 -1 0
0 0 0 -1 0 -1
1 0 0 -1 -2 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1-3t+t^2,-3+t,0,0)
the Blanchfield form on it
-2t^-2+7t^-1-8+7t-2t^2
135
First homology
of the double branched cover of 11a_6
Z/135
-2 2
11a_7
2

detected by
the Lickorish test
-1+5t-12t^2+19t^3-21t^4+19t^5-12t^6+5t^7-t^8
Seifert matrix of 11a_7
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 1 0
0 -1 -1 0 -1 0 0 0
0 -1 0 1 -1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,-1,0,0)
the Blanchfield form on it
t^-2-2t^-1+1-2t+t^2
95
First homology
of the double branched cover of 11a_7
Z/95
2 2
11a_8
1

detected by
an unknotting move
-2+11t-27t^2+37t^3-27t^4+11t^5-2t^6
Seifert matrix of 11a_8
-1 -1 -1 0 -1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 2 0 0
0 -1 -1 0 -1 0
0 -1 0 -1 -1 1
1
Generator of the Alexander module
(-2t+4t^2,1-10t-4t^2,-1+2t+2t^2+8t^5-16t^6,1,-2t^2-4t^5+8t^6,-4+10t)
the Blanchfield form on it
x
117
First homology
of the double branched cover of 11a_8
Z/117
0 0
11a_9
2

detected by
the signature
1-5t+10t^2-11t^3+11t^4-11t^5+10t^6-5t^7+t^8
Seifert matrix of 11a_9
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 -1 -1 -1
0 0 1 0 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1
-1 0 -1 0 -1 -1 0 -1
-1 0 -1 0 0 -1 0 0
-1 0 -1 0 -1 -1 -1 -1
-1 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-3-5t^-2+10t^-1-11+10t-5t^2+t^3
65
First homology
of the double branched cover of 11a_9
Z/65
-4 4
11a_10
1

detected by
an unknotting move
2-11t+25t^2-31t^3+25t^4-11t^5+2t^6
Seifert matrix of 11a_10
1 0 0 0 0 0
-1 -1 0 -1 1 -1
0 0 1 0 0 0
-1 0 -1 -1 1 -1
1 0 1 0 -2 1
-1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
107
First homology
of the double branched cover of 11a_10
Z/107
-2 2
11a_11
1

detected by
an unknotting move
-2+11t-26t^2+35t^3-26t^4+11t^5-2t^6
Seifert matrix of 11a_11
-1 0 -1 1 0 0
0 -1 0 -1 0 0
0 0 1 0 0 0
0 0 1 -2 0 0
0 0 0 1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,2-t,0,0,-1+t,0)
the Blanchfield form on it
2t^-2-9t^-1+14-9t+2t^2
113
First homology
of the double branched cover of 11a_11
Z/113
0 0
11a_12
1

detected by
an unknotting move
2-11t+24t^2-29t^3+24t^4-11t^5+2t^6
Seifert matrix of 11a_12
1 0 0 0 0 0
-1 -1 0 0 1 0
0 0 1 0 0 0
0 0 0 -1 0 -1
1 0 1 -1 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
1
103
First homology
of the double branched cover of 11a_12
Z/103
-2 2
11a_13
1

detected by
an unknotting move
3-15t+25t^2-15t^3+3t^4
Seifert matrix of 11a_13
1 0 0 0
-1 -1 0 -1
0 0 1 0
-1 0 -1 -3
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-t^-2+5t^-1-8+5t-t^2
61
First homology
of the double branched cover of 11a_13
Z/61
0 0
11a_14
1

detected by
an unknotting move
-1+5t-15t^2+28t^3-35t^4+28t^5-15t^6+5t^7-t^8
Seifert matrix of 11a_14
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
-1 -1 1 1 1 1 1 0
0 0 0 0 1 0 0 0
-1 -1 1 0 1 1 1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,2-4t+t^2+8t^3-9t^4-2t^5+3t^6,4-6t+9t^3-9t^4-2t^5+3t^6,2-10t^2+22t^3-14t^4-7t^5+6t^6,1+t-7t^2+8t^3+2t^4-3t^5,-4t^2+7t^3-7t^4-2t^5+3t^6,4t-7t^2+7t^3+2t^4-3t^5,-6t+14t^2-10t^3-4t^4+4t^5)
the Blanchfield form on it
x
133
First homology
of the double branched cover of 11a_14
Z/133
0 0
11a_15
1

detected by
an unknotting move
1-5t+13t^2-22t^3+25t^4-22t^5+13t^6-5t^7+t^8
Seifert matrix of 11a_15
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
0 0 0 -1 0 -1 -1 -1
0 0 0 0 1 0 0 0
-1 -1 1 0 1 1 0 0
-1 -1 1 0 1 1 1 1
-1 -1 1 0 1 1 0 1
1
Generator of the Alexander module
(0,0,1+t^2,2+t^2,0,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-9t^-1+12-9t+4t^2-t^3
107
First homology
of the double branched cover of 11a_15
Z/107
2 2
11a_16
2

detected by
the Lickorish test
-2+10t-24t^2+33t^3-24t^4+10t^5-2t^6
Seifert matrix of 11a_16
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 1 0
0 0 0 -1 0 1
0 0 0 0 1 0
1 1 -1 0 -1 2
1
Generator of the Alexander module
(0,0,0,t,0,1)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
105
First homology
of the double branched cover of 11a_16
Z/105
0 0
11a_17
2

detected by
the Lickorish test
1-10t+30t^2-41t^3+30t^4-10t^5+t^6
Seifert matrix of 11a_17
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
-1 -1 0 -1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,t,1+t,0,1+t,0)
the Blanchfield form on it
t^-2-7t^-1+13-7t+t^2
123
First homology
of the double branched cover of 11a_17
Z/123
-2 2
11a_18
1

detected by
an unknotting move
3-13t+29t^2-37t^3+29t^4-13t^5+3t^6
Seifert matrix of 11a_18
-1 -1 -1 -1 0 0
0 -2 -1 -2 0 0
0 -1 -2 -1 0 0
0 -1 -1 -2 0 0
0 1 0 1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(3-2t,0,0,0,-1+t,0)
the Blanchfield form on it
3t^-2-7t^-1+11-7t+3t^2
127
First homology
of the double branched cover of 11a_18
Z/127
-2 2
11a_19
2

detected by
the Lickorish test
1-6t+18t^2-33t^3+39t^4-33t^5+18t^6-6t^7+t^8
Seifert matrix of 11a_19
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
0 0 -1 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 -1 0 -1 0 -1
-1 -1 1 0 1 0 1 0
0 0 -1 -1 0 0 0 -1
1
Generator of the Alexander module
(0,-t,-1-2t,-2t^2,1,1-t+t^2,0,0)
the Blanchfield form on it
t^-3-5t^-2+12t^-1-17+12t-5t^2+t^3
155
First homology
of the double branched cover of 11a_19
Z/155
-2 2
11a_20
2

detected by
the signature
-3+13t-25t^2+31t^3-25t^4+13t^5-3t^6
Seifert matrix of 11a_20
-1 -1 0 0 -1 0
0 -2 0 0 -1 0
0 0 -1 0 -1 0
0 0 0 1 -1 0
0 -1 0 0 -2 0
0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,t,1,1)
the Blanchfield form on it
-3t^-2+10t^-1-14+10t-3t^2
113
First homology
of the double branched cover of 11a_20
Z/113
-4 4
11a_21
2

detected by
the Lickorish test
-5+19t-27t^2+19t^3-5t^4
Seifert matrix of 11a_21
-1 -1 1 0
0 -2 1 0
0 1 -3 0
0 0 1 1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-2t^-1+3-2t
75
First homology
of the double branched cover of 11a_21
Z/75
-2 2
11a_22
2

detected by
the signature
-1+5t-13t^2+20t^3-23t^4+20t^5-13t^6+5t^7-t^8
Seifert matrix of 11a_22
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 1 1 0 1
0 0 0 1 0 0 0 0
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,-1-t+t^3,0,1-t^3,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-9t^-1+10-9t+4t^2-t^3
101
First homology
of the double branched cover of 11a_22
Z/101
-4 4
11a_23
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 11a_23
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 1 0 -1
0 0 0 1 0 0
0 0 0 0 -1 1
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
103
First homology
of the double branched cover of 11a_23
Z/103
-2 2
11a_24
1

detected by
an unknotting move
-1+6t-18t^2+33t^3-41t^4+33t^5-18t^6+6t^7-t^8
Seifert matrix of 11a_24
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 1 1 1 0
0 0 0 1 0 0 0 0
-1 -1 0 1 1 1 1 1
0 0 0 0 0 -1 0 0
-1 -1 0 1 0 1 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(7-21t+28t^2-22t^3-2t^4+20t^5-20t^6+10t^7-2t^8,-4t+4t^2-12t^3+7t^4+5t^5-11t^6+8t^7-2t^8,-20t+24t^2-30t^3+10t^4+16t^5-24t^6+16t^7-4t^8,10-12t+15t^2-5t^3-8t^4+12t^5-8t^6+2t^7,-17t+13t^2-19t^3-3t^4+20t^5-16t^6+4t^7+4t^8-2t^9,10-12t+15t^2-5t^3-8t^4+12t^5-8t^6+2t^7,7-21t+28t^2-22t^3-2t^4+20t^5-20t^6+10t^
the Blanchfield form on it
x
157
First homology
of the double branched cover of 11a_24
Z/157
0 0
11a_25
2

detected by
the Lickorish test
1-6t+18t^2-33t^3+39t^4-33t^5+18t^6-6t^7+t^8
Seifert matrix of 11a_25
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 0 1 1 1
0 0 0 1 0 0 0 0
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
-1 -1 0 1 1 1 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(-1+2t-t^2,-1+2t-t^2,-2t+5t^2-13t^3+19t^4-15t^5+6t^6-t^7,0,0,0,2-5t+12t^2-8t^3-4t^4+9t^5-5t^6+t^7,2-t^2+4t^3-9t^4+10t^5-5t^6+t^7)
the Blanchfield form on it
x
155
First homology
of the double branched cover of 11a_25
Z/155
-2 2
11a_26
1

detected by
an unknotting move
-1+6t-18t^2+33t^3-41t^4+33t^5-18t^6+6t^7-t^8
Seifert matrix of 11a_26
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
0 0 -1 -1 0 0 -1 -1
0 0 0 0 1 0 0 0
0 0 -1 -1 0 -1 0 0
-1 -1 1 0 1 0 1 1
-1 -1 1 0 1 0 0 1
1
Generator of the Alexander module
(0,0,1+t-t^2,-t-t^2+t^3,0,-t-t^2+t^3,1+t-t^2,-t)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
157
First homology
of the double branched cover of 11a_26
Z/157
0 0
11a_27
2

detected by
the Lickorish test
2-13t+34t^2-45t^3+34t^4-13t^5+2t^6
Seifert matrix of 11a_27
1 0 0 0 0 0
-1 -1 0 0 -1 1
0 0 1 0 0 0
0 0 0 1 0 0
-1 0 -1 0 -1 0
0 0 1 -1 0 2
1
Generator of the Alexander module
(0,0,1,0,4-4t+t^2,1)
the Blanchfield form on it
2t^-1-3+2t
143
First homology
of the double branched cover of 11a_27
Z/143
2 2
11a_28
1

detected by
an unknotting move
-1+6t-15t^2+24t^3-29t^4+24t^5-15t^6+6t^7-t^8
Seifert matrix of 11a_28
1 0 0 0 0 0 0 0
-1 -1 -1 0 -1 -1 -1 -1
0 0 1 1 0 0 1 0
0 0 0 1 0 0 0 0
-1 0 -1 0 -1 -1 0 -1
-1 0 -1 0 0 -1 0 0
0 0 0 1 0 0 1 0
-1 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+17-14t+6t^2-t^3
121
First homology
of the double branched cover of 11a_28
Z/121
0 0
11a_29
1

detected by
an unknotting move
2-12t+27t^2-33t^3+27t^4-12t^5+2t^6
Seifert matrix of 11a_29
1 0 0 0 0 0
-1 -1 -1 0 -1 1
0 0 1 1 1 0
0 0 0 1 0 0
0 0 0 1 1 0
1 0 1 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+6t^-2-13t^-1+16-13t+6t^2-t^3
115
First homology
of the double branched cover of 11a_29
Z/115
2 2
11a_30
1

detected by
an unknotting move
-2+13t-35t^2+49t^3-35t^4+13t^5-2t^6
Seifert matrix of 11a_30
-1 -1 0 0 0 0
0 1 0 0 0 0
1 1 -2 0 0 0
0 0 -1 -1 0 0
-1 0 0 -1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+6t^-1-11+6t-t^2
149
First homology
of the double branched cover of 11a_30
Z/149
0 0
11a_31
2

detected by
the signature
-3+14t-28t^2+35t^3-28t^4+14t^5-3t^6
Seifert matrix of 11a_31
-1 -1 0 -1 -1 -1
0 -2 0 -1 -2 -2
0 0 1 0 0 0
0 -1 0 -2 -1 -1
0 -1 -1 -1 -2 -2
0 -1 0 -1 -1 -2
1
Generator of the Alexander module
(t,0,0,1,0,0)
the Blanchfield form on it
-3t^-2+10t^-1-12+10t-3t^2
125
First homology
of the double branched cover of 11a_31
Z/125
-4 4
11a_32
1

detected by
an unknotting move
3-14t+32t^2-41t^3+32t^4-14t^5+3t^6
Seifert matrix of 11a_32
-1 -1 0 -1 0 -1
0 -2 0 -1 0 -2
0 0 1 0 0 -1
0 -1 0 -2 0 -1
0 0 1 0 1 -1
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(t,0,0,1,0,0)
the Blanchfield form on it
3t^-2-10t^-1+16-10t+3t^2
139
First homology
of the double branched cover of 11a_32
Z/139
-2 2
11a_33
2

detected by
the Lickorish test
1-5t+12t^2-19t^3+21t^4-19t^5+12t^6-5t^7+t^8
Seifert matrix of 11a_33
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
-1 -1 1 1 0 1 1 0
0 0 0 0 -1 0 0 -1
0 0 0 0 0 1 0 0
-1 -1 1 0 0 1 1 0
-1 -1 1 1 0 1 1 1
1
Generator of the Alexander module
(0,1+2t-3t^2+3t^3-3t^4+t^5,2t-7t^2+11t^3-16t^4+14t^5-14t^6+7t^7-5t^8+2t^9,2t^2-5t^3+4t^4-5t^5+2t^6,4t^3-10t^4+8t^5-10t^6+4t^7,0,-2+t-2t^2+3t^3-5t^4+4t^5-5t^6+2t^7,0)
the Blanchfield form on it
x
95
First homology
of the double branched cover of 11a_33
Z/95
2 2
11a_34
1

detected by
an unknotting move
1-5t+14t^2-25t^3+29t^4-25t^5+14t^6-5t^7+t^8
Seifert matrix of 11a_34
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 -1 0
0 0 0 0 0 1 0 0
-1 -1 1 0 0 1 1 0
0 0 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+12t^-1-17+12t-5t^2+t^3
119
First homology
of the double branched cover of 11a_34
Z/119
-2 2
11a_35
1

detected by
an unknotting move
-1+5t-14t^2+25t^3-31t^4+25t^5-14t^6+5t^7-t^8
Seifert matrix of 11a_35
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
0 0 0 -1 0 0 -1 0
-1 -1 1 0 1 1 0 1
0 0 0 0 0 1 0 0
0 0 0 0 0 0 -1 0
-1 -1 1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
1
121
First homology
of the double branched cover of 11a_35
Z/121
0 0
11a_36
1

detected by
an unknotting move
-2+12t-28t^2+37t^3-28t^4+12t^5-2t^6
Seifert matrix of 11a_36
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 -1 0
0 0 0 1 0 0
0 0 0 0 -1 0
1 1 -1 1 1 2
1
Generator of the Alexander module
(0,-t,-1,0,0,1+t)
the Blanchfield form on it
t^-4-4t^-3+4t^-2+4t^-1-10+4t+4t^2-4t^3+t^4
121
First homology
of the double branched cover of 11a_36
Z/121
0 0
11a_37
1

detected by
an unknotting move
-2+9t-21t^2+29t^3-21t^4+9t^5-2t^6
Seifert matrix of 11a_37
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 1 0 0
0 0 0 1 0 0
-1 -1 1 1 1 0
0 0 0 0 1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-4t^-2+9t^-1-12+9t-4t^2+t^3
93
First homology
of the double branched cover of 11a_37
Z/93
0 0
11a_38
1

detected by
an unknotting move
-2+11t-27t^2+37t^3-27t^4+11t^5-2t^6
Seifert matrix of 11a_38
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 1 0 0
1 1 0 -1 2 0
-1 -1 0 1 -1 1
1
Generator of the Alexander module
(0,1+t+2t^2+t^3-t^4,-1-t-2t^2+t^3,-1-2t^2+t^3,-t-2t^3+t^4,2t+4t^3-2t^4)
the Blanchfield form on it
2t^-2-5t^-1+8-5t+2t^2
117
First homology
of the double branched cover of 11a_38
Z/117
0 0
11a_39
1

detected by
an unknotting move
-3+12t-22t^2+27t^3-22t^4+12t^5-3t^6
Seifert matrix of 11a_39
-1 0 -1 0 0 -1
0 1 0 0 1 0
0 0 -2 0 0 -1
0 1 0 1 1 -1
0 0 0 0 1 0
0 0 -1 0 0 -2
1
Generator of the Alexander module
(1+t^2,0,t,0,0,0)
the Blanchfield form on it
-3t^-2+8t^-1-8+8t-3t^2
101
First homology
of the double branched cover of 11a_39
Z/101
0 2
11a_40
2

detected by
the signature
-1+5t-12t^2+17t^3-19t^4+17t^5-12t^6+5t^7-t^8
Seifert matrix of 11a_40
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
0 0 -1 0 0 -1 0 -1
-1 -1 0 1 1 1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 -1 0 0 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,-t,0,0,1,-t,-t)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+15-12t+5t^2-t^3
89
First homology
of the double branched cover of 11a_40
Z/89
-4 4
11a_41
1

detected by
an unknotting move
2-11t+27t^2-35t^3+27t^4-11t^5+2t^6
Seifert matrix of 11a_41
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -2 0 0 1
-1 -1 0 1 1 1
0 0 0 0 1 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
115
First homology
of the double branched cover of 11a_41
Z/115
-2 2
11a_42
1

detected by
an unknotting move
1-9t+26t^2-35t^3+26t^4-9t^5+t^6
Seifert matrix of 11a_42
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 1 0
0 0 0 -1 0 0
0 0 0 0 -1 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-2-5t^-1+7-5t+t^2
107
First homology
of the double branched cover of 11a_42
Z/107
-2 2
11a_43
3

detected by
the signature
4-15t+30t^2-37t^3+30t^4-15t^5+4t^6
Seifert matrix of 11a_43
-1 -1 -1 -1 -1 -1
0 -2 -1 -1 -1 -2
0 -1 -2 -1 -2 -1
0 -1 -1 -2 -1 -1
0 -1 -1 -1 -2 -1
0 -1 -1 -1 -1 -2
2
135
First homology
of the double branched cover of 11a_43
Z/45+Z/3
-6 6
11a_44
2

detected by
the Nakanishi index
-1+5t-14t^2+24t^3-29t^4+24t^5-14t^6+5t^7-t^8
Seifert matrix of 11a_44
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 1 0
-1 -1 1 1 1 1 1 0
0 0 0 0 1 0 0 0
-1 -1 1 0 1 1 1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
117
First homology
of the double branched cover of 11a_44
Z/39+Z/3
0 0
11a_45
2

detected by
the Lickorish test
-6+22t-31t^2+22t^3-6t^4
Seifert matrix of 11a_45
-1 0 -1 -1
0 2 0 1
0 0 -2 -1
0 0 -1 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-3t^-2+10t^-1-14+10t-3t^2
87
First homology
of the double branched cover of 11a_45
Z/87
-2 2
11a_46
1

detected by
an unknotting move
2-9t+20t^2-25t^3+20t^4-9t^5+2t^6
Seifert matrix of 11a_46
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 -1 2 -1 0
0 0 0 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,-1,0,1-t)
the Blanchfield form on it
2t^-2-6t^-1+9-6t+2t^2
87
First homology
of the double branched cover of 11a_46
Z/87
-2 2
11a_47
2

detected by
the Nakanishi index
-1+5t-14t^2+24t^3-29t^4+24t^5-14t^6+5t^7-t^8
Seifert matrix of 11a_47
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
-1 -1 1 1 0 1 0 1
0 0 -1 -1 -1 0 0 -1
0 0 0 0 0 1 0 0
0 0 -1 -1 -1 0 -1 -1
-1 -1 1 0 0 1 0 1
2
117
First homology
of the double branched cover of 11a_47
Z/39+Z/3
0 0
11a_48
2

detected by
the signature
-2+12t-26t^2+33t^3-26t^4+12t^5-2t^6
Seifert matrix of 11a_48
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 0 1 0
0 0 0 1 0 0
0 0 0 0 1 0
1 0 -1 1 -1 2
1 or 2
113
First homology
of the double branched cover of 11a_48
Z/113
4 4
11a_49
2

detected by
the signature
-3+13t-23t^2+27t^3-23t^4+13t^5-3t^6
Seifert matrix of 11a_49
1 0 0 0 0 0
1 -2 -1 -1 -2 -1
1 -1 -2 0 -1 0
0 0 0 -1 0 -1
1 -1 -1 -1 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,t,0,1+t+t^2,0)
the Blanchfield form on it
-6t^-2+17t^-1-16+17t-6t^2
105
First homology
of the double branched cover of 11a_49
Z/105
-4 4
11a_50
1

detected by
an unknotting move
-5+21t-31t^2+21t^3-5t^4
Seifert matrix of 11a_50
1 0 0 0
1 -2 1 0
-1 1 -3 0
0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-2t^-1+5-2t
83
First homology
of the double branched cover of 11a_50
Z/83
-2 2
11a_51
1

detected by
an unknotting move
1-9t+28t^2-39t^3+28t^4-9t^5+t^6
Seifert matrix of 11a_51
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 1 1 0
0 0 0 1 0 0
0 0 0 0 -1 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,3-t)
the Blanchfield form on it
t^-2-5t^-1+7-5t+t^2
115
First homology
of the double branched cover of 11a_51
Z/115
2 2
11a_52
1

detected by
an unknotting move
-2+13t-32t^2+43t^3-32t^4+13t^5-2t^6
Seifert matrix of 11a_52
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 -1 0 -1 0
-1 0 0 1 1 1
1 1 0 0 -2 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,4-4t+t^2,0,1)
the Blanchfield form on it
-2t^-1+3-2t
137
First homology
of the double branched cover of 11a_52
Z/137
0 0
11a_53
2

detected by
the signature
-1+6t-14t^2+18t^3-19t^4+18t^5-14t^6+6t^7-t^8
Seifert matrix of 11a_53
1 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 -1
0 0 1 1 1 0 1 1
0 0 0 1 0 0 0 0
0 0 0 1 1 0 1 0
-1 0 -1 0 0 -1 0 0
0 0 0 1 0 0 1 0
0 0 0 1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
97
First homology
of the double branched cover of 11a_53
Z/97
4 4
11a_54
1

detected by
an unknotting move
2-13t+33t^2-43t^3+33t^4-13t^5+2t^6
Seifert matrix of 11a_54
1 0 0 0 0 0
-1 -1 -1 -1 0 -1
0 0 1 0 0 1
-1 0 -1 -1 0 0
0 0 1 0 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,0,0,1-2t,0)
the Blanchfield form on it
t^-1-3+t
139
First homology
of the double branched cover of 11a_54
Z/139
2 2
11a_55
1

detected by
an unknotting move
1-5t+10t^2-13t^3+13t^4-13t^5+10t^6-5t^7+t^8
Seifert matrix of 11a_55
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 -1 0 0
-1 -1 1 1 0 -1 1 0
-1 -1 1 1 1 -1 1 1
0 0 0 0 0 -1 0 0
-1 -1 1 0 0 -1 1 0
-1 -1 1 1 0 -1 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+13-10t+5t^2-t^3
71
First homology
of the double branched cover of 11a_55
Z/71
2 2
11a_56
1

detected by
an unknotting move
-2+11t-25t^2+33t^3-25t^4+11t^5-2t^6
Seifert matrix of 11a_56
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 0 -1
1 1 -1 2 0 1
-1 -1 1 -1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
109
First homology
of the double branched cover of 11a_56
Z/109
0 0
11a_57
2

detected by
the Nakanishi index
1-5t+12t^2-20t^3+23t^4-20t^5+12t^6-5t^7+t^8
Seifert matrix of 11a_57
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 -1 1 0
-1 -1 1 1 1 -1 1 1
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 1 0 1 0
-1 -1 1 0 1 -1 1 1
2
99
First homology
of the double branched cover of 11a_57
Z/33+Z/3
2 2
11a_58
1

detected by
an unknotting move
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 11a_58
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 1
0 0 0 -1 0 0
1 1 1 1 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,-1,0,0,1,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
81
First homology
of the double branched cover of 11a_58
Z/81
0 0
11a_59
1

detected by
an unknotting move
-3+11t-15t^2+11t^3-3t^4
Seifert matrix of 11a_59
-1 0 0 0
-1 -1 0 0
-1 -1 3 -1
0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-2+3t^-1-4+3t-t^2
43
First homology
of the double branched cover of 11a_59
Z/43
-2 2
11a_60
2

detected by
the signature
-3+12t-18t^2+19t^3-18t^4+12t^5-3t^6
Seifert matrix of 11a_60
1 0 0 0 0 0
1 -2 -2 -1 -2 -2
1 -1 -2 -1 -1 -2
1 -1 -1 -2 -1 -1
1 -1 -2 -1 -2 -2
1 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-3t^-2+12t^-1-17+12t-3t^2
85
First homology
of the double branched cover of 11a_60
Z/85
-4 4
11a_61
1

detected by
an unknotting move
-6+26t-39t^2+26t^3-6t^4
Seifert matrix of 11a_61
1 0 0 0
1 -2 2 -1
-1 1 -3 1
1 -1 1 -2
1
Generator of the Alexander module
(0,t,1,-t)
the Blanchfield form on it
-3t^-1+8-3t
103
First homology
of the double branched cover of 11a_61
Z/103
-2 2
11a_62
3

detected by
the signature
-1+5t-8t^2+9t^3-9t^4+9t^5-8t^6+5t^7-t^8
Seifert matrix of 11a_62
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 0 0 1 0 0
-1 0 1 1 0 1 1 0
-1 0 1 1 1 1 1 1
0 0 0 0 0 1 0 0
-1 0 1 0 0 1 1 0
-1 0 1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+8t^-1-9+8t-5t^2+t^3
55
First homology
of the double branched cover of 11a_62
Z/55
6 6
11a_63
2

detected by
the signature
-2+11t-21t^2+25t^3-21t^4+11t^5-2t^6
Seifert matrix of 11a_63
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 0 0 1
1 0 -1 2 0 -1
-1 0 1 -1 1 1
0 0 0 0 0 1
1 or 2
93
First homology
of the double branched cover of 11a_63
Z/93
4 4
11a_64
2

detected by
the signature
-2+11t-22t^2+27t^3-22t^4+11t^5-2t^6
Seifert matrix of 11a_64
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 1
0 0 0 1 0 0
1 0 1 -1 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,t,0,1+t,0)
the Blanchfield form on it
2t^-2-10t^-1+15-10t+2t^2
97
First homology
of the double branched cover of 11a_64
Z/97
4 4
11a_65
1

detected by
an unknotting move
-3+15t-23t^2+15t^3-3t^4
Seifert matrix of 11a_65
-1 -1 0 0
0 1 0 0
-1 0 3 1
0 0 0 1
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
t^-1-3+t
59
First homology
of the double branched cover of 11a_65
Z/59
2 2
11a_66
2

detected by
the Lickorish test
-1+6t-15t^2+24t^3-27t^4+24t^5-15t^6+6t^7-t^8
Seifert matrix of 11a_66
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 0
-1 0 -1 1 0 -1 1 0
-1 0 -1 1 1 -1 1 1
-1 -1 -1 0 0 -1 0 0
0 0 -1 0 0 -1 1 0
-1 0 -1 1 0 -1 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-6t^-2+14t^-1-19+14t-6t^2+t^3
119
First homology
of the double branched cover of 11a_66
Z/119
2 2
11a_67
1

detected by
an unknotting move
-2+12t-29t^2+39t^3-29t^4+12t^5-2t^6
Seifert matrix of 11a_67
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 -1 -1 0 0 0
-1 -1 -1 -1 0 0
0 0 -1 -1 1 0
1 0 1 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
125
First homology
of the double branched cover of 11a_67
Z/125
0 0
11a_68
1

detected by
an unknotting move
-1+6t-14t^2+20t^3-21t^4+20t^5-14t^6+6t^7-t^8
Seifert matrix of 11a_68
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 -1 0
-1 -1 0 -1 0 0 0 0
-1 0 -1 -1 1 -1 -1 1
-1 -1 -1 -1 0 -1 -1 0
-1 -1 0 -1 0 0 -1 0
0 0 -1 -1 0 -1 -1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
103
First homology
of the double branched cover of 11a_68
Z/103
-2 2
11a_69
1

detected by
an unknotting move
-2+13t-33t^2+45t^3-33t^4+13t^5-2t^6
Seifert matrix of 11a_69
-1 -1 0 0 0 0
0 1 0 0 0 0
1 1 -2 1 0 0
-1 -1 0 -1 0 0
-1 0 1 -1 1 1
0 0 1 -1 0 1
1
Generator of the Alexander module
(0,t,1+3t^2,-t-t^2,-3t^2-t^3,t-t^2-t^3)
the Blanchfield form on it
-t^-3+8t^-2-24t^-1+34-24t+8t^2-t^3
141
First homology
of the double branched cover of 11a_69
Z/141
0 0
11a_70
1

detected by
an unknotting move
2-14t+36t^2-47t^3+36t^4-14t^5+2t^6
Seifert matrix of 11a_70
1 0 0 0 0 0
-1 -1 0 -1 1 1
0 0 -1 1 -1 -1
0 0 0 1 0 0
1 0 0 1 -2 -2
1 0 0 1 -1 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
1
151
First homology
of the double branched cover of 11a_70
Z/151
-2 2
11a_71
1

detected by
an unknotting move
-1+6t-18t^2+34t^3-41t^4+34t^5-18t^6+6t^7-t^8
Seifert matrix of 11a_71
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 -1 0 -1
-1 0 -1 0 0 0 0 0
-1 0 -1 1 1 0 1 0
0 0 0 0 1 0 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 1 0 1 0
0 0 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,t,-1,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
159
First homology
of the double branched cover of 11a_71
Z/159
-2 2
11a_72
1

detected by
an unknotting move
1-6t+18t^2-32t^3+39t^4-32t^5+18t^6-6t^7+t^8
Seifert matrix of 11a_72
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 1 0 1 1
0 0 0 0 1 1 1 0
0 0 0 0 0 -1 0 0
0 1 0 0 0 1 1 0
0 0 0 0 1 1 1 1
1
Generator of the Alexander module
(0,0,t,1+t,0,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-9+8t-4t^2+t^3
153
First homology
of the double branched cover of 11a_72
Z/153
0 0
11a_73
1

detected by
an unknotting move
1-7t+21t^2-37t^3+45t^4-37t^5+21t^6-7t^7+t^8
Seifert matrix of 11a_73
-1 0 -1 -1 -1 0 -1 0
0 1 0 0 0 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 1 -1 0 -1 1 -1 1
0 0 -1 -1 -1 0 -1 0
0 1 0 0 -1 0 -1 1
1
Generator of the Alexander module
(-1-t-2t^2+4t^4-t^5+2t^7,0,1+3t+t^2+3t^3+t^4-4t^5+t^6-2t^8,2t-4t^3+t^4-2t^6,0,-2t^2-4t^3+4t^4-t^5-2t^6+2t^7,0,-4t^2-2t^3+2t^4-6t^5+3t^6+t^7-2t^8+2t^9)
the Blanchfield form on it
x
177
First homology
of the double branched cover of 11a_73
Z/177
0 2
11a_74
2

detected by
the signature
1-5t+10t^2-13t^3+15t^4-13t^5+10t^6-5t^7+t^8
Seifert matrix of 11a_74
1 0 0 0 0 0 0 0
-1 -1 -1 0 -1 -1 -1 -1
-1 0 -1 0 0 -1 -1 -1
0 0 0 1 0 0 0 0
-1 0 -1 0 -1 -1 -1 -1
-1 0 0 -1 0 -1 -1 -1
-1 0 0 -1 0 0 -1 0
-1 0 0 -1 0 0 -1 -1
1
Generator of the Alexander module
(-1,0,0,0,0,0,1,0)
the Blanchfield form on it
5t^-3-17t^-2+26t^-1-29+26t-17t^2+5t^3
73
First homology
of the double branched cover of 11a_74
Z/73
-4 4
11a_75
1

detected by
an unknotting move
2-10t+19t^2-21t^3+19t^4-10t^5+2t^6
Seifert matrix of 11a_75
1 0 0 0 0 0
-1 -1 -1 0 -1 1
-1 0 -1 0 0 1
0 0 0 1 0 0
-1 0 -1 0 -1 1
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,0,0,1,0,1)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
83
First homology
of the double branched cover of 11a_75
Z/83
-2 2
11a_76
2

detected by
the Lickorish test
1-6t+17t^2-30t^3+37t^4-30t^5+17t^6-6t^7+t^8
Seifert matrix of 11a_76
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 0 -1 -1
0 0 1 0 0 0 0 0
0 0 1 1 0 1 0 0
-1 0 -1 -1 -1 -1 -1 -1
0 0 1 0 0 1 0 0
-1 0 0 -1 0 0 -1 0
-1 0 0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-13+11t-5t^2+t^3
145
First homology
of the double branched cover of 11a_76
Z/145
0 0
11a_77
1

detected by
an unknotting move
2-12t+31t^2-41t^3+31t^4-12t^5+2t^6
Seifert matrix of 11a_77
1 0 0 0 0 0
-1 -1 0 0 -1 0
0 0 1 0 0 0
0 0 0 1 0 0
-1 0 -1 0 -1 1
0 0 -1 1 0 2
1
Generator of the Alexander module
(-10+28t+10t^2-6t^3,-4t+26t^2+10t^3-6t^4,6+10t-4t^2,-3-5t+2t^2,-5+14t+5t^2-3t^3,12t^2-4t^3)
the Blanchfield form on it
4454t^-2-9088t^-1+11025-9088t+4454t^2
131
First homology
of the double branched cover of 11a_77
Z/131
2 2
11a_78
1

detected by
an unknotting move
2-12t+29t^2-37t^3+29t^4-12t^5+2t^6
Seifert matrix of 11a_78
1 0 0 0 0 0
-1 -1 0 0 -1 1
0 0 1 0 0 0
0 0 0 -1 0 -1
-1 0 -1 0 -1 1
1 0 0 0 0 -2
1
Generator of the Alexander module
(1+5t-4t^3,1+t-2t^2-3t^3,0,1+3t-2t^3,2+t+6t^2-8t^4,-1-t)
the Blanchfield form on it
-169t^-2+396t^-1-561+396t-169t^2
123
First homology
of the double branched cover of 11a_78
Z/123
-2 2
11a_79
1

detected by
an unknotting move
-1+6t-17t^2+30t^3-35t^4+30t^5-17t^6+6t^7-t^8
Seifert matrix of 11a_79
-1 0 -1 -1 0 0 -1 0
0 1 0 0 0 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 1 0 0 1 0 -1 0
0 1 -1 0 1 1 -1 1
0 0 -1 -1 0 0 -1 0
0 1 -1 0 1 0 -1 1
1
Generator of the Alexander module
(0,t,1,0,-t,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-7+4t-3t^2+t^3
143
First homology
of the double branched cover of 11a_79
Z/143
2 2
11a_80
1

detected by
an unknotting move
1-6t+16t^2-28t^3+35t^4-28t^5+16t^6-6t^7+t^8
Seifert matrix of 11a_80
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 0 -1 0
0 0 1 0 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1
0 0 1 0 0 1 0 0
-1 0 0 -1 0 -1 -1 -1
0 0 1 0 0 1 0 1
1
Generator of the Alexander module
(0,2t-14t^2-8t^3-8t^4-6t^5,-1+11t-16t^2-64t^3-73t^4-60t^5-40t^6-12t^7,1-7t-8t^2+24t^3+13t^4+16t^5+12t^6,-1+13t-16t^2-37t^3-111t^4-91t^5-70t^6-41t^7-6t^8,0,-12t+17t^2-6t^3-93t^4-72t^5-69t^6-47t^7-6t^8,4-15t+14t^2+38t^3+39t^4+65t^5+39t^6+22t^7+12t^8)
the Blanchfield form on it
x
137
First homology
of the double branched cover of 11a_80
Z/137
0 0
11a_81
1

detected by
an unknotting move
-1+6t-16t^2+26t^3-29t^4+26t^5-16t^6+6t^7-t^8
Seifert matrix of 11a_81
-1 0 -1 -1 -1 0 -1 -1
0 1 0 0 0 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 -1 -1 0 0 -1
0 1 0 0 -1 1 -1 -1
0 0 -1 -1 -1 0 -1 -1
0 0 -1 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,1-t^2+t^3,0,-1,-t+2t^2-t^3,t,-1)
the Blanchfield form on it
-t^-3+5t^-2-11t^-1+15-11t+5t^2-t^3
127
First homology
of the double branched cover of 11a_81
Z/127
-2 2
11a_82
1

detected by
an unknotting move
-1+5t-12t^2+19t^3-21t^4+19t^5-12t^6+5t^7-t^8
Seifert matrix of 11a_82
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 -1 -1 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 1 1 1 1
0 0 0 0 1 0 0 0
0 0 0 0 1 1 1 0
0 0 0 0 1 0 1 0
0 0 0 0 1 1 1 1
1
Generator of the Alexander module
(0,-t,1,2,1,1,1,0)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-6+5t-3t^2+t^3
95
First homology
of the double branched cover of 11a_82
Z/95
2 2
11a_83
2

detected by
the signature
1-5t+14t^2-23t^3+27t^4-23t^5+14t^6-5t^7+t^8
Seifert matrix of 11a_83
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 0 0 1
0 -1 0 0 -1 -1 0 0
0 0 0 0 0 -1 0 0
0 -1 0 0 -1 -1 -1 0
0 1 0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,1,2,1,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-4+3t-t^2
113
First homology
of the double branched cover of 11a_83
Z/113
-4 4
11a_84
1

detected by
an unknotting move
-2+10t-23t^2+31t^3-23t^4+10t^5-2t^6
Seifert matrix of 11a_84
-1 0 0 0 0 0
0 -1 0 0 1 0
-1 0 -1 0 0 0
-1 0 -1 1 -1 1
0 0 0 0 2 0
0 0 0 0 -1 1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
101
First homology
of the double branched cover of 11a_84
Z/101
0 0
11a_85
1

detected by
an unknotting move
2-10t+25t^2-33t^3+25t^4-10t^5+2t^6
Seifert matrix of 11a_85
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 0 1
0 0 0 -2 0 0
0 0 0 -1 -1 0
0 0 0 -1 0 1
1
Generator of the Alexander module
(0,t,1+t,0,0,0)
the Blanchfield form on it
2t^-2-6t^-1+9-6t+2t^2
107
First homology
of the double branched cover of 11a_85
Z/107
-2 2
11a_86
1

detected by
an unknotting move
-1+5t-12t^2+18t^3-19t^4+18t^5-12t^6+5t^7-t^8
Seifert matrix of 11a_86
-1 -1 -1 -1 -1 -1 0 0
0 -1 -1 -1 0 -1 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 -1 -1 -1 -1 0 0
0 0 -1 -1 0 -1 0 0
0 -1 -1 0 -1 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1+t,0,1+2t,0)
the Blanchfield form on it
-t^-3+3t^-2-5t^-1+5-5t+3t^2-t^3
91
First homology
of the double branched cover of 11a_86
Z/91
-2 2
11a_87
2

detected by
-2+11t-28t^2+39t^3-28t^4+11t^5-2t^6
Seifert matrix of 11a_87
-1 1 -1 -1 0 0
0 -2 1 1 0 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 1 -1 0 1 1
0 0 0 0 0 1
2
121
First homology
of the double branched cover of 11a_87
Z/121
0 0
11a_88
1

detected by
an unknotting move
1-5t+12t^2-20t^3+25t^4-20t^5+12t^6-5t^7+t^8
Seifert matrix of 11a_88
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 -1 0 -1
0 0 1 0 0 0 0 0
0 0 1 1 0 0 1 0
-1 0 -1 -1 -1 -1 -1 -1
-1 0 -1 -1 0 -1 -1 0
0 0 1 0 0 0 1 0
-1 0 -1 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,t^2,0,-1-t-t^4,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
101
First homology
of the double branched cover of 11a_88
Z/101
0 0
11a_89
2

detected by
the Lickorish test
2-12t+28t^2-35t^3+28t^4-12t^5+2t^6
Seifert matrix of 11a_89
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 -1 0 -1 -1
0 0 0 1 0 0
0 0 0 -1 -1 -1
1 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,-1,1,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
119
First homology
of the double branched cover of 11a_89
Z/119
-2 2
11a_90
2

detected by
the Lickorish test
2-10t+20t^2-23t^3+20t^4-10t^5+2t^6
Seifert matrix of 11a_90
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 1 0 0 0
0 0 1 1 1 0
0 0 1 0 1 0
1 0 1 1 1 -2
1
Generator of the Alexander module
(0,0,0,t,0,1+t)
the Blanchfield form on it
-2t^-2+10t^-1-17+10t-2t^2
87
First homology
of the double branched cover of 11a_90
Z/87
2 2
11a_91
1

detected by
an unknotting move
-2+12t-30t^2+41t^3-30t^4+12t^5-2t^6
Seifert matrix of 11a_91
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 -1 0 0 -1
0 0 -1 1 1 -1
0 0 0 0 1 0
1 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,1,2,0,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
129
First homology
of the double branched cover of 11a_91
Z/129
0 0
11a_92
1

detected by
an unknotting move
-1+5t-12t^2+21t^3-25t^4+21t^5-12t^6+5t^7-t^8
Seifert matrix of 11a_92
-1 0 -1 -1 0 0 0 -1
0 1 0 0 1 0 1 -1
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 1 0
0 1 0 0 1 1 1 -1
0 0 0 0 0 0 1 0
0 0 -1 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1-t-t^3,0,-1-t^2)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-12+8t-4t^2+t^3
103
First homology
of the double branched cover of 11a_92
Z/103
2 2
11a_93
1

detected by
an unknotting move
-2+10t-21t^2+27t^3-21t^4+10t^5-2t^6
Seifert matrix of 11a_93
-1 -1 -1 0 0 -1
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 2 1 1
0 0 0 0 1 0
0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,1,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
93
First homology
of the double branched cover of 11a_93
Z/93
0 2
11a_94
3

detected by
the signature
4-13t+23t^2-27t^3+23t^4-13t^5+4t^6
Seifert matrix of 11a_94
-1 0 -1 0 0 0
0 -1 0 0 -1 0
0 0 -2 0 0 0
0 0 0 -1 -1 0
0 0 1 0 -2 0
0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
4t^-2-11t^-1+15-11t+4t^2
107
First homology
of the double branched cover of 11a_94
Z/107
-6 6
11a_95
2

detected by
the signature
6-18t+25t^2-18t^3+6t^4
Seifert matrix of 11a_95
-1 0 -1 0
0 -1 0 1
0 0 -2 0
0 0 -1 -3
1
Generator of the Alexander module
(0,t,0,1)
the Blanchfield form on it
2t^-1-3+2t
73
First homology
of the double branched cover of 11a_95
Z/73
-4 4
11a_96
1

detected by
an unknotting move
-1+9t-29t^2+43t^3-29t^4+9t^5-t^6
Seifert matrix of 11a_96
1 0 0 0 0 0
-1 -1 0 0 -1 0
0 0 1 0 0 0
0 0 0 1 0 0
-1 0 0 -1 -1 0
0 0 1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-2-9t^-1+15-9t+2t^2
121
First homology
of the double branched cover of 11a_96
Z/121
0 0
11a_97
2

detected by
2-9t+16t^2-17t^3+16t^4-9t^5+2t^6
Seifert matrix of 11a_97
1 0 0 0 0 0
-1 -1 -1 -1 0 -1
-1 0 -1 -1 1 -1
-1 0 0 -1 1 0
0 0 0 0 2 0
-1 0 0 -1 1 -1
2
71
First homology
of the double branched cover of 11a_97
Z/71
-2 2
11a_98
1

detected by
an unknotting move
4-19t+31t^2-19t^3+4t^4
Seifert matrix of 11a_98
1 0 0 0
-1 -1 0 1
0 0 2 0
1 0 -1 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
1
77
First homology
of the double branched cover of 11a_98
Z/77
0 0
11a_99
2

detected by
the Lickorish test
-1+6t-17t^2+28t^3-31t^4+28t^5-17t^6+6t^7-t^8
Seifert matrix of 11a_99
-1 -1 -1 -1 -1 0 -1 0
0 -1 -1 -1 -1 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 -1 -1 0 -1 1 -1 1
0 -1 -1 -1 -1 0 -1 0
0 -1 0 0 0 0 -1 1
1
Generator of the Alexander module
(1,0,-1-t,0,0,t-t^2,0,0)
the Blanchfield form on it
t^-3-4t^-2+6t^-1-6+6t-4t^2+t^3
135
First homology
of the double branched cover of 11a_99
Z/135
-2 2
11a_100
2

detected by
the signature
-3+15t-32t^2+41t^3-32t^4+15t^5-3t^6
Seifert matrix of 11a_100
1 0 0 0 0 0
-1 -1 0 0 1 1
0 0 -1 0 0 -1
0 0 0 -1 -1 0
1 0 0 0 -2 -1
1 0 0 0 -1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
141
First homology
of the double branched cover of 11a_100
Z/141
-4 4
11a_101
1

detected by
an unknotting move
3-16t+39t^2-51t^3+39t^4-16t^5+3t^6
Seifert matrix of 11a_101
-1 0 -1 -1 0 -1
0 1 0 -1 0 -1
0 0 -2 -1 0 -1
0 0 -2 -2 0 -1
0 1 -1 -1 1 -1
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,1,0)
the Blanchfield form on it
-3t^-2+10t^-1-14+10t-3t^2
167
First homology
of the double branched cover of 11a_101
Z/167
-2 2
11a_102
2

detected by
the Lickorish test
2-11t+23t^2-27t^3+23t^4-11t^5+2t^6
Seifert matrix of 11a_102
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 1 1 1
-1 -1 0 -1 -1 -1
-1 -1 0 0 -1 0
-1 -1 0 0 -1 -1
1 or 2
99
First homology
of the double branched cover of 11a_102
Z/99
-2 2
11a_103
1

detected by
an unknotting move
4-20t+33t^2-20t^3+4t^4
Seifert matrix of 11a_103
1 0 0 0
0 1 0 0
1 0 -2 -1
1 1 0 -2
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-2t^-2+10t^-1-16+10t-2t^2
81
First homology
of the double branched cover of 11a_103
Z/81
0 0
11a_104
1

detected by
an unknotting move
-2+12t-29t^2+39t^3-29t^4+12t^5-2t^6
Seifert matrix of 11a_104
-1 0 -1 0 0 1
0 -1 0 0 0 -1
0 0 1 0 0 0
-1 0 0 1 1 0
0 0 0 0 1 0
0 0 1 0 0 -2
1
Generator of the Alexander module
(0,0,0,1,1,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
125
First homology
of the double branched cover of 11a_104
Z/125
0 0
11a_105
2

detected by
the signature
-3+13t-24t^2+29t^3-24t^4+13t^5-3t^6
Seifert matrix of 11a_105
-1 0 -1 0 0 -1
0 -1 -1 0 0 0
0 0 -2 0 0 -1
0 -1 -1 -1 0 0
0 0 0 0 1 -1
0 0 -1 0 0 -2
1
Generator of the Alexander module
(1,0,0,1,0,0)
the Blanchfield form on it
-6t^-2+23t^-1-32+23t-6t^2
109
First homology
of the double branched cover of 11a_105
Z/109
-4 4
11a_106
1

detected by
an unknotting move
1-5t+12t^2-18t^3+21t^4-18t^5+12t^6-5t^7+t^8
Seifert matrix of 11a_106
-1 0 0 0 0 0 0 0
0 1 0 0 1 0 0 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 1 1 1 0
0 0 0 0 1 0 0 0
0 1 0 0 1 1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,-1,0,0,0,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
93
First homology
of the double branched cover of 11a_106
Z/93
0 2
11a_107
2

detected by
the Lickorish test
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 11a_107
-1 0 0 0 0 0
0 2 0 0 0 0
-1 0 -1 0 0 0
-1 -1 -1 1 1 0
0 0 0 0 -1 0
0 0 0 0 -1 -1
2
111
First homology
of the double branched cover of 11a_107
Z/111
-2 2
11a_108
1

detected by
an unknotting move
-1+5t-12t^2+20t^3-23t^4+20t^5-12t^6+5t^7-t^8
Seifert matrix of 11a_108
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 1 1 0
-1 0 -1 1 1 1 1 1
0 0 0 0 0 1 0 0
0 0 0 0 0 1 1 0
-1 0 -1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-15+11t-5t^2+t^3
99
First homology
of the double branched cover of 11a_108
Z/99
2 2
11a_109
1

detected by
an unknotting move
1-5t+14t^2-24t^3+29t^4-24t^5+14t^6-5t^7+t^8
Seifert matrix of 11a_109
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 0 1 0
-1 0 -1 1 1 0 1 1
0 0 0 0 0 -1 0 0
0 1 0 0 0 1 1 0
-1 0 -1 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-13t^-1+17-13t+5t^2-t^3
117
First homology
of the double branched cover of 11a_109
Z/117
0 0
11a_110
1

detected by
an unknotting move
-2+10t-22t^2+29t^3-22t^4+10t^5-2t^6
Seifert matrix of 11a_110
-1 0 0 0 0 0
0 -1 0 -1 0 0
-1 0 -1 0 0 0
0 0 0 1 0 0
0 0 0 1 1 0
1 0 1 -1 -1 2
1
Generator of the Alexander module
(0,0,-t,0,0,1+t)
the Blanchfield form on it
-2t^-2+7t^-1-9+7t-2t^2
97
First homology
of the double branched cover of 11a_110
Z/97
0 0
11a_111
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 11a_111
-1 0 0 0 0 0
0 -1 0 -1 0 0
-1 0 -1 0 0 0
0 0 0 -1 0 0
0 1 0 1 1 0
1 0 1 0 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-14+11t-5t^2+t^3
103
First homology
of the double branched cover of 11a_111
Z/103
-2 2
11a_112
1

detected by
an unknotting move
-1+6t-15t^2+25t^3-31t^4+25t^5-15t^6+6t^7-t^8
Seifert matrix of 11a_112
1 0 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 -1 -1
-1 0 -1 -1 0 0 -1 -1
0 0 0 1 1 0 0 1
0 0 0 0 1 0 0 0
-1 0 -1 -1 0 -1 -1 -1
-1 0 0 -1 0 0 -1 0
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
125
First homology
of the double branched cover of 11a_112
Z/125
0 0
11a_113
2

detected by
the signature
-1+6t-15t^2+21t^3-23t^4+21t^5-15t^6+6t^7-t^8
Seifert matrix of 11a_113
1 0 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 -1 -1
0 0 1 0 1 0 0 1
0 0 1 1 1 0 1 1
0 0 0 0 1 0 0 0
-1 0 -1 -1 0 -1 -1 0
0 0 1 0 1 0 1 1
0 0 0 0 1 0 0 1
1 or 2
109
First homology
of the double branched cover of 11a_113
Z/109
4 4
11a_114
1

detected by
an unknotting move
3-15t+35t^2-45t^3+35t^4-15t^5+3t^6
Seifert matrix of 11a_114
-1 0 -1 -1 0 -1
0 1 0 -1 0 -1
0 0 -2 -1 0 -2
0 0 -1 -2 0 -1
0 1 0 -1 1 -1
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(2t,0,0,-1,2,0)
the Blanchfield form on it
-t^-1+2-t
151
First homology
of the double branched cover of 11a_114
Z/151
-2 2
11a_115
1

detected by
an unknotting move
-3+13t-27t^2+35t^3-27t^4+13t^5-3t^6
Seifert matrix of 11a_115
-1 0 -1 0 0 -1
0 1 -1 1 0 -1
0 0 -2 0 0 -1
0 0 0 1 0 -1
0 1 -1 1 1 -1
0 0 -1 0 0 -2
1 or 2
121
First homology
of the double branched cover of 11a_115
Z/121
0 0
11a_116
2

detected by
the signature
-3+15t-31t^2+39t^3-31t^4+15t^5-3t^6
Seifert matrix of 11a_116
-1 -1 -1 -1 0 -1
0 -2 -2 -1 0 -1
0 -1 -2 -1 0 -1
0 -2 -2 -2 0 -1
0 -1 0 -1 1 -1
0 -1 -1 -1 0 -2
1
Generator of the Alexander module
(-t^2-4t^3+6t^4-t^5-4t^6+2t^7,-t^2-2t^3+4t^4-t^5-2t^6+t^7,-3-7t+12t^2-t^3-7t^4+3t^5,-3-8t+12t^2+t^3-8t^4+3t^5,-1-2t+4t^2-t^3-2t^4+t^5,-2t^2-4t^3+8t^4-2t^5-4t^6+2t^7)
the Blanchfield form on it
x
137
First homology
of the double branched cover of 11a_116
Z/137
-4 4
11a_117
2

detected by
the signature
-2+12t-27t^2+35t^3-27t^4+12t^5-2t^6
Seifert matrix of 11a_117
-1 0 0 0 0 0
0 -1 0 0 0 -1
-1 0 -1 0 0 0
-1 0 -1 1 -1 0
0 0 0 0 -1 0
0 0 0 0 1 -2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
117
First homology
of the double branched cover of 11a_117
Z/117
-4 4
11a_118
2

detected by
the Lickorish test
2-10t+20t^2-23t^3+20t^4-10t^5+2t^6
Seifert matrix of 11a_118
1 0 0 0 0 0
0 -1 0 -1 -1 -1
1 -1 -2 -1 -1 -1
0 0 0 -1 0 -1
0 0 0 0 1 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
87
First homology
of the double branched cover of 11a_118
Z/87
-2 2
11a_119
1

detected by
an unknotting move
4-19t+31t^2-19t^3+4t^4
Seifert matrix of 11a_119
1 0 0 0
0 1 0 0
1 0 -2 0
0 -1 -1 -2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-2t^-2+9t^-1-14+9t-2t^2
77
First homology
of the double branched cover of 11a_119
Z/77
0 0
11a_120
2

detected by
the signature
-2+12t-25t^2+31t^3-25t^4+12t^5-2t^6
Seifert matrix of 11a_120
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 1 -1 0
0 0 0 1 0 0
0 0 0 -1 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,-7+8t-8t^2+2t^3,24t-32t^2+32t^3-14t^4+2t^5,-10+16t-16t^2+10t^3-2t^4,7-18t+11t^2-8t^3+2t^4,3+2t-t^2)
the Blanchfield form on it
-2t^-2+4t^-1-5+4t-2t^2
109
First homology
of the double branched cover of 11a_120
Z/109
4 4
11a_121
1

detected by
an unknotting move
1-9t+29t^2-41t^3+29t^4-9t^5+t^6
Seifert matrix of 11a_121
1 0 0 0 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 0 1 1 0
0 0 0 0 1 0
-1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-2t^-2+11t^-1-17+11t-2t^2
119
First homology
of the double branched cover of 11a_121
Z/119
2 2
11a_122
1

detected by
an unknotting move
2-12t+30t^2-39t^3+30t^4-12t^5+2t^6
Seifert matrix of 11a_122
1 0 0 0 0 0
-1 -1 0 -1 1 -1
0 0 1 0 0 0
-1 0 0 -1 1 0
0 0 -1 0 2 -1
0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,2t-t^2,-1+t,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
127
First homology
of the double branched cover of 11a_122
Z/127
2 2
11a_123
3

detected by
the new u==2 criterion
9-29t+41t^2-29t^3+9t^4
Seifert matrix of 11a_123
-1 1 1 0
0 -3 -2 -1
0 -2 -3 0
0 -1 -1 -2
2
117
First homology
of the double branched cover of 11a_123
Z/39+Z/3
-4 4
11a_124
3

detected by
the signature
5-18t+34t^2-41t^3+34t^4-18t^5+5t^6
Seifert matrix of 11a_124
-1 0 -1 -1 -1 0
0 -1 0 0 0 -1
0 0 -2 -1 -2 -1
0 0 -1 -2 -1 0
0 0 -1 -1 -2 -1
0 0 0 1 0 -2
1 or 2
155
First homology
of the double branched cover of 11a_124
Z/155
-6 6
11a_125
2

detected by
the Lickorish test
-1+6t-19t^2+38t^3-47t^4+38t^5-19t^6+6t^7-t^8
Seifert matrix of 11a_125
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 -1
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 1 0 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 0 1 0 0
-1 0 -1 1 0 1 1 0
0 0 0 -1 -1 -1 0 -1
1
Generator of the Alexander module
(0,-2t^2+2t^3-t^4,0,-1,2t-2t^2+t^3,0,0,2t-2t^2+t^3)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+17-12t+5t^2-t^3
175
First homology
of the double branched cover of 11a_125
Z/175
-2 2
11a_126
2

detected by
the Lickorish test
1-5t+16t^2-31t^3+39t^4-31t^5+16t^6-5t^7+t^8
Seifert matrix of 11a_126
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 -1
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 1 0 0
-1 0 -1 1 1 1 1 0
0 0 0 0 0 1 0 0
-1 0 -1 1 0 1 1 0
0 0 0 -1 0 -1 -1 -1
1
Generator of the Alexander module
(4+1008t+8229t^2-10426t^3+25894t^4-58677t^5+95235t^6-99024t^7+59742t^8-20583t^9+1350t^10,-3683-29891t+13190t^2-100609t^3+190095t^4-314028t^5+397118t^6-419952t^7+379077t^8-214416t^9+78426t^10-2700t^11,-1939-15386t+12890t^2-42939t^3+94043t^4-146510t^5+146888t^6-92947t^7+47490t^8-16341t^9+6894t^10,2794
the Blanchfield form on it
x
145
First homology
of the double branched cover of 11a_126
Z/145
0 0
11a_127
2

detected by
the signature
1-6t+17t^2-28t^3+33t^4-28t^5+17t^6-6t^7+t^8
Seifert matrix of 11a_127
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 -1 -1
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 1 0 0
0 0 0 -1 -1 -1 0 0
0 0 0 0 0 1 0 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 -1 -1 -1 -1
1
Generator of the Alexander module
(0,1-t,0,1,-t+t^2,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+13t^-1-17+13t-5t^2+t^3
137
First homology
of the double branched cover of 11a_127
Z/137
-4 4
11a_128
1

detected by
an unknotting move
-1+9t-31t^2+47t^3-31t^4+9t^5-t^6
Seifert matrix of 11a_128
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 1 -1 0 0
-1 -1 0 -1 0 0
-1 0 0 0 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,3-t,0,1,0)
the Blanchfield form on it
-t^-2+6t^-1-12+6t-t^2
129
First homology
of the double branched cover of 11a_128
Z/129
0 0
11a_129
2

detected by
the signature
-1+6t-15t^2+22t^3-25t^4+22t^5-15t^6+6t^7-t^8
Seifert matrix of 11a_129
1 0 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 -1 -1
0 0 1 0 1 0 1 0
0 0 1 1 1 0 1 1
0 0 0 0 1 0 0 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 1 0 1 0
0 0 1 0 1 0 1 1
1
Generator of the Alexander module
(0,1-t^2,0,t^2,0,-t^2,0,0)
the Blanchfield form on it
t^-3-6t^-2+14t^-1-17+14t-6t^2+t^3
113
First homology
of the double branched cover of 11a_129
Z/113
4 4
11a_130
1

detected by
an unknotting move
2-12t+29t^2-37t^3+29t^4-12t^5+2t^6
Seifert matrix of 11a_130
1 0 0 0 0 0
-1 -1 1 -1 0 -1
0 0 2 0 -1 0
0 0 -1 1 1 0
0 0 0 0 1 0
-1 0 0 -1 0 -1
1 or 2
123
First homology
of the double branched cover of 11a_130
Z/123
2 2
11a_131
1

detected by
an unknotting move
1-6t+16t^2-27t^3+31t^4-27t^5+16t^6-6t^7+t^8
Seifert matrix of 11a_131
1 0 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 -1 -1
-1 0 -1 -1 0 0 -1 0
0 0 0 1 1 0 1 1
0 0 0 0 1 0 0 0
-1 0 -1 -1 0 -1 -1 -1
0 0 0 0 1 0 1 1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-1+1-t
131
First homology
of the double branched cover of 11a_131
Z/131
2 2
11a_132
2

detected by
the Lickorish test
2-13t+32t^2-41t^3+32t^4-13t^5+2t^6
Seifert matrix of 11a_132
1 0 0 0 0 0
0 1 0 0 0 0
0 -1 -1 -1 0 -1
1 0 0 -2 1 0
-1 -1 0 0 -1 0
0 -1 0 -1 0 -1
2
135
First homology
of the double branched cover of 11a_132
Z/135
-2 2
11a_133
2

detected by
A(F_2)
-5+20t-29t^2+20t^3-5t^4
Seifert matrix of 11a_133
-1 1 0 -1
0 -3 0 1
0 0 1 -1
0 1 0 -2
2
79
First homology
of the double branched cover of 11a_133
Z/79
-2 2
11a_134
1

detected by
an unknotting move
3-13t+28t^2-35t^3+28t^4-13t^5+3t^6
Seifert matrix of 11a_134
-1 -1 -1 0 0 -1
0 -2 -1 0 0 -2
0 -1 -2 0 0 -1
0 0 1 1 1 0
0 0 0 0 1 0
0 -1 -1 0 0 -2
1
Generator of the Alexander module
(1-t,0,0,2-t,0,0)
the Blanchfield form on it
3t^-2-10t^-1+14-10t+3t^2
123
First homology
of the double branched cover of 11a_134
Z/123
-2 2
11a_135
2

detected by
the Nakanishi index
-2+13t-36t^2+51t^3-36t^4+13t^5-2t^6
Seifert matrix of 11a_135
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 -2 0 -2 0
0 0 0 1 0 0
1 -1 -1 -1 -2 -1
0 0 0 1 0 1
2
153
First homology
of the double branched cover of 11a_135
Z/51+Z/3
0 0
11a_136
1

detected by
an unknotting move
2-14t+39t^2-53t^3+39t^4-14t^5+2t^6
Seifert matrix of 11a_136
1 0 0 0 0 0
-1 -1 0 -1 -1 -1
0 0 2 0 0 1
0 0 -1 1 0 0
-1 0 0 -1 -1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,1-2t,1,t,2-2t,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
163
First homology
of the double branched cover of 11a_136
Z/163
2 2
11a_137
2

detected by
the Lickorish test
2-12t+26t^2-31t^3+26t^4-12t^5+2t^6
Seifert matrix of 11a_137
1 0 0 0 0 0
0 1 1 0 0 1
0 0 1 0 0 0
1 1 0 -2 1 1
-1 -1 0 0 -1 0
0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,3-2t,-1+5t-2t^2,0)
the Blanchfield form on it
19t^-4-159t^-3+535t^-2-990t^-1+1188-990t+535t^2-159t^3+19t^4
111
First homology
of the double branched cover of 11a_137
Z/111
2 2
11a_138
1

detected by
an unknotting move
-2+14t-38t^2+53t^3-38t^4+14t^5-2t^6
Seifert matrix of 11a_138
-1 0 0 0 -1 0
0 1 0 0 0 0
0 0 1 -1 1 1
0 -1 0 -1 1 0
0 1 0 0 -2 0
1 0 0 -1 1 1
1
Generator of the Alexander module
(0,0,1-2t,-2,0,0)
the Blanchfield form on it
t^-2-5t^-1+8-5t+t^2
161
First homology
of the double branched cover of 11a_138
Z/161
0 0
11a_139
1

detected by
an unknotting move
-1+5t-12t^2+20t^3-23t^4+20t^5-12t^6+5t^7-t^8
Seifert matrix of 11a_139
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 -1 0 0
-1 0 -1 1 1 -1 0 1
0 0 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 0
-1 0 -1 1 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-11+9t-5t^2+t^3
99
First homology
of the double branched cover of 11a_139
Z/99
-2 2
11a_140
2

detected by
the signature
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 11a_140
-1 0 0 0 0 0
0 -1 0 -1 0 0
-1 0 -1 0 0 0
0 0 0 -1 0 0
0 -1 0 -1 -1 0
1 0 1 1 0 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+3t^-2-5t^-1+6-5t+3t^2-t^3
65
First homology
of the double branched cover of 11a_140
Z/65
-4 4
11a_141
1

detected by
an unknotting move
2-11t+24t^2-29t^3+24t^4-11t^5+2t^6
Seifert matrix of 11a_141
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 -2 -1 -1 -1
0 0 0 1 1 0
0 0 0 0 1 0
0 0 0 1 1 1
1
Generator of the Alexander module
(0,2,3-t,1,0,0)
the Blanchfield form on it
3t^-4-22t^-3+70t^-2-128t^-1+154-128t+70t^2-22t^3+3t^4
103
First homology
of the double branched cover of 11a_141
Z/103
2 2
11a_142
3

detected by
the signature
-1+5t-8t^2+10t^3-11t^4+10t^5-8t^6+5t^7-t^8
Seifert matrix of 11a_142
1 0 0 0 0 1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
1 -1 0 1 0 1 1 0
1 -1 0 1 1 1 1 1
0 0 0 0 0 1 0 0
1 0 0 0 0 1 1 0
1 -1 0 1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,1+t+t^4,0,0,t^2,0)
the Blanchfield form on it
2t^-3-9t^-2+10t^-1-8+10t-9t^2+2t^3
59
First homology
of the double branched cover of 11a_142
Z/59
6 6
11a_143
2

detected by
the signature
-2+11t-20t^2+23t^3-20t^4+11t^5-2t^6
Seifert matrix of 11a_143
2 0 0 0 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
-1 -1 0 1 0 0
-1 -1 0 1 1 1
-1 -1 0 1 0 1
2
89
First homology
of the double branched cover of 11a_143
Z/89
4 4
11a_144
2

detected by
the signature
-2+10t-16t^2+17t^3-16t^4+10t^5-2t^6
Seifert matrix of 11a_144
1 0 0 1 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
1 0 0 1 1 0
-1 1 0 -1 -1 2
1
Generator of the Alexander module
(0,0,0,0,-t,1+t)
the Blanchfield form on it
2t^-2-10t^-1+15-10t+2t^2
73
First homology
of the double branched cover of 11a_144
Z/73
4 4
11a_145
1

detected by
an unknotting move
-4+21t-33t^2+21t^3-4t^4
Seifert matrix of 11a_145
2 0 0 0
0 -1 -1 0
0 0 1 0
1 1 0 2
1 or 2
83
First homology
of the double branched cover of 11a_145
Z/83
2 2
11a_146
1

detected by
an unknotting move
-1+6t-15t^2+25t^3-29t^4+25t^5-15t^6+6t^7-t^8
Seifert matrix of 11a_146
1 0 0 0 0 1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
1 -1 0 -1 1 1 -1 1
0 0 0 0 0 1 0 0
0 -1 -1 -1 0 0 -1 0
1 0 0 -1 0 1 -1 1
1
Generator of the Alexander module
(0,1,0,1,t,0,1,0)
the Blanchfield form on it
t^-3-6t^-2+14t^-1-19+14t-6t^2+t^3
123
First homology
of the double branched cover of 11a_146
Z/123
2 2
11a_147
1

detected by
an unknotting move
-1+6t-17t^2+32t^3-39t^4+32t^5-17t^6+6t^7-t^8
Seifert matrix of 11a_147
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 -1 -1 1 1 -1 -1 1
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 0
0 -1 0 0 1 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,1,0,0,1)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-11+9t-5t^2+t^3
151
First homology
of the double branched cover of 11a_147
Z/151
-2 2
11a_148
2

detected by
the Lickorish test
-7+29t-43t^2+29t^3-7t^4
Seifert matrix of 11a_148
1 0 0 0
-1 -3 1 -1
1 2 -2 1
0 -1 0 -2
1 or 2
115
First homology
of the double branched cover of 11a_148
Z/115
-2 2
11a_149
1

detected by
an unknotting move
2-12t+30t^2-39t^3+30t^4-12t^5+2t^6
Seifert matrix of 11a_149
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 -2 -2 -2 0
1 -1 -1 -2 -1 -1
1 -1 -1 -2 -2 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,0,1-t,0,0)
the Blanchfield form on it
2t^-2-8t^-1+12-8t+2t^2
127
First homology
of the double branched cover of 11a_149
Z/127
-2 2
11a_150
2

detected by
the signature
-2+13t-29t^2+37t^3-29t^4+13t^5-2t^6
Seifert matrix of 11a_150
2 0 0 1 0 1
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 0 1 0 0
-1 -1 0 0 1 0
0 -1 0 1 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-1+3-2t
125
First homology
of the double branched cover of 11a_150
Z/125
4 4
11a_151
1

detected by
an unknotting move
-1+6t-15t^2+26t^3-31t^4+26t^5-15t^6+6t^7-t^8
Seifert matrix of 11a_151
1 0 0 -1 0 -1 1 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
1 -1 0 -1 1 -1 1 1
0 -1 -1 -1 0 -1 0 0
0 0 0 -1 0 -1 1 0
1 0 0 -1 0 -1 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,-1+t)
the Blanchfield form on it
t^-1-2+t
127
First homology
of the double branched cover of 11a_151
Z/127
2 2
11a_152
1

detected by
an unknotting move
-2+12t-27t^2+35t^3-27t^4+12t^5-2t^6
Seifert matrix of 11a_152
2 0 0 1 0 1
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 -1 -1 0 0
-1 -1 0 -1 1 -1
0 -1 -1 -1 0 -1
1
Generator of the Alexander module
(0,-2t-3t^2+4t^3,2+3t-4t^2,-2t-4t^2+3t^3+2t^4,1-2t-6t^2+4t^3+2t^4,-1-5t-4t^2+8t^3)
the Blanchfield form on it
2t^-2-8t^-1+9-8t+2t^2
117
First homology
of the double branched cover of 11a_152
Z/117
0 2
11a_153
1

detected by
an unknotting move
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 11a_153
-1 -1 0 0 0 0
0 -2 0 0 0 0
0 1 1 0 -1 0
0 1 1 1 -1 1
0 0 0 0 -1 0
0 1 1 0 -1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-10t^-1+15-10t+2t^2
89
First homology
of the double branched cover of 11a_153
Z/89
0 2
11a_154
1

detected by
an unknotting move
-4+17t-25t^2+17t^3-4t^4
Seifert matrix of 11a_154
-1 -1 0 0
0 -2 0 0
0 0 -1 0
0 -1 1 2
1
Generator of the Alexander module
(2t-t^2,0,-2+t,1+4t-2t^2)
the Blanchfield form on it
-4t^-1+7-4t
67
First homology
of the double branched cover of 11a_154
Z/67
-2 2
11a_155
2

detected by
the Nakanishi index
3-16t+40t^2-53t^3+40t^4-16t^5+3t^6
Seifert matrix of 11a_155
-1 0 0 0 0 0
0 2 0 1 1 0
-1 0 -1 0 0 0
-1 0 -1 1 0 0
0 1 0 0 2 0
-1 -1 -1 0 -1 1
2
171
First homology
of the double branched cover of 11a_155
Z/57+Z/3
2 2
11a_156
2

detected by
the Lickorish test
-1+5t-11t^2+18t^3-21t^4+18t^5-11t^6+5t^7-t^8
Seifert matrix of 11a_156
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
-1 -1 0 -1 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+10t^-1-13+10t-5t^2+t^3
91
First homology
of the double branched cover of 11a_156
Z/91
2 2
11a_157
2

detected by
the Lickorish test
-1+6t-16t^2+28t^3-33t^4+28t^5-16t^6+6t^7-t^8
Seifert matrix of 11a_157
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 0 0 1 0 0 1 0
0 -1 -1 0 -1 0 0 0
-1 -1 0 1 -1 1 1 1
0 0 0 0 0 0 1 0
-1 0 0 1 0 0 1 1
2
135
First homology
of the double branched cover of 11a_157
Z/135
2 2
11a_158
1

detected by
an unknotting move
-1+5t-14t^2+25t^3-29t^4+25t^5-14t^6+5t^7-t^8
Seifert matrix of 11a_158
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 1 0 1 0
0 1 0 0 1 0 1 0
-1 1 -1 1 1 1 1 0
0 0 0 0 0 0 1 0
0 -1 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,-2,0,-5)
the Blanchfield form on it
45t^-3-195t^-2+415t^-1-517+415t-195t^2+45t^3
119
First homology
of the double branched cover of 11a_158
Z/119
2 2
11a_159
2

detected by
the Lickorish test
1-9t+27t^2-37t^3+27t^4-9t^5+t^6
Seifert matrix of 11a_159
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
0 0 0 1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,-1,t,1)
the Blanchfield form on it
2t^-2-9t^-1+13-9t+2t^2
111
First homology
of the double branched cover of 11a_159
Z/111
-2 2
11a_160
1

detected by
an unknotting move
1-6t+17t^2-30t^3+37t^4-30t^5+17t^6-6t^7+t^8
Seifert matrix of 11a_160
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 1 0 1 0
0 1 0 0 1 0 1 0
0 -1 0 -1 -1 -1 0 0
0 0 0 0 0 0 1 0
0 -1 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,1,0,0,1,1,0,-t)
the Blanchfield form on it
1
145
First homology
of the double branched cover of 11a_160
Z/145
0 0
11a_161
2

detected by
the signature
-2+8t-12t^2+13t^3-12t^4+8t^5-2t^6
Seifert matrix of 11a_161
1 0 0 0 0 0
1 -2 0 0 0 0
0 1 1 0 1 0
0 1 1 1 1 1
0 0 0 0 1 0
0 1 1 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
57
First homology
of the double branched cover of 11a_161
Z/57
4 4
11a_162
1

detected by
an unknotting move
-1+7t-20t^2+35t^3-41t^4+35t^5-20t^6+7t^7-t^8
Seifert matrix of 11a_162
1 0 0 1 0 0 -1 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 -1 0
0 -1 -1 0 -1 0 0 0
1 -1 0 1 -1 1 -1 1
0 -1 -1 0 -1 0 -1 0
1 0 0 1 -1 0 -1 1
1
Generator of the Alexander module
(0,1+2t+t^2+t^3+2t^4,0,0,0,0,1+t-t^2+2t^3,-1-t-3t^3+t^4-2t^5)
the Blanchfield form on it
x
167
First homology
of the double branched cover of 11a_162
Z/167
2 2
11a_163
2

detected by
the Lickorish test
-1+6t-15t^2+24t^3-27t^4+24t^5-15t^6+6t^7-t^8
Seifert matrix of 11a_163
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 -1 -1 -1 -1 0 0 0
0 -1 -1 0 -1 0 0 0
-1 -1 0 -1 -1 1 -1 1
-1 -1 -1 -1 -1 0 -1 0
0 0 0 -1 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,-1,0,0)
the Blanchfield form on it
-t^-3+7t^-2-19t^-1+26-19t+7t^2-t^3
119
First homology
of the double branched cover of 11a_163
Z/119
-2 2
11a_164
2

detected by
the Lickorish test
-1+7t-20t^2+35t^3-43t^4+35t^5-20t^6+7t^7-t^8
Seifert matrix of 11a_164
1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1
-1 0 -1 -1 0 -1 0 -1
0 0 0 1 1 0 0 1
0 0 0 0 1 0 0 0
-1 0 0 -1 0 -1 0 0
-1 0 -1 -1 -1 -1 -1 -1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,1-3t+3t^2-t^3,0,0,-3+4t-4t^2+3t^3-t^4,0)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-11+9t-5t^2+t^3
169
First homology
of the double branched cover of 11a_164
Z/169
0 0
11a_165
2

detected by
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 11a_165
-1 0 0 0 0 0
0 -2 0 0 0 0
-1 0 -1 0 0 0
-1 1 -1 1 0 0
-1 1 -1 1 1 1
-1 1 -1 1 0 1
2
81
First homology
of the double branched cover of 11a_165
Z/81
0 0
11a_166
1

detected by
an unknotting move
-4+15t-21t^2+15t^3-4t^4
Seifert matrix of 11a_166
-1 0 0 0
0 -2 0 0
-1 0 -1 0
1 -1 1 2
1
Generator of the Alexander module
(0,0,-1,1)
the Blanchfield form on it
-2t^-1+5-2t
59
First homology
of the double branched cover of 11a_166
Z/59
-2 2
11a_167
1

detected by
an unknotting move
-2+11t-26t^2+35t^3-26t^4+11t^5-2t^6
Seifert matrix of 11a_167
-1 0 -1 0 0 0
0 1 0 0 0 0
0 1 -2 0 0 0
-1 0 -1 -1 0 0
0 0 1 0 1 1
1 0 1 0 0 1
1
Generator of the Alexander module
(0,0,1+t,1+t,-t-t^2,t)
the Blanchfield form on it
2t^-1-5+2t
113
First homology
of the double branched cover of 11a_167
Z/113
0 0
11a_168
1

detected by
an unknotting move
-2+12t-29t^2+39t^3-29t^4+12t^5-2t^6
Seifert matrix of 11a_168
1 0 0 0 0 0
-1 -1 1 0 0 0
1 0 -2 0 0 0
0 -1 1 1 -1 1
-1 -1 1 0 -1 0
0 -1 0 0 -1 1
1
Generator of the Alexander module
(0,-t,1,t,0,0)
the Blanchfield form on it
-2t^-2+10t^-1-15+10t-2t^2
125
First homology
of the double branched cover of 11a_168
Z/125
0 0
11a_169
1

detected by
an unknotting move
-2+12t-28t^2+37t^3-28t^4+12t^5-2t^6
Seifert matrix of 11a_169
2 0 0 1 1 1
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 -1 -1 0 0
0 -1 0 0 1 0
0 -1 -1 -1 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+18-14t+6t^2-t^3
121
First homology
of the double branched cover of 11a_169
Z/121
0 0
11a_170
2

detected by
the Lickorish test
1-6t+20t^2-40t^3+51t^4-40t^5+20t^6-6t^7+t^8
Seifert matrix of 11a_170
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 -1 -1
-1 0 -1 0 0 0 0 0
-1 0 -1 1 1 0 1 0
0 0 0 0 1 0 1 0
-1 0 -1 1 1 1 1 0
0 0 0 0 0 0 1 0
0 0 0 -1 -1 0 -1 -1
1
Generator of the Alexander module
(0,-t,t,t,0,2t,1,1)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+16-12t+5t^2-t^3
185
First homology
of the double branched cover of 11a_170
Z/185
0 0
11a_171
1

detected by
an unknotting move
-1+7t-21t^2+39t^3-47t^4+39t^5-21t^6+7t^7-t^8
Seifert matrix of 11a_171
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 -1 -1
-1 0 -1 0 0 0 0 0
-1 0 -1 1 1 0 1 0
0 0 0 0 1 0 1 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 0 0 1 0
0 0 0 0 -1 -1 -1 -1
1
Generator of the Alexander module
(0,2-t,0,0,0,1,0,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
183
First homology
of the double branched cover of 11a_171
Z/183
-2 2
11a_172
1

detected by
an unknotting move
2-13t+33t^2-43t^3+33t^4-13t^5+2t^6
Seifert matrix of 11a_172
-1 0 0 -1 0 0
0 1 0 0 0 0
0 -1 -1 1 0 0
0 1 0 -2 0 0
1 0 -1 1 1 -1
0 -1 -1 1 0 -1
1
Generator of the Alexander module
(0,0,0,1+2t,2t,1)
the Blanchfield form on it
2t^-2-11t^-1+20-11t+2t^2
139
First homology
of the double branched cover of 11a_172
Z/139
-2 2
11a_173
2

detected by
the Nakanishi index
2-12t+32t^2-43t^3+32t^4-12t^5+2t^6
Seifert matrix of 11a_173
-1 0 -1 0 0 0
0 -1 -1 0 0 -1
0 0 -2 0 0 -1
0 -1 0 1 -1 0
0 -1 -1 0 -1 0
0 0 0 0 0 1
2
135
First homology
of the double branched cover of 11a_173
Z/45+Z/3
-2 2
11a_174
1

detected by
an unknotting move
-1+5t-11t^2+15t^3-15t^4+15t^5-11t^6+5t^7-t^8
Seifert matrix of 11a_174
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
0 0 -1 0 0 0 -1 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 1 1 1
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
0 1 0 0 0 1 1 1
1
Generator of the Alexander module
(0,0,0,2,2,0,0,-1)
the Blanchfield form on it
-t^-3+3t^-2-3t^-1+3-3t+3t^2-t^3
79
First homology
of the double branched cover of 11a_174
Z/79
2 2
11a_175
2

detected by
the Lickorish test
1-5t+13t^2-21t^3+25t^4-21t^5+13t^6-5t^7+t^8
Seifert matrix of 11a_175
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
0 0 -1 0 0 0 -1 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 1 0 1
0 0 0 0 0 1 0 0
0 0 0 0 0 0 -1 0
0 1 1 0 0 1 1 1
1
Generator of the Alexander module
(0,0,0,t,1+t,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-5+5t-3t^2+t^3
105
First homology
of the double branched cover of 11a_175
Z/105
0 2
11a_176
1

detected by
an unknotting move
-1+5t-13t^2+23t^3-27t^4+23t^5-13t^6+5t^7-t^8
Seifert matrix of 11a_176
-1 0 0 0 0 0 0 0
0 -1 -1 0 0 -1 -1 0
0 0 -1 0 0 -1 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 1 0 1
0 0 0 0 0 1 0 0
0 0 -1 0 0 -1 -1 0
0 0 0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-11t^-1+15-11t+5t^2-t^3
111
First homology
of the double branched cover of 11a_176
Z/111
-2 2
11a_177
2

detected by
the signature
1-5t+13t^2-19t^3+21t^4-19t^5+13t^6-5t^7+t^8
Seifert matrix of 11a_177
-1 0 0 0 0 0 0 0
0 -1 -1 0 0 -1 -1 0
0 0 -1 0 0 0 -1 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 0 1
0 0 -1 0 0 -1 -1 0
0 0 0 0 0 0 -1 0
0 1 1 0 0 1 1 1
1
Generator of the Alexander module
(0,0,0,1,1,0,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
97
First homology
of the double branched cover of 11a_177
Z/97
-4 4
11a_178
2

detected by
the Lickorish test
2-11t+29t^2-39t^3+29t^4-11t^5+2t^6
Seifert matrix of 11a_178
-1 0 0 0 0 0
0 -1 1 0 0 0
0 0 -2 0 0 0
-1 0 0 -1 0 0
-1 0 0 -1 1 1
0 1 -1 0 0 1
1
Generator of the Alexander module
(0,1+t,0,2-t-2t^2,3-t-4t^2,0)
the Blanchfield form on it
2t^-2-7t^-1+11-7t+2t^2
123
First homology
of the double branched cover of 11a_178
Z/123
-2 2
11a_179
2

detected by
the signature
1-5t+9t^2-9t^3+9t^4-9t^5+9t^6-5t^7+t^8
Seifert matrix of 11a_179
1 0 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 -1 -1
-1 0 -1 -1 0 0 -1 -1
-1 0 0 -1 0 0 0 -1
0 0 0 0 1 0 0 0
-1 0 -1 -1 0 -1 -1 -1
-1 0 0 -1 0 0 -1 -1
-1 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,1,0,t^2,-1,t,t,1)
the Blanchfield form on it
t^-3-3t^-2+3t^-1-3+3t-3t^2+t^3
57
First homology
of the double branched cover of 11a_179
Z/57
-4 4
11a_180
1

detected by
an unknotting move
1-5t+11t^2-17t^3+21t^4-17t^5+11t^6-5t^7+t^8
Seifert matrix of 11a_180
1 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 -1 0
-1 0 -1 0 0 0 -1 0
0 0 0 1 0 0 0 0
0 0 0 1 1 0 0 1
-1 0 -1 0 0 -1 -1 0
-1 0 0 -1 -1 0 -1 -1
0 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
1
89
First homology
of the double branched cover of 11a_180
Z/89
0 0
11a_181
2

detected by
the Nakanishi index
2-11t+23t^2-27t^3+23t^4-11t^5+2t^6
Seifert matrix of 11a_181
1 0 0 0 0 0
-1 -1 1 -1 0 -1
1 0 -2 1 0 1
-1 0 0 -1 0 -1
0 0 0 0 1 0
-1 0 0 0 -1 -1
2
99
First homology
of the double branched cover of 11a_181
Z/33+Z/3
-2 2
11a_182
2

detected by
the signature
1-5t+11t^2-13t^3+13t^4-13t^5+11t^6-5t^7+t^8
Seifert matrix of 11a_182
1 0 0 0 0 0 0 0
-1 -1 0 0 0 -1 0 0
0 0 1 0 0 0 0 0
0 0 1 1 0 0 1 0
0 0 1 1 1 0 1 1
-1 0 -1 -1 -1 -1 -1 -1
0 0 1 0 0 0 1 0
0 0 1 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,-t^3,0,1+t,0,0)
the Blanchfield form on it
-t^-3+5t^-2-11t^-1+13-11t+5t^2-t^3
73
First homology
of the double branched cover of 11a_182
Z/73
4 4
11a_183
2

detected by
the Lickorish test
2-11t+27t^2-35t^3+27t^4-11t^5+2t^6
Seifert matrix of 11a_183
1 0 0 0 0 0
-1 -1 0 0 0 -1
0 0 1 0 0 0
0 0 -1 2 0 0
0 0 1 -1 1 0
-1 0 -1 1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,-2)
the Blanchfield form on it
2t^-2-3t^-1+3-3t+2t^2
115
First homology
of the double branched cover of 11a_183
Z/115
2 2
11a_184
1

detected by
an unknotting move
-1+5t-11t^2+17t^3-19t^4+17t^5-11t^6+5t^7-t^8
Seifert matrix of 11a_184
-1 0 0 -1 -1 0 0 -1
0 1 0 0 0 0 0 -1
0 1 1 0 0 1 0 -1
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 1 0 0 0 1 0 -1
0 1 1 0 0 1 1 -1
0 0 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-15+11t-5t^2+t^3
87
First homology
of the double branched cover of 11a_184
Z/87
2 2
11a_185
1

detected by
an unknotting move
-2+11t-25t^2+33t^3-25t^4+11t^5-2t^6
Seifert matrix of 11a_185
-1 0 0 -1 -1 -1
0 1 0 0 0 -1
0 -1 2 0 0 1
0 0 0 -1 -1 0
0 0 0 0 1 0
0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+18-14t+6t^2-t^3
109
First homology
of the double branched cover of 11a_185
Z/109
0 0
11a_186
3

detected by
the signature
4-12t+20t^2-23t^3+20t^4-12t^5+4t^6
Seifert matrix of 11a_186
-1 0 0 -1 0 0
0 -1 0 -1 0 1
0 0 -1 0 0 -1
0 0 0 -2 0 0
0 -1 0 -1 -1 1
0 0 0 1 0 -2
1
Generator of the Alexander module
(-1,0,1-2t,0,1,0)
the Blanchfield form on it
4t^-2-6t^-1+8-6t+4t^2
95
First homology
of the double branched cover of 11a_186
Z/95
-6 6
11a_187
1

detected by
an unknotting move
-2+11t-27t^2+37t^3-27t^4+11t^5-2t^6
Seifert matrix of 11a_187
-1 0 0 0 0 0
0 2 0 0 0 0
-1 0 -1 0 0 0
-1 -1 -1 1 0 1
0 0 0 0 -1 0
0 -1 0 0 1 1
1
Generator of the Alexander module
(-2t,0,-t,1-t,0,-1+t+2t^2-2t^3)
the Blanchfield form on it
-11t^-2+14t^-1+10+14t-11t^2
117
First homology
of the double branched cover of 11a_187
Z/117
0 0
11a_188
1

detected by
an unknotting move
2-9t+15t^2-15t^3+15t^4-9t^5+2t^6
Seifert matrix of 11a_188
1 0 0 0 0 0
-1 -1 -1 -1 -1 0
-1 0 -1 0 -1 0
-1 0 -1 -1 -1 0
-1 0 0 0 -1 1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-9t^-1+15-9t+2t^2
67
First homology
of the double branched cover of 11a_188
Z/67
-2 2
11a_189
1

detected by
an unknotting move
1-6t+17t^2-31t^3+39t^4-31t^5+17t^6-6t^7+t^8
Seifert matrix of 11a_189
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 -1 0 -1
0 0 1 0 0 0 0 0
-1 0 0 -1 -1 0 -1 0
0 0 1 0 1 0 1 0
-1 0 -1 -1 -1 -1 -1 -1
0 0 1 0 0 0 1 0
-1 0 0 -1 -1 0 -1 -1
1
Generator of the Alexander module
(0,-1-3t-2t^2-t^3-t^4,0,1+2t+3t^2+4t^3+3t^4+t^5+t^6,0,-t-3t^2-2t^3-t^4-t^5,1+2t+t^3,t+2t^2+t^4)
the Blanchfield form on it
x
149
First homology
of the double branched cover of 11a_189
Z/149
0 0
11a_190
1

detected by
an unknotting move
-2+9t-19t^2+25t^3-19t^4+9t^5-2t^6
Seifert matrix of 11a_190
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 1 0 1
0 0 0 1 0 0
0 0 0 1 -2 0
0 0 0 1 0 1
1
Generator of the Alexander module
(-3+2t-t^2,-3t+2t^2-t^3,0,0,1-6t+4t^2-2t^3,3-2t+t^2)
the Blanchfield form on it
-79t^-4+492t^-3-1413t^-2+2558t^-1-3080+2558t-1413t^2+492t^3-79t^4
85
First homology
of the double branched cover of 11a_190
Z/85
0 0
11a_191
3

detected by
the signature
4-11t+17t^2-19t^3+17t^4-11t^5+4t^6
Seifert matrix of 11a_191
-1 0 0 -1 0 0
0 -1 -1 0 -1 -1
0 0 -1 0 0 -1
0 0 0 -2 0 0
0 0 -1 0 -1 -1
0 0 0 1 0 -2
1
Generator of the Alexander module
(0,-t^2,0,0,0,1+t)
the Blanchfield form on it
4t^-2-11t^-1+15-11t+4t^2
83
First homology
of the double branched cover of 11a_191
Z/83
-6 6
11a_192
2

detected by
the signature
8-24t+33t^2-24t^3+8t^4
Seifert matrix of 11a_192
-1 -1 0 0
0 -2 0 0
0 0 -2 0
0 1 -1 -2
1 or 2
97
First homology
of the double branched cover of 11a_192
Z/97
-4 4
11a_193
2

detected by
the Lickorish test
2-10t+22t^2-27t^3+22t^4-10t^5+2t^6
Seifert matrix of 11a_193
1 0 0 0 0 0
-1 -1 0 -1 0 0
0 0 1 0 0 1
-1 0 0 -1 1 0
0 0 1 0 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,2-2t+3t^2,-2t,1-t+t^2,-t)
the Blanchfield form on it
-5t^-2+13t^-1-21+13t-5t^2
95
First homology
of the double branched cover of 11a_193
Z/95
2 2
11a_194
2

detected by
the signature
1-5t+12t^2-18t^3+21t^4-18t^5+12t^6-5t^7+t^8
Seifert matrix of 11a_194
1 0 0 0 0 0 0 0
-1 -1 0 0 0 -1 0 0
0 0 1 0 0 0 0 0
0 0 1 1 0 0 0 1
0 0 1 1 1 0 1 1
-1 0 0 -1 -1 -1 -1 0
0 0 1 1 0 0 1 1
0 0 1 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,-1,1,0,0)
the Blanchfield form on it
-t^-3+5t^-2-11t^-1+13-11t+5t^2-t^3
93
First homology
of the double branched cover of 11a_194
Z/93
4 4
11a_195
1

detected by
an unknotting move
3-13t+21t^2-13t^3+3t^4
Seifert matrix of 11a_195
1 0 0 0
-1 -1 0 -1
0 0 3 0
-1 0 -1 -1
1
Generator of the Alexander module
(12t-12t^2,-1-11t+11t^2,0,11-11t)
the Blanchfield form on it
-368t^-1+655-368t
53
First homology
of the double branched cover of 11a_195
Z/53
0 0
11a_196
2

detected by
the Nakanishi index
-1+6t-17t^2+31t^3-37t^4+31t^5-17t^6+6t^7-t^8
Seifert matrix of 11a_196
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 -1 0 0
0 0 1 0 0 0 0 0
-1 0 0 -1 -1 0 -1 0
0 0 1 0 1 0 1 1
-1 0 0 -1 -1 -1 -1 -1
0 0 1 0 0 0 1 1
0 0 1 0 0 0 0 1
2
147
First homology
of the double branched cover of 11a_196
Z/21+Z/7
2 2
11a_197
1

detected by
an unknotting move
3-14t+33t^2-43t^3+33t^4-14t^5+3t^6
Seifert matrix of 11a_197
-1 -1 -1 0 -1 0
0 -2 -1 0 -2 0
0 -1 -2 0 -1 0
0 1 1 1 1 1
0 -1 -1 0 -2 0
0 1 0 0 1 1
1 or 2
143
First homology
of the double branched cover of 11a_197
Z/143
-2 2
11a_198
1

detected by
an unknotting move
2-11t+27t^2-35t^3+27t^4-11t^5+2t^6
Seifert matrix of 11a_198
-1 0 0 0 0 0
0 2 -1 0 1 -1
0 0 -1 0 0 -1
-1 0 0 -1 0 0
-1 0 -1 -1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,1+2t,2,0,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
115
First homology
of the double branched cover of 11a_198
Z/115
-2 2
11a_199
2

detected by
the Lickorish test
2-11t+23t^2-27t^3+23t^4-11t^5+2t^6
Seifert matrix of 11a_199
1 0 0 0 0 0
0 1 0 0 0 0
0 1 1 0 0 1
1 0 0 -2 1 0
-1 -1 -1 0 -1 -1
0 1 0 0 0 1
1
Generator of the Alexander module
(2-24t^2+17t^3-16t^4-80t^5+8t^6,-t+80t^3-8t^4,72t^3,1-16t^2+8t^3,8t^2-t^3-72t^4+80t^5-8t^6,t-32t^3+8t^4)
the Blanchfield form on it
x
99
First homology
of the double branched cover of 11a_199
Z/99
2 2
11a_200
2

detected by
the signature
7-21t+29t^2-21t^3+7t^4
Seifert matrix of 11a_200
-1 1 1 1
0 -3 -2 -2
0 -1 -3 -2
0 -1 -3 -3
1 or 2
85
First homology
of the double branched cover of 11a_200
Z/85
-4 4
11a_201
1

detected by
an unknotting move
4-20t+33t^2-20t^3+4t^4
Seifert matrix of 11a_201
1 0 0 0
1 -2 1 0
-1 0 -1 1
0 0 0 2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-2t^-2+11t^-1-18+11t-2t^2
81
First homology
of the double branched cover of 11a_201
Z/81
0 0
11a_202
2

detected by
the Lickorish test
2-12t+26t^2-31t^3+26t^4-12t^5+2t^6
Seifert matrix of 11a_202
1 0 0 0 0 0
0 -1 0 0 -1 0
0 0 1 0 0 0
1 -1 0 -2 -1 1
0 0 0 0 -1 0
-1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,-3t+5t^2-6t^3+3t^4-6t^5,0,11-15t+11t^2-21t^3+3t^4-6t^5,3-5t+6t^2-3t^3+6t^4,-5+6t-3t^2+6t^3)
the Blanchfield form on it
-875t^-3+5253t^-2-11392t^-1+13592-11392t+5253t^2-875t^3
111
First homology
of the double branched cover of 11a_202
Z/111
-2 2
11a_203
3

detected by
the signature
-1+5t-9t^2+11t^3-11t^4+11t^5-9t^6+5t^7-t^8
Seifert matrix of 11a_203
-1 0 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 -1
0 0 -1 0 0 -1 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 -1 0 0
0 0 0 0 0 -1 0 0
0 -1 -1 0 0 -1 -1 -1
0 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-9t^-1+11-9t+5t^2-t^3
63
First homology
of the double branched cover of 11a_203
Z/63
-6 6
11a_204
2

detected by
the signature
-2+11t-23t^2+29t^3-23t^4+11t^5-2t^6
Seifert matrix of 11a_204
-1 0 0 0 0 0
0 -2 1 0 0 1
0 0 -1 0 0 -1
-1 0 0 -1 0 0
-1 0 0 -1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,1+5t-8t^2,-3t+2t^3+6t^4,t+3t^2,6t^2,0)
the Blanchfield form on it
-t^-6-5t^-5+59t^-4+13t^-3-714t^-2+1924t^-1-2546+1924t-714t^2+13t^3+59t^4-5t^5-t^6
101
First homology
of the double branched cover of 11a_204
Z/101
-4 4
11a_205
2

detected by
the Lickorish test
2-10t+21t^2-25t^3+21t^4-10t^5+2t^6
Seifert matrix of 11a_205
1 0 0 0 0 0
0 -1 0 0 0 -1
0 0 1 0 1 0
1 -1 0 -2 0 -1
0 0 0 0 1 0
0 0 1 0 1 1
1
Generator of the Alexander module
(2+4t-6t^2,5+10t-14t^2,3+8t+6t^2+5t^3+51t^4-72t^5+30t^6,-11-22t+31t^2,1+4t+6t^2+5t^3+20t^4-36t^5+15t^6,2+3t+2t^2-15t^3+9t^4)
the Blanchfield form on it
x
91
First homology
of the double branched cover of 11a_205
Z/91
2 2
11a_206
3

detected by
the signature
1-5t+7t^2-7t^3+7t^4-7t^5+7t^6-5t^7+t^8
Seifert matrix of 11a_206
1 0 0 0 0 1 0 0
1 1 0 0 0 1 1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
1 1 -1 0 1 1 1 1
0 0 0 0 0 1 0 0
1 0 0 0 0 1 1 0
1 1 0 0 0 1 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-2t^-3+3t^-2-3t^-1+3-3t+3t^2-2t^3
47
First homology
of the double branched cover of 11a_206
Z/47
6 6
11a_207
2

detected by
the signature
-2+11t-19t^2+21t^3-19t^4+11t^5-2t^6
Seifert matrix of 11a_207
1 0 0 0 0 1
-1 2 0 0 0 -1
0 0 -1 -1 0 0
0 0 0 1 0 0
1 -1 -1 0 1 1
0 0 0 0 0 1
1 or 2
85
First homology
of the double branched cover of 11a_207
Z/85
4 4
11a_208
2

detected by
the signature
-2+12t-24t^2+29t^3-24t^4+12t^5-2t^6
Seifert matrix of 11a_208
2 1 0 0 0 1
2 2 0 0 0 2
0 0 -1 -1 0 0
0 0 0 1 0 0
-1 -1 -1 0 1 -1
2 1 0 0 0 2
1 or 2
105
First homology
of the double branched cover of 11a_208
Z/105
4 4
11a_209
1

detected by
an unknotting move
-1+10t-34t^2+51t^3-34t^4+10t^5-t^6
Seifert matrix of 11a_209
1 0 0 0 0 0
-1 -1 -1 0 -1 -1
0 0 1 0 0 0
0 0 -1 -1 0 -1
-1 0 -1 0 -1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,2-t,1-t,0)
the Blanchfield form on it
-2t^-2+10t^-1-17+10t-2t^2
141
First homology
of the double branched cover of 11a_209
Z/141
0 0
11a_210
1

detected by
an unknotting move
4-18t+29t^2-18t^3+4t^4
Seifert matrix of 11a_210
1 0 0 0
0 -1 1 0
0 0 2 0
1 -1 1 -2
1 or 2
73
First homology
of the double branched cover of 11a_210
Z/73
0 0
11a_211
1

detected by
an unknotting move
-3+17t-27t^2+17t^3-3t^4
Seifert matrix of 11a_211
-1 -1 0 0
0 1 0 0
-1 0 1 1
0 0 0 3
1 or 2
67
First homology
of the double branched cover of 11a_211
Z/67
2 2
11a_212
2

detected by
the signature
-3+16t-35t^2+45t^3-35t^4+16t^5-3t^6
Seifert matrix of 11a_212
-1 0 -1 -1 0 -1
0 -1 0 -1 0 0
0 0 -2 -1 0 -2
0 0 -1 -2 0 -1
0 1 1 1 1 1
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
153
First homology
of the double branched cover of 11a_212
Z/153
-4 4
11a_213
2

detected by
the signature
-3+16t-33t^2+41t^3-33t^4+16t^5-3t^6
Seifert matrix of 11a_213
-1 -1 -1 0 0 -1
0 -2 -2 0 0 -1
0 -1 -2 0 0 -1
0 -1 -1 -1 0 0
0 -1 0 0 1 -1
0 -1 -1 0 0 -2
1
Generator of the Alexander module
(-t+t^2,0,0,t-t^2,1,1-t)
the Blanchfield form on it
13t^-3-70t^-2+145t^-1-180+145t-70t^2+13t^3
145
First homology
of the double branched cover of 11a_213
Z/145
-4 4
11a_214
1

detected by
an unknotting move
3-17t+29t^2-17t^3+3t^4
Seifert matrix of 11a_214
-3 -1 0 0
0 1 0 0
0 0 1 -1
-1 -1 0 -1
1
Generator of the Alexander module
(0,0,t,1)
the Blanchfield form on it
3t^-1-7+3t
69
First homology
of the double branched cover of 11a_214
Z/69
0 0
11a_215
2

detected by
the signature
1-6t+17t^2-27t^3+31t^4-27t^5+17t^6-6t^7+t^8
Seifert matrix of 11a_215
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 -1 -1 1 -1 -1 0 1
0 -1 0 0 -1 -1 0 0
0 0 0 0 0 -1 0 0
0 -1 0 0 -1 -1 -1 0
0 0 0 0 -1 0 0 1
1 or 2
133
First homology
of the double branched cover of 11a_215
Z/133
-4 4
11a_216
1

detected by
an unknotting move
-1+6t-17t^2+31t^3-37t^4+31t^5-17t^6+6t^7-t^8
Seifert matrix of 11a_216
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 -1 -1 1 1 -1 0 1
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 0
0 -1 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,t,1+t,0,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+11-8t+4t^2-t^3
147
First homology
of the double branched cover of 11a_216
Z/147
-2 2
11a_217
1

detected by
an unknotting move
-1+6t-16t^2+29t^3-35t^4+29t^5-16t^6+6t^7-t^8
Seifert matrix of 11a_217
-1 0 -1 -1 -1 0 0 0
-1 1 0 0 -1 0 1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 -1 -1 0 0 0
-1 1 -1 0 -1 1 1 1
0 0 0 0 0 0 1 0
-1 1 0 0 -1 0 1 1
1
Generator of the Alexander module
(0,-2+2t,1,0,0,0,0,0)
the Blanchfield form on it
t^-1-3+t
139
First homology
of the double branched cover of 11a_217
Z/139
2 2
11a_218
1

detected by
an unknotting move
1-10t+32t^2-45t^3+32t^4-10t^5+t^6
Seifert matrix of 11a_218
-1 0 0 0 0 0
1 1 -1 0 0 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 0 -1 0 1 1
1 0 -1 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
131
First homology
of the double branched cover of 11a_218
Z/131
2 2
11a_219
2

detected by
the Lickorish test
-4+22t-35t^2+22t^3-4t^4
Seifert matrix of 11a_219
2 1 0 0
0 -1 -1 0
0 0 1 0
1 1 0 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-2t^-2+11t^-1-18+11t-2t^2
87
First homology
of the double branched cover of 11a_219
Z/87
2 2
11a_220
2

detected by
the signature
-2+10t-19t^2+23t^3-19t^4+10t^5-2t^6
Seifert matrix of 11a_220
-1 0 -1 0 0 0
0 -1 0 0 -1 0
0 0 -2 0 0 0
0 0 1 1 -1 0
0 0 0 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
85
First homology
of the double branched cover of 11a_220
Z/85
-4 4
11a_221
1

detected by
an unknotting move
-1+5t-10t^2+15t^3-17t^4+15t^5-10t^6+5t^7-t^8
Seifert matrix of 11a_221
1 0 0 0 0 0 1 0
0 -1 -1 -1 -1 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 -1 -1 0 0 0
1 -1 -1 0 -1 1 1 1
0 0 0 0 0 0 1 0
1 0 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-7t^-1+7-7t+5t^2-t^3
79
First homology
of the double branched cover of 11a_221
Z/79
2 2
11a_222
1

detected by
an unknotting move
-2+11t-23t^2+29t^3-23t^4+11t^5-2t^6
Seifert matrix of 11a_222
2 0 0 0 0 0
0 -1 -1 -1 -1 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 0 -1 -1 -1 0
-1 -1 -1 0 -1 1
1
Generator of the Alexander module
(0,2t^3-4t^4+4t^5-t^6,1+2t^3-4t^4+6t^5-7t^6+8t^7-5t^8+t^9,-2t^2+4t^3-4t^4+t^5,-2t^2+6t^3-8t^4+5t^5-t^6,1+2t^2-2t^3+3t^5-t^6)
the Blanchfield form on it
x
101
First homology
of the double branched cover of 11a_222
Z/101
0 2
11a_223
3

detected by
the signature
-1+5t-10t^2+14t^3-15t^4+14t^5-10t^6+5t^7-t^8
Seifert matrix of 11a_223
-1 0 0 0 0 0 0 0
0 -1 -1 0 0 -1 -1 0
0 0 -1 0 0 0 -1 0
-1 0 0 -1 0 0 0 0
-1 0 -1 -1 1 -1 -1 0
0 0 -1 0 0 -1 -1 0
0 0 0 0 0 0 -1 0
0 -1 -1 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,-t,0,1,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-9t^-1+11-9t+5t^2-t^3
75
First homology
of the double branched cover of 11a_223
Z/75
-6 6
11a_224
2

detected by
the signature
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 11a_224
-1 0 0 0 0 0
0 -1 1 0 0 0
0 0 -2 0 0 0
-1 0 0 -1 0 0
-1 0 1 -1 1 0
0 -1 1 0 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-2t^-2+9t^-1-13+9t-2t^2
89
First homology
of the double branched cover of 11a_224
Z/89
-4 4
11a_225
2

detected by
the signature
-2+8t-11t^2+11t^3-11t^4+8t^5-2t^6
Seifert matrix of 11a_225
1 0 0 0 1 0
0 1 0 0 0 0
0 1 -2 0 0 0
1 0 1 1 1 1
0 0 0 0 1 0
1 0 0 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-4+4t-3t^2+t^3
53
First homology
of the double branched cover of 11a_225
Z/53
4 4
11a_226
1

detected by
an unknotting move
-4+18t-27t^2+18t^3-4t^4
Seifert matrix of 11a_226
2 0 0 0
0 1 0 0
0 1 -2 0
-1 0 1 1
1 or 2
71
First homology
of the double branched cover of 11a_226
Z/71
2 2
11a_227
3

detected by
the signature
5-17t+31t^2-37t^3+31t^4-17t^5+5t^6
Seifert matrix of 11a_227
-1 -1 -1 -1 0 0
0 -2 -1 -2 0 0
0 -1 -2 -1 0 -1
0 -1 -1 -2 0 0
0 -1 0 -1 -1 1
0 1 0 1 0 -2
1 or 2
143
First homology
of the double branched cover of 11a_227
Z/143
-6 6
11a_228
1

detected by
an unknotting move
-1+10t-32t^2+47t^3-32t^4+10t^5-t^6
Seifert matrix of 11a_228
-1 0 0 0 0 0
1 1 -1 0 0 1
0 0 -1 -1 0 0
0 0 0 1 0 0
1 0 -1 0 1 0
-1 0 0 0 0 -1
1
Generator of the Alexander module
(-1+3t-5t^2-77t^3+28t^4+80t^5-44t^6,3-27t+120t^2+16t^3-172t^4+80t^5,-2+31t-127t^2-111t^3+304t^4+136t^5-300t^6+48t^7+32t^8,-1+15t-58t^2-70t^3+197t^4+76t^5-212t^6+52t^7+16t^8,2-16t+65t^2+4t^3-92t^4+44t^5,1-8t+38t^2+12t^3-56t^4+24t^5)
the Blanchfield form on it
x
133
First homology
of the double branched cover of 11a_228
Z/133
0 0
11a_229
1

detected by
an unknotting move
-4+18t-27t^2+18t^3-4t^4
Seifert matrix of 11a_229
-1 0 -1 0
0 -2 0 0
0 0 -2 0
0 1 1 1
1 or 2
71
First homology
of the double branched cover of 11a_229
Z/71
-2 2
11a_230
1

detected by
an unknotting move
-3+13t-19t^2+13t^3-3t^4
Seifert matrix of 11a_230
-1 0 0 0
-1 -1 0 0
-1 -1 1 -1
0 0 0 -3
1
Generator of the Alexander module
(0,1,1,0)
the Blanchfield form on it
1
51
First homology
of the double branched cover of 11a_230
Z/51
-2 2
11a_231
2

detected by
the Nakanishi index
-1+5t-12t^2+20t^3-23t^4+20t^5-12t^6+5t^7-t^8
Seifert matrix of 11a_231
-1 0 0 0 0 0 0 0
0 1 0 1 0 0 0 0
0 0 -1 0 0 -1 -1 -1
0 0 0 1 0 0 0 0
-1 0 0 0 -1 0 0 0
-1 1 0 1 -1 1 0 0
-1 1 0 1 -1 1 1 1
-1 1 0 1 -1 1 0 1
2
99
First homology
of the double branched cover of 11a_231
Z/33+Z/3
2 2
11a_232
1

detected by
an unknotting move
-1+5t-14t^2+26t^3-31t^4+26t^5-14t^6+5t^7-t^8
Seifert matrix of 11a_232
-1 0 0 0 0 0 0 0
0 -1 0 -1 0 -1 -1 0
-1 0 1 1 -1 1 1 1
0 0 0 1 0 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 1 -1 1 1 0
0 0 0 1 0 0 1 0
-1 0 0 1 -1 1 1 1
1
Generator of the Alexander module
(0,1-t,0,0,0,0,0,t)
the Blanchfield form on it
-t^-2+2t^-1-4+2t-t^2
123
First homology
of the double branched cover of 11a_232
Z/123
2 2
11a_233
1

detected by
an unknotting move
1-6t+19t^2-37t^3+47t^4-37t^5+19t^6-6t^7+t^8
Seifert matrix of 11a_233
-1 0 0 0 0 0 0 0
0 -1 0 -1 0 0 -1 -1
-1 0 1 1 -1 1 1 0
0 0 0 1 0 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 1 -1 1 1 0
0 0 0 1 0 0 1 0
0 0 0 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,-2+t,0,0,0,0,0,-1+3t-3t^2+t^3)
the Blanchfield form on it
-t^-2+2t^-1-4+2t-t^2
173
First homology
of the double branched cover of 11a_233
Z/173
0 0
11a_234
4

detected by
the signature
2-4t+5t^2-5t^3+5t^4-5t^5+5t^6-4t^7+2t^8
Seifert matrix of 11a_234
-1 0 0 0 -1 0 0 0
0 -1 -1 -1 -1 0 -1 -1
0 0 -1 -1 -1 0 0 -1
0 0 0 -1 -1 0 0 0
0 0 0 0 -2 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 0 -1 -1
0 0 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,-20,-5,16,0,8,7)
the Blanchfield form on it
908t^-3-1298t^-2+1538t^-1-1255+1538t-1298t^2+908t^3
37
First homology
of the double branched cover of 11a_234
Z/37
-8 8
11a_235
3

detected by
the signature
4-10t+14t^2-15t^3+14t^4-10t^5+4t^6
Seifert matrix of 11a_235
-1 0 0 0 -1 0
0 -1 1 -1 -1 0
0 0 -2 1 1 0
0 0 0 -1 -1 0
0 0 0 0 -2 0
0 -1 1 -1 -1 -1
1 or 2
71
First homology
of the double branched cover of 11a_235
Z/71
-6 6
11a_236
3

detected by
the signature
4-12t+21t^2-25t^3+21t^4-12t^5+4t^6
Seifert matrix of 11a_236
-1 0 0 0 -1 0
0 -2 -2 1 1 -2
0 -1 -2 1 1 -1
0 0 0 -1 -1 0
0 0 0 0 -2 0
0 -1 -2 1 1 -2
1 or 2
99
First homology
of the double branched cover of 11a_236
Z/99
-6 6
11a_237
2

detected by
the signature
8-23t+31t^2-23t^3+8t^4
Seifert matrix of 11a_237
-1 0 -1 0
0 -2 1 -1
0 0 -2 0
0 0 1 -2
1 or 2
93
First homology
of the double branched cover of 11a_237
Z/93
-4 4
11a_238
2

detected by
the signature
6-16t+21t^2-16t^3+6t^4
Seifert matrix of 11a_238
-1 0 -1 0
0 -1 -1 0
0 0 -2 0
0 -1 -1 -3
1 or 2
65
First homology
of the double branched cover of 11a_238
Z/65
-4 4
11a_239
2

detected by
the Lickorish test
-1+7t-22t^2+42t^3-51t^4+42t^5-22t^6+7t^7-t^8
Seifert matrix of 11a_239
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 -1 -1
-1 0 1 -1 1 0 1 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 1 0
0 0 -1 0 -1 -1 -1 0
0 0 0 0 0 0 1 0
0 0 0 0 -1 -1 -1 -1
2
195
First homology
of the double branched cover of 11a_239
Z/195
-2 2
11a_240
4

detected by
the signature
2-5t+8t^2-10t^3+11t^4-10t^5+8t^6-5t^7+2t^8
Seifert matrix of 11a_240
-1 0 0 -1 -1 -1 0 0
0 -1 -1 -1 -1 -1 0 -1
0 0 -1 -1 -1 -1 0 0
0 0 0 -2 -1 -2 0 0
0 0 0 -2 -2 -2 0 0
0 0 0 -1 -1 -2 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 -1 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+3t^-1-3+3t-2t^2+t^3
61
First homology
of the double branched cover of 11a_240
Z/61
-8 8
11a_241
3

detected by
the signature
4-12t+20t^2-23t^3+20t^4-12t^5+4t^6
Seifert matrix of 11a_241
-1 0 0 -1 -1 -1
0 -2 1 1 1 1
0 0 -1 -1 -1 -1
0 0 0 -2 -1 -2
0 0 0 -2 -2 -2
0 0 0 -1 -1 -2
1 or 2
95
First homology
of the double branched cover of 11a_241
Z/95
-6 6
11a_242
3

detected by
the signature
3-7t+9t^2-9t^3+9t^4-7t^5+3t^6
Seifert matrix of 11a_242
-1 0 0 1 0 0
0 -1 -1 1 0 -1
0 0 -1 1 0 0
0 0 0 -3 0 0
0 -1 -1 1 -1 -1
0 0 -1 1 0 -1
1
Generator of the Alexander module
(t,0,0,1,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
47
First homology
of the double branched cover of 11a_242
Z/47
-6 6
11a_243
2

detected by
the signature
6-17t+23t^2-17t^3+6t^4
Seifert matrix of 11a_243
-1 0 0 1
0 -2 1 -1
0 0 -1 1
0 0 0 -3
1 or 2
69
First homology
of the double branched cover of 11a_243
Z/69
-4 4
11a_244
3

detected by
the signature
5-17t+32t^2-39t^3+32t^4-17t^5+5t^6
Seifert matrix of 11a_244
-1 -1 -1 -1 0 0
0 -2 -1 -1 0 -1
0 -2 -2 -1 0 -1
0 -1 -1 -2 0 0
0 0 0 -1 -1 1
0 0 0 1 0 -2
1 or 2
147
First homology
of the double branched cover of 11a_244
Z/147
-6 6
11a_245
3

detected by
the signature
3-9t+16t^2-19t^3+16t^4-9t^5+3t^6
Seifert matrix of 11a_245
-1 0 1 1 1 0
0 -1 1 1 1 0
0 0 -3 -3 -3 0
0 0 -2 -3 -2 0
0 0 -2 -3 -3 0
0 -1 1 1 1 -1
1
Generator of the Alexander module
(-1,0,0,0,0,1)
the Blanchfield form on it
3t^-2-6t^-1+8-6t+3t^2
75
First homology
of the double branched cover of 11a_245
Z/75
-6 6
11a_246
2

detected by
the signature
4-10t+13t^2-10t^3+4t^4
Seifert matrix of 11a_246
-1 0 -1 0
0 -1 -1 0
0 0 -4 0
0 -1 -1 -1
1
Generator of the Alexander module
(1,0,0,-1)
the Blanchfield form on it
4t^-1-6+4t
41
First homology
of the double branched cover of 11a_246
Z/41
-4 4
11a_247
1

detected by
an unknotting move
5-9t+5t^2
Seifert matrix of 11a_247
-1 1
0 -5
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
1
19
First homology
of the double branched cover of 11a_247
Z/19
-2 2
11a_248
1

detected by
an unknotting move
1-6t+18t^2-34t^3+41t^4-34t^5+18t^6-6t^7+t^8
Seifert matrix of 11a_248
-1 0 -1 -1 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 -1 -1 0 -1 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 1
0 0 0 1 0 1 0 0
-1 0 -1 0 1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,2t-3t^2+2t^4-2t^5+t^6,-2t^2+t^3-t^4,2t-t^2-t^3+t^4-t^5,2t+t^2-2t^3+2t^4-t^5,0,1+5t-8t^2+8t^3-4t^4+t^5,2t+t^2-2t^3+2t^4-t^5)
the Blanchfield form on it
x
159
First homology
of the double branched cover of 11a_248
Z/159
2 2
11a_249
2

detected by
the Nakanishi index
-2+11t-27t^2+37t^3-27t^4+11t^5-2t^6
Seifert matrix of 11a_249
-1 0 -1 -1 0 0
-1 -1 -1 -1 0 0
0 0 -1 -1 0 -1
0 0 0 1 0 0
1 0 1 0 2 0
0 0 0 1 0 1
2
117
First homology
of the double branched cover of 11a_249
Z/39+Z/3
0 0
11a_250
2

detected by
the signature
1-5t+11t^2-16t^3+19t^4-16t^5+11t^6-5t^7+t^8
Seifert matrix of 11a_250
-1 0 0 -1 0 -1 -1 -1
0 1 0 0 0 0 0 0
-1 0 -1 -1 0 -1 -1 -1
0 -1 0 -1 0 -1 -1 -1
0 0 0 0 1 0 0 0
0 -1 0 0 -1 -1 -1 -1
0 -1 0 0 -1 0 -1 0
0 -1 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
t^-3-5t^-2+10t^-1-11+10t-5t^2+t^3
85
First homology
of the double branched cover of 11a_250
Z/85
-4 4
11a_251
1

detected by
an unknotting move
1-6t+16t^2-27t^3+33t^4-27t^5+16t^6-6t^7+t^8
Seifert matrix of 11a_251
-1 0 0 -1 0 0 -1 0
0 1 0 0 0 0 0 0
-1 0 -1 -1 0 0 -1 0
0 -1 0 -1 -1 0 -1 -1
0 0 0 0 1 1 0 1
0 0 0 0 0 1 0 0
0 -1 0 0 -1 0 -1 0
0 0 0 0 0 1 0 1
1
Generator of the Alexander module
(0,3-12t+10t^2-3t^3,1+6t^3-6t^4+2t^5,-6t+24t^2-20t^3+6t^4,-6t-3t^2+7t^3-3t^4,9t-9t^2+3t^3,3-6t-5t^2+17t^3-12t^4+3t^5,0)
the Blanchfield form on it
x
133
First homology
of the double branched cover of 11a_251
Z/133
0 0
11a_252
1

detected by
an unknotting move
1-6t+16t^2-27t^3+31t^4-27t^5+16t^6-6t^7+t^8
Seifert matrix of 11a_252
-1 0 -1 0 -1 0 -1 0
-1 -1 -1 0 -1 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 0 -1 0 -1 1 -1 1
0 0 -1 -1 -1 0 -1 0
0 0 0 0 -1 0 -1 1
1
Generator of the Alexander module
(0,0,0,0,1,t,1,t)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
131
First homology
of the double branched cover of 11a_252
Z/131
-2 2
11a_253
1

detected by
an unknotting move
-1+6t-16t^2+27t^3-33t^4+27t^5-16t^6+6t^7-t^8
Seifert matrix of 11a_253
-1 0 -1 0 0 0 -1 0
-1 -1 -1 0 0 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 -1 0
0 0 -1 0 1 1 -1 1
0 0 -1 -1 0 0 -1 0
0 0 -1 0 1 0 -1 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,3-4t+3t^2-t^3)
the Blanchfield form on it
t^-3-5t^-2+10t^-1-11+10t-5t^2+t^3
133
First homology
of the double branched cover of 11a_253
Z/133
0 0
11a_254
1

detected by
an unknotting move
-1+6t-16t^2+27t^3-31t^4+27t^5-16t^6+6t^7-t^8
Seifert matrix of 11a_254
-1 0 0 -1 0 0 -1 -1
0 1 0 0 0 0 0 0
-1 0 -1 -1 0 0 -1 -1
0 -1 0 -1 -1 -1 -1 -1
0 0 0 0 1 1 0 0
0 0 0 0 0 1 0 0
0 -1 0 0 -1 0 -1 0
0 -1 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,-1,0,1,0)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
131
First homology
of the double branched cover of 11a_254
Z/131
-2 2
11a_255
1

detected by
an unknotting move
1-6t+17t^2-30t^3+35t^4-30t^5+17t^6-6t^7+t^8
Seifert matrix of 11a_255
-1 0 -1 -1 -1 -1 0 0
-1 -1 -1 -1 -1 -1 0 0
0 0 -1 -1 -1 -1 -1 0
0 0 0 1 0 0 0 0
0 0 0 1 1 1 0 0
0 0 0 1 0 1 0 0
0 0 0 1 1 1 1 0
-1 0 -1 0 0 0 0 1
1
Generator of the Alexander module
(-7t+2t^2+38t^4+39t^5+23t^6+8t^7-38t^8-14t^9+12t^10,4+2t^2-28t^3-26t^4-33t^5-12t^6+18t^7,-5t-26t^2-28t^3-25t^4+15t^5+18t^6+4t^7+7t^8-6t^9,10-10t-4t^2-82t^3-78t^4-54t^5-73t^6+20t^7-2t^8-14t^9+12t^10,1+2t-10t^2-13t^3-76t^4-40t^5-26t^6+29t^7+113t^8-t^9-46t^10+32t^11+14t^12-12t^13,9-9t+t^2-73t^3-52t^4-4
the Blanchfield form on it
x
143
First homology
of the double branched cover of 11a_255
Z/143
2 2
11a_256
1

detected by
an unknotting move
-2+12t-31t^2+43t^3-31t^4+12t^5-2t^6
Seifert matrix of 11a_256
-1 0 -1 1 0 0
-1 -1 -1 1 0 0
0 0 -1 1 -1 0
0 0 0 2 0 0
0 0 0 -1 1 0
-1 0 -1 0 0 1
1
Generator of the Alexander module
(2,0,0,0,0,1)
the Blanchfield form on it
-6t^-2+20t^-1-23+20t-6t^2
133
First homology
of the double branched cover of 11a_256
Z/133
0 0
11a_257
1

detected by
an unknotting move
1-5t+12t^2-19t^3+23t^4-19t^5+12t^6-5t^7+t^8
Seifert matrix of 11a_257
-1 0 0 -1 0 0 -1 0
0 1 0 0 0 0 0 0
-1 0 -1 -1 0 0 -1 0
0 -1 0 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 1
0 -1 0 0 -1 -1 -1 -1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+6t^-1-7+6t-3t^2+t^3
97
First homology
of the double branched cover of 11a_257
Z/97
0 0
11a_258
2

detected by
the Lickorish test
2-9t+17t^2-19t^3+17t^4-9t^5+2t^6
Seifert matrix of 11a_258
-1 0 0 -1 -1 0
0 1 0 0 0 0
-1 0 -1 -1 -1 0
0 -1 0 -1 -1 0
0 -1 0 0 -1 1
0 0 0 0 0 2
1
Generator of the Alexander module
(1-t+t^2,10-52t+76t^2-67t^3+45t^4-8t^5+4t^6+6t^7,8t-14t^2+14t^3-13t^4+3t^5-2t^6-2t^7,3-5t+3t^2-t^3-t^4,-2+38t-62t^2+54t^3-42t^4+6t^5-6t^6-6t^7,0)
the Blanchfield form on it
x
75
First homology
of the double branched cover of 11a_258
Z/75
-2 2
11a_259
3

detected by
the signature
-1+5t-10t^2+15t^3-17t^4+15t^5-10t^6+5t^7-t^8
Seifert matrix of 11a_259
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 -1 0 0 -1 0
0 -1 0 0 -1 0 0 0
0 -1 0 0 -1 1 -1 0
0 0 0 0 0 0 -1 0
0 0 0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-8t^-1+9-8t+5t^2-t^3
79
First homology
of the double branched cover of 11a_259
Z/79
-6 6
11a_260
2

detected by
the signature
-2+9t-15t^2+17t^3-15t^4+9t^5-2t^6
Seifert matrix of 11a_260
-1 -1 0 0 -1 0
0 -1 0 0 0 0
-1 -1 -1 0 -1 0
0 0 0 -2 0 0
0 -1 0 0 -1 0
0 -1 0 1 -1 1
1
Generator of the Alexander module
(0,0,t-t^4,0,0,1+t-t^3)
the Blanchfield form on it
-2t^-2+7t^-1-8+7t-2t^2
69
First homology
of the double branched cover of 11a_260
Z/69
-4 4
11a_261
2

detected by
the signature
1-6t+16t^2-26t^3+31t^4-26t^5+16t^6-6t^7+t^8
Seifert matrix of 11a_261
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
-1 -1 -1 -1 0 0 -1 0
1 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 1
0 -1 0 0 -1 -1 -1 -1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,1+t,-t-t^2,0,0,2t+t^2,-2t-2t^2,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+17-14t+6t^2-t^3
129
First homology
of the double branched cover of 11a_261
Z/129
4 4
11a_262
1

detected by
an unknotting move
2-11t+25t^2-31t^3+25t^4-11t^5+2t^6
Seifert matrix of 11a_262
1 0 0 0 0 0
1 1 0 1 0 0
-1 -1 -1 -1 -1 0
1 0 0 1 0 0
0 -1 0 0 -1 1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,-1,2,0,1,0)
the Blanchfield form on it
t^-1-1+t
107
First homology
of the double branched cover of 11a_262
Z/107
2 2
11a_263
4

detected by
the signature
2-6t+11t^2-14t^3+15t^4-14t^5+11t^6-6t^7+2t^8
Seifert matrix of 11a_263
-1 0 0 0 1 1 1 0
0 -1 0 0 -1 -1 -1 0
-1 0 -1 0 1 1 1 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 -2 -1 -2 0
0 0 0 0 -2 -2 -2 0
0 0 0 0 -1 -1 -2 0
0 0 0 -1 -1 -1 -1 -1
2
81
First homology
of the double branched cover of 11a_263
Z/27+Z/3
-8 8
11a_264
1

detected by
an unknotting move
-1+6t-16t^2+28t^3-33t^4+28t^5-16t^6+6t^7-t^8
Seifert matrix of 11a_264
1 0 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
1 0 1 0 0 -1 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 -1 0
0 -1 0 0 0 -1 0 0
1 -1 1 0 0 -1 1 0
0 0 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+19-14t+6t^2-t^3
135
First homology
of the double branched cover of 11a_264
Z/135
-2 2
11a_265
1

detected by
an unknotting move
-2+11t-25t^2+33t^3-25t^4+11t^5-2t^6
Seifert matrix of 11a_265
1 0 0 -1 0 0
0 -1 0 0 0 0
1 0 1 -1 0 0
0 -1 0 -1 0 0
1 -1 1 -1 1 0
0 0 0 0 1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-14+11t-5t^2+t^3
109
First homology
of the double branched cover of 11a_265
Z/109
0 0
11a_266
1

detected by
an unknotting move
-1+7t-23t^2+45t^3-57t^4+45t^5-23t^6+7t^7-t^8
Seifert matrix of 11a_266
-1 0 0 -1 -1 -1 0 0
-1 -1 0 -1 -1 -1 0 0
-1 0 1 0 0 0 0 0
0 0 0 -1 -1 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 1 0 1 0
-1 0 1 0 0 -1 0 1
1
Generator of the Alexander module
(2,0,1,1,0,0,2,-1)
the Blanchfield form on it
-2t^-3+23t^-2-61t^-1+83-61t+23t^2-2t^3
209
First homology
of the double branched cover of 11a_266
Z/209
0 0
11a_267
1

detected by
an unknotting move
1-7t+22t^2-41t^3+49t^4-41t^5+22t^6-7t^7+t^8
Seifert matrix of 11a_267
-1 0 0 -1 -1 0 0 0
-1 -1 0 -1 -1 0 0 0
-1 0 1 0 0 0 0 0
0 0 0 -1 -1 0 -1 0
0 0 0 0 1 0 0 0
-1 0 1 0 0 1 0 0
0 0 0 0 1 0 1 0
-1 0 1 -1 0 1 0 1
1
Generator of the Alexander module
(0,t-2t^2+t^3,-1+t,4-4t+t^3,0,-t+2t^2-t^3,-t+2t^2-t^3,0)
the Blanchfield form on it
-2t^-3+12t^-2-31t^-1+43-31t+12t^2-2t^3
191
First homology
of the double branched cover of 11a_267
Z/191
2 2
11a_268
1

detected by
an unknotting move
1-6t+17t^2-29t^3+33t^4-29t^5+17t^6-6t^7+t^8
Seifert matrix of 11a_268
-1 0 -1 -1 -1 0 -1 0
-1 -1 -1 -1 -1 0 -1 0
0 0 -1 -1 -1 -1 -1 0
0 0 0 -1 -1 -1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 0
0 0 0 -1 -1 -1 -1 0
-1 0 -1 -1 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-6t^-2+16t^-1-23+16t-6t^2+t^3
139
First homology
of the double branched cover of 11a_268
Z/139
-2 2
11a_269
1

detected by
an unknotting move
1-6t+18t^2-32t^3+37t^4-32t^5+18t^6-6t^7+t^8
Seifert matrix of 11a_269
-1 0 -1 -1 -1 -1 0 0
-1 -1 -1 -1 -1 -1 0 0
0 0 -1 -1 -1 -1 -1 0
0 0 0 -1 -1 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 1 0 1 0
-1 0 -1 0 0 0 0 1
1
Generator of the Alexander module
(0,2t-4t^2-2t^3-2t^4-2t^6,-2t-2t^2-8t^3-4t^4-2t^5-2t^6-2t^7,4+6t+4t^2-4t^3-2t^4-2t^6-2t^7,2+6t-2t^2-2t^3-2t^6,2-8t^3-4t^4-2t^5-2t^6-2t^7,2+2t-4t^2+2t^3+4t^4+2t^7,1+4t+2t^2+2t^3+2t^4)
the Blanchfield form on it
x
151
First homology
of the double branched cover of 11a_269
Z/151
-2 2
11a_270
1

detected by
an unknotting move
-2+12t-32t^2+45t^3-32t^4+12t^5-2t^6
Seifert matrix of 11a_270
-1 0 -1 0 1 0
-1 -1 -1 0 1 0
0 0 1 0 0 0
0 0 1 1 0 0
0 0 1 1 -2 0
-1 0 0 0 1 1
1
Generator of the Alexander module
(0,-1,0,1,1,-1)
the Blanchfield form on it
-t^-2+4t^-1-7+4t-t^2
137
First homology
of the double branched cover of 11a_270
Z/137
0 0
11a_271
1

detected by
an unknotting move
3-17t+40t^2-51t^3+40t^4-17t^5+3t^6
Seifert matrix of 11a_271
1 0 0 0 0 0
1 -1 1 -1 0 0
1 0 1 0 0 0
1 0 1 -2 0 -1
1 -1 0 -1 -1 0
1 0 1 -1 0 -2
1 or 2
171
First homology
of the double branched cover of 11a_271
Z/171
-2 2
11a_272
1

detected by
an unknotting move
-2+13t-35t^2+49t^3-35t^4+13t^5-2t^6
Seifert matrix of 11a_272
1 0 0 0 0 0
1 -1 1 0 0 -1
1 0 1 0 0 0
0 -1 0 1 -1 0
1 -1 0 0 -1 -1
1 0 1 0 0 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+9t^-1-15+9t-2t^2
149
First homology
of the double branched cover of 11a_272
Z/149
0 0
11a_273
1

detected by
an unknotting move
3-16t+37t^2-47t^3+37t^4-16t^5+3t^6
Seifert matrix of 11a_273
1 0 -1 0 0 -1
-1 -1 1 0 -1 1
0 0 2 1 0 1
0 0 0 1 0 0
-1 0 0 0 -1 1
0 0 1 1 0 2
1
Generator of the Alexander module
(0,1+4t+5t^2-51t^3+108t^4-124t^5+81t^6-28t^7+4t^8,0,-t+6t^2-45t^3+63t^4+17t^5-155t^6+224t^7-158t^8+56t^9-8t^10,1+5t-16t^2+26t^3-24t^4+11t^5-2t^6,-1-5t+t^2+6t^3-45t^4+141t^5-236t^6+252t^7-162t^8+56t^9-8t^10)
the Blanchfield form on it
x
159
First homology
of the double branched cover of 11a_273
Z/159
2 2
11a_274
2

detected by
the Lickorish test
-1+6t-18t^2+35t^3-45t^4+35t^5-18t^6+6t^7-t^8
Seifert matrix of 11a_274
-1 0 0 -1 0 0 0 -1
-1 -1 0 -1 0 0 0 -1
-1 -1 1 0 0 0 1 0
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
-1 -1 1 0 0 1 1 -1
0 0 0 0 0 0 1 0
0 0 0 -1 -1 0 0 -1
1 or 2
165
First homology
of the double branched cover of 11a_274
Z/165
0 0
11a_275
2

detected by
the signature
-3+15t-29t^2+35t^3-29t^4+15t^5-3t^6
Seifert matrix of 11a_275
-1 0 -1 0 0 -1
0 -1 0 0 0 0
0 1 -2 1 0 -1
0 -1 0 -1 0 0
0 -1 1 -1 1 0
0 1 -1 1 0 -2
1
Generator of the Alexander module
(-t,0,1-3t,0,3t,0)
the Blanchfield form on it
13t^-3-65t^-2+126t^-1-152+126t-65t^2+13t^3
129
First homology
of the double branched cover of 11a_275
Z/129
-4 4
11a_276
2

detected by
the signature
-3+17t-37t^2+47t^3-37t^4+17t^5-3t^6
Seifert matrix of 11a_276
-2 1 -1 0 0 -1
0 -1 0 0 0 0
-1 1 -2 0 0 -2
1 -1 0 1 -1 0
0 0 -1 0 -1 -1
-1 1 -1 0 0 -2
1 or 2
161
First homology
of the double branched cover of 11a_276
Z/161
-4 4
11a_277
2

detected by
the Nakanishi index
-1+6t-17t^2+28t^3-31t^4+28t^5-17t^6+6t^7-t^8
Seifert matrix of 11a_277
1 0 0 1 0 0 1 0
-1 -1 0 0 -1 -1 -1 -1
0 0 -1 0 0 0 0 0
0 0 -1 1 0 0 0 0
-1 0 0 0 -1 -1 0 -1
-1 0 0 0 0 -1 0 0
0 0 -1 1 0 0 1 0
-1 0 0 0 0 -1 0 -1
2
135
First homology
of the double branched cover of 11a_277
Z/45+Z/3
-2 2
11a_278
1

detected by
an unknotting move
-2+12t-33t^2+47t^3-33t^4+12t^5-2t^6
Seifert matrix of 11a_278
1 0 0 1 1 0
-1 -1 0 0 -1 1
0 0 -1 0 0 0
0 0 -1 1 0 0
0 0 -1 1 1 0
1 0 0 0 0 -2
1 or 2
141
First homology
of the double branched cover of 11a_278
Z/141
0 0
11a_279
1

detected by
an unknotting move
3-12t+20t^2-21t^3+20t^4-12t^5+3t^6
Seifert matrix of 11a_279
-1 1 -1 -1 1 -1
0 2 0 0 1 0
0 0 -1 -1 1 -1
0 0 0 -1 1 0
0 1 0 0 2 0
0 0 0 -1 1 -1
1
Generator of the Alexander module
(-10t^2+8t^3,0,1-8t^2+4t^3,2-7t^2+3t^3-3t^4,4t,1+4t-8t^2)
the Blanchfield form on it
-487t^-3+1950t^-2-3255t^-1+3422-3255t+1950t^2-487t^3
91
First homology
of the double branched cover of 11a_279
Z/91
-2 2
11a_280
1

detected by
an unknotting move
6-26t+41t^2-26t^3+6t^4
Seifert matrix of 11a_280
-1 1 1 1
0 2 1 0
0 1 2 0
0 0 -1 -2
1
Generator of the Alexander module
(-1+t,0,0,2-t)
the Blanchfield form on it
9t^-3-54t^-2+137t^-1-184+137t-54t^2+9t^3
105
First homology
of the double branched cover of 11a_280
Z/105
0 0
11a_281
2

detected by
the Lickorish test
1-6t+18t^2-33t^3+39t^4-33t^5+18t^6-6t^7+t^8
Seifert matrix of 11a_281
-1 0 -1 -1 0 0 -1 0
-1 -1 -1 -1 0 0 -1 0
0 0 -1 -1 -1 0 -1 0
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
-1 0 -1 0 0 1 0 0
0 0 0 -1 -1 0 -1 0
-1 0 -1 -1 0 1 -1 1
1
Generator of the Alexander module
(0,-t-2t^3+t^4,0,0,0,1+2t^2-t^3,0,1-3t+3t^2-3t^3+t^4)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
155
First homology
of the double branched cover of 11a_281
Z/155
-2 2
11a_282
1

detected by
an unknotting move
-1+6t-16t^2+26t^3-29t^4+26t^5-16t^6+6t^7-t^8
Seifert matrix of 11a_282
1 0 0 1 1 0 1 1
-1 -1 0 0 0 -1 0 -1
0 0 -1 0 0 0 0 0
0 0 -1 1 0 0 0 0
0 0 -1 1 1 0 1 0
-1 0 0 0 0 -1 0 0
0 0 -1 1 0 0 1 0
0 0 -1 1 1 0 1 1
1
Generator of the Alexander module
(0,-1+4t+t^2-13t^3+5t^4+5t^5+t^6-3t^7+2t^8,1+2t-2t^2+t^3-t^5+2t^6,-3t-3t^2+t^4-2t^5,2+t-2t^2-t^3+5t^4+5t^5-3t^6+2t^7,-1+t+3t^2-10t^3-5t^4+t^6-2t^7,0,0)
the Blanchfield form on it
x
127
First homology
of the double branched cover of 11a_282
Z/127
2 2
11a_283
1

detected by
an unknotting move
3-15t+34t^2-43t^3+34t^4-15t^5+3t^6
Seifert matrix of 11a_283
-1 0 0 -1 1 -1
0 2 1 0 1 1
0 0 1 0 0 0
0 0 0 -1 1 0
0 1 0 0 2 0
0 0 1 0 0 1
1
Generator of the Alexander module
(0,-t,0,0,1-t,0)
the Blanchfield form on it
-t^-4+8t^-3-28t^-2+56t^-1-70+56t-28t^2+8t^3-t^4
147
First homology
of the double branched cover of 11a_283
Z/147
2 2
11a_284
1

detected by
an unknotting move
-1+7t-21t^2+38t^3-45t^4+38t^5-21t^6+7t^7-t^8
Seifert matrix of 11a_284
1 0 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
0 0 -1 0 -1 0 0 -1
1 0 0 1 0 -1 0 0
-1 0 0 -1 -1 0 -1 0
0 -1 0 0 0 -1 0 0
1 -1 0 1 0 -1 1 0
-1 0 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,-2+t-t^2,0,0,0,1,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+18-14t+6t^2-t^3
179
First homology
of the double branched cover of 11a_284
Z/179
-2 2
11a_285
1

detected by
an unknotting move
-2+14t-38t^2+53t^3-38t^4+14t^5-2t^6
Seifert matrix of 11a_285
1 0 -1 0 -1 0
-1 -1 1 -1 0 0
0 0 2 0 0 1
-1 0 0 -1 0 0
0 0 0 0 -1 0
0 0 0 0 -1 1
1
Generator of the Alexander module
(0,1+2t-3t^2,-t,t-4t^2+2t^3,-1,0)
the Blanchfield form on it
-15t^-2+39t^-1-17+39t-15t^2
161
First homology
of the double branched cover of 11a_285
Z/161
0 0
11a_286
2

detected by
the Lickorish test
1-6t+17t^2-31t^3+37t^4-31t^5+17t^6-6t^7+t^8
Seifert matrix of 11a_286
-1 0 0 -1 0 -1 -1 0
-1 -1 0 -1 0 -1 -1 0
-1 0 1 0 0 0 0 0
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 0 0 -1 -1 -1 0 0
0 0 0 -1 -1 -1 -1 0
-1 0 1 0 0 -1 -1 1
1
Generator of the Alexander module
(-2t^3,0,1,0,0,-2t^2,0,-2+t-t^2)
the Blanchfield form on it
19t^-3-36t^-2+84t^-1-85+84t-36t^2+19t^3
147
First homology
of the double branched cover of 11a_286
Z/147
-2 2
11a_287
1

detected by
an unknotting move
-1+7t-21t^2+38t^3-47t^4+38t^5-21t^6+7t^7-t^8
Seifert matrix of 11a_287
-1 0 0 -1 0 0 -1 0
-1 -1 0 -1 0 0 -1 0
-1 0 1 0 0 0 0 0
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
-1 0 1 0 0 1 -1 0
0 0 0 -1 -1 0 -1 0
-1 0 1 -1 0 1 -1 1
1
Generator of the Alexander module
(2+3t-4t^3+5t^4+2t^5-4t^6+2t^7,t+2t^2+t^3-6t^4+6t^5-2t^6,-2-5t+5t^2+8t^3-5t^4-19t^5+34t^6-22t^7+6t^8,-2-t+t^2+3t^3-8t^4+6t^5-2t^6,-2-6t-11t^2-2t^3-18t^4+28t^5-2t^6-8t^7-32t^8+72t^9-52t^10+16t^11,-4-6t+4t^2-2t^3-27t^4+10t^5-22t^6+28t^7-2t^8-8t^9-32t^10+72t^11-52t^12+16t^13,-3t^2+11t^3+23t^4-25t^5-24t
the Blanchfield form on it
x
181
First homology
of the double branched cover of 11a_287
Z/181
0 0
11a_288
2

detected by
the Lickorish test
1-7t+23t^2-44t^3+55t^4-44t^5+23t^6-7t^7+t^8
Seifert matrix of 11a_288
1 0 0 0 -1 0 1 0
0 -1 0 0 0 0 0 0
0 0 -1 0 0 0 -1 -1
1 0 0 1 -1 0 1 0
0 -1 0 0 -1 0 0 0
1 -1 0 1 -1 1 1 0
0 0 0 0 0 0 1 0
-1 0 0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,-4+15t^2-21t^3-13t^4+22t^5-6t^6,4t+4t^2+5t^3-10t^4+3t^5,4+9t^2-11t^3+3t^4,5-9t+13t^2+3t^3-10t^4+3t^5,20t^2+4t^3-19t^4+6t^5,4t+8t^2-11t^3+3t^4)
the Blanchfield form on it
x
205
First homology
of the double branched cover of 11a_288
Z/205
0 0
11a_289
1

detected by
an unknotting move
1-6t+17t^2-30t^3+37t^4-30t^5+17t^6-6t^7+t^8
Seifert matrix of 11a_289
1 0 0 1 1 0 1 0
-1 -1 0 0 -1 -1 0 -1
0 0 -1 0 0 0 0 0
0 0 -1 1 0 0 0 0
0 0 -1 1 1 0 1 0
-1 0 0 0 0 -1 0 0
0 0 -1 1 0 0 1 0
-1 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(8t-12t^3+34t^4-6t^5-71t^6+39t^7+43t^8-39t^9-2t^10+11t^11-3t^12,1+t+2t^2+8t^3-2t^4-4t^5+4t^6-16t^7+6t^8+11t^9-11t^10+3t^11,21+24t-23t^2+28t^3+92t^4-124t^5-254t^6+165t^7+176t^8-174t^9+88t^10+8t^11-78t^12+66t^13-18t^14,-4+4t^2-17t^3+5t^4+27t^5-17t^6-8t^7+11t^8-3t^9,7+8t-7t^2+4t^3+31t^4-33t^5-113t^6+56
the Blanchfield form on it
x
145
First homology
of the double branched cover of 11a_289
Z/145
0 0
11a_290
1

detected by
an unknotting move
-3+15t-32t^2+41t^3-32t^4+15t^5-3t^6
Seifert matrix of 11a_290
-1 0 -1 -1 1 -1
0 2 1 0 1 0
0 0 1 0 0 0
0 0 0 -1 1 0
0 1 0 0 2 0
0 0 0 -1 1 -1
1
Generator of the Alexander module
(1-2t-22t^2+12t^3-2t^4+45t^5-92t^6+65t^7-15t^8,30-46t-130t^2+24t^3+180t^4-306t^5-30t^6+296t^7-194t^8+72t^9-16t^10,35-52t-229t^2+18t^3+221t^4-225t^5-213t^6+359t^7-151t^8+60t^9-20t^10,5-2t-118t^2+49t^3+33t^4+48t^5-265t^6+264t^7-94t^8+18t^9-4t^10,-9+3t+t^2+16t^3-32t^4+22t^5-5t^6,-48+74t+78t^2+26t^3-266
the Blanchfield form on it
x
141
First homology
of the double branched cover of 11a_290
Z/141
0 2
11a_291
3

detected by
the signature
5-14t+20t^2-21t^3+20t^4-14t^5+5t^6
Seifert matrix of 11a_291
-2 1 1 0 1 1
0 -2 -2 -1 -2 -2
0 -1 -2 -1 -1 -2
-1 -1 -1 -2 -1 -1
0 -1 -2 -1 -2 -2
0 -1 -1 -1 -1 -2
2
99
First homology
of the double branched cover of 11a_291
Z/33+Z/3
-6 6
11a_292
2

detected by
the signature
10-32t+45t^2-32t^3+10t^4
Seifert matrix of 11a_292
-2 1 -1 0
0 -2 2 -1
0 1 -3 1
-1 -1 1 -2
1 or 2
129
First homology
of the double branched cover of 11a_292
Z/129
-4 4
11a_293
2

detected by
the Nakanishi index
1-5t+12t^2-15t^3+15t^4-15t^5+12t^6-5t^7+t^8
Seifert matrix of 11a_293
1 0 0 1 1 1 1 1
-1 -1 0 0 0 -1 0 0
0 0 -1 0 0 0 0 0
0 0 -1 1 0 0 0 0
0 0 -1 1 1 0 1 0
0 0 -1 1 1 1 1 1
0 0 -1 1 0 0 1 0
0 0 -1 1 1 0 1 1
2
81
First homology
of the double branched cover of 11a_293
Z/27+Z/3
4 4
11a_294
1

detected by
an unknotting move
2-11t+29t^2-39t^3+29t^4-11t^5+2t^6
Seifert matrix of 11a_294
1 0 0 1 -1 1
-1 -1 0 0 0 -1
0 0 -1 0 0 0
0 0 -1 1 0 0
0 0 1 -1 2 0
0 0 -1 1 -1 1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-2t^-2+11t^-1-17+11t-2t^2
123
First homology
of the double branched cover of 11a_294
Z/123
2 2
11a_295
2

detected by
the signature
-3+14t-24t^2+27t^3-24t^4+14t^5-3t^6
Seifert matrix of 11a_295
-1 0 0 -1 1 0
0 2 1 1 1 1
0 0 1 0 0 0
0 0 1 1 0 1
0 1 0 0 2 0
0 0 1 0 0 1
1 or 2
109
First homology
of the double branched cover of 11a_295
Z/109
4 4
11a_296
2

detected by
the Lickorish test
-6+28t-43t^2+28t^3-6t^4
Seifert matrix of 11a_296
-1 1 1 1
0 2 1 0
0 1 2 0
0 1 0 2
1 or 2
111
First homology
of the double branched cover of 11a_296
Z/111
2 2
11a_297
2

detected by
the Nakanishi index
2-15t+42t^2-57t^3+42t^4-15t^5+2t^6
Seifert matrix of 11a_297
1 0 -1 0 -1 0
-1 -1 0 -1 0 0
0 0 2 1 0 1
0 0 0 1 0 0
0 0 0 0 -1 0
0 0 0 0 -1 1
2
175
First homology
of the double branched cover of 11a_297
Z/35+Z/5
2 2
11a_298
3

detected by
the signature
5-16t+28t^2-33t^3+28t^4-16t^5+5t^6
Seifert matrix of 11a_298
-1 1 0 1 1 0
0 -2 0 -1 -1 0
0 0 -1 0 -1 0
0 -1 0 -2 -1 0
0 0 0 -1 -2 0
0 0 -1 0 -1 -1
1 or 2
131
First homology
of the double branched cover of 11a_298
Z/131
-6 6
11a_299
2

detected by
the signature
8-24t+33t^2-24t^3+8t^4
Seifert matrix of 11a_299
-1 1 -1 1
0 -2 1 -1
0 0 -3 1
0 -1 1 -2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
6t^-1-11+6t
97
First homology
of the double branched cover of 11a_299
Z/97
-4 4
11a_300
1

detected by
an unknotting move
-1+6t-17t^2+32t^3-41t^4+32t^5-17t^6+6t^7-t^8
Seifert matrix of 11a_300
-1 0 -1 0 0 -1 0 0
-1 -1 -1 0 0 -1 0 0
0 0 -1 0 0 -1 -1 0
-1 -1 -1 1 1 -1 0 1
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 -1 0
0 0 0 0 0 0 1 0
-1 -1 -1 0 1 0 0 1
1 or 2
153
First homology
of the double branched cover of 11a_300
Z/153
0 0
11a_301
1

detected by
an unknotting move
-1+7t-22t^2+43t^3-53t^4+43t^5-22t^6+7t^7-t^8
Seifert matrix of 11a_301
-1 -1 0 -1 0 -1 0 0
0 1 0 0 1 0 0 0
-1 0 1 0 0 0 0 0
0 -1 0 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 -1 0 -1 0 -1 -1 0
0 1 0 0 1 0 1 0
-1 0 1 0 0 -1 0 1
1
Generator of the Alexander module
(0,0,3-3t+t^2,0,0,2-t,0,0)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-15+11t-5t^2+t^3
199
First homology
of the double branched cover of 11a_301
Z/199
2 2
11a_302
2

detected by
the signature
1-7t+20t^2-33t^3+39t^4-33t^5+20t^6-7t^7+t^8
Seifert matrix of 11a_302
-1 -1 0 -1 0 0 0 0
0 1 0 0 1 0 0 0
-1 0 1 0 0 0 0 0
0 -1 0 -1 0 0 -1 0
0 0 0 0 1 0 0 0
-1 0 1 0 0 1 0 0
0 1 0 0 1 0 1 0
-1 0 1 -1 0 1 0 1
1
Generator of the Alexander module
(4t-2t^2+18t^3-12t^4+18t^5-10t^6+6t^7-2t^8,0,2t-t^2+9t^3-6t^4+9t^5-5t^6+3t^7-t^8,8-3t+2t^2-8t^3-2t^4-23t^5+6t^6-12t^7+6t^8,0,t+4t^3-t^4+2t^5-t^6,-5+2t+5t^3+2t^4+15t^5-4t^6+8t^7-4t^8,-t^2-4t^4+t^5-2t^6+t^7)
the Blanchfield form on it
x
161
First homology
of the double branched cover of 11a_302
Z/161
4 4
11a_303
1

detected by
an unknotting move
-3+15t-34t^2+45t^3-34t^4+15t^5-3t^6
Seifert matrix of 11a_303
1 0 0 0 0 0
1 1 1 0 0 0
1 0 1 0 0 0
1 1 1 -2 0 -1
1 0 1 -1 -1 0
1 1 1 -1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-2-7t^-1+13-7t+t^2
149
First homology
of the double branched cover of 11a_303
Z/149
0 0
11a_304
2

detected by
the signature
-3+14t-26t^2+31t^3-26t^4+14t^5-3t^6
Seifert matrix of 11a_304
-1 -1 -1 0 -1 -1
0 -1 -1 0 0 -1
0 0 -2 0 0 -1
0 -1 0 1 -1 -1
0 -1 -1 0 -1 -1
0 0 -1 0 0 -2
1
Generator of the Alexander module
(3-8t+16t^2-20t^3+16t^4-9t^5+2t^6,0,0,2-5t+11t^2-13t^3+10t^4-5t^5+t^6,0,0)
the Blanchfield form on it
x
117
First homology
of the double branched cover of 11a_304
Z/117
-4 4
11a_305
1

detected by
an unknotting move
-1+6t-16t^2+28t^3-33t^4+28t^5-16t^6+6t^7-t^8
Seifert matrix of 11a_305
1 0 1 -1 1 1 0 1
-1 -1 -1 0 0 -1 0 0
0 0 1 -1 1 1 -1 1
0 0 0 -1 0 0 0 0
0 0 0 -1 1 0 -1 0
0 0 0 -1 1 1 -1 1
0 0 0 -1 0 0 -1 0
0 0 0 -1 1 0 -1 1
1
Generator of the Alexander module
(0,-2t-t^2+t^3,-t,1+t,-1,-t,t,0)
the Blanchfield form on it
t^-1-2+t
135
First homology
of the double branched cover of 11a_305
Z/135
2 2
11a_306
2

detected by
the signature
1-5t+13t^2-21t^3+25t^4-21t^5+13t^6-5t^7+t^8
Seifert matrix of 11a_306
1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
-1 -1 -1 0 0 -1 -1 0
0 0 0 1 0 0 0 0
0 0 0 1 1 0 0 1
1 0 0 0 0 1 0 0
-1 -1 0 -1 -1 -1 -1 -1
0 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,1,-2,0,1,0,-3,0)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
105
First homology
of the double branched cover of 11a_306
Z/105
4 4
11a_307
1

detected by
an unknotting move
2-9t+19t^2-23t^3+19t^4-9t^5+2t^6
Seifert matrix of 11a_307
1 0 0 0 0 0
1 1 0 1 0 0
-1 -1 -1 -1 -1 0
1 0 0 1 0 0
-1 -1 0 -1 -1 1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,2,-3,0,-2,0)
the Blanchfield form on it
-2t^-2+9t^-1-15+9t-2t^2
83
First homology
of the double branched cover of 11a_307
Z/83
2 2
11a_308
3

detected by
the signature
-1+5t-9t^2+13t^3-15t^4+13t^5-9t^6+5t^7-t^8
Seifert matrix of 11a_308
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
0 0 -1 0 0 0 -1 0
-1 -1 0 -1 -1 0 0 0
0 -1 0 0 -1 0 0 0
-1 -1 0 -1 -1 1 -1 0
0 0 0 0 0 0 -1 0
0 0 -1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-7t^-1+7-7t+5t^2-t^3
71
First homology
of the double branched cover of 11a_308
Z/71
-6 6
11a_309
2

detected by
the signature
-2+11t-21t^2+25t^3-21t^4+11t^5-2t^6
Seifert matrix of 11a_309
-2 1 0 0 0 0
0 -1 0 0 0 0
0 0 -1 0 -1 0
1 -1 0 1 -1 0
0 0 0 0 -1 0
0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1+t,0,t^2)
the Blanchfield form on it
-2t^-2+11t^-1-17+11t-2t^2
93
First homology
of the double branched cover of 11a_309
Z/93
-4 4
11a_310
2

detected by
the signature
-2+9t-13t^2+13t^3-13t^4+9t^5-2t^6
Seifert matrix of 11a_310
-1 -1 0 0 -1 0
0 -1 0 0 0 0
0 0 -2 0 0 0
-1 -1 0 -1 -1 0
0 -1 0 0 -1 0
-1 -1 1 -1 -1 1
1
Generator of the Alexander module
(0,0,-1-t,2t+t^2,0,2t+2t^2)
the Blanchfield form on it
-2t^-2+9t^-1-13+9t-2t^2
61
First homology
of the double branched cover of 11a_310
Z/61
-4 4
11a_311
1

detected by
an unknotting move
-4+20t-31t^2+20t^3-4t^4
Seifert matrix of 11a_311
-2 1 0 0
0 -1 0 0
0 0 -2 0
1 -1 1 1
1 or 2
79
First homology
of the double branched cover of 11a_311
Z/79
-2 2
11a_312
1

detected by
an unknotting move
3-13t+27t^2-33t^3+27t^4-13t^5+3t^6
Seifert matrix of 11a_312
-1 1 1 -1 1 1
0 2 1 0 1 1
0 2 2 0 1 2
0 0 0 -1 1 0
0 1 1 0 2 1
0 2 1 0 1 2
1 or 2
119
First homology
of the double branched cover of 11a_312
Z/119
2 2
11a_313
1

detected by
an unknotting move
5-19t+29t^2-19t^3+5t^4
Seifert matrix of 11a_313
-1 -1 1 -1
0 -1 1 0
0 0 2 -1
0 0 -1 3
1
Generator of the Alexander module
(239-66t,-447+123t+239t^2-66t^3,-184+53t-478t^2+132t^3,68-18t+239t^2-66t^3)
the Blanchfield form on it
1414953t^-4-4454218t^-3+3008857t^-2+7669373t^-1-15104086+7669373t+3008857t^2-4454218t^3+1414953t^4
77
First homology
of the double branched cover of 11a_313
Z/77
0 0
11a_314
2

detected by
the Nakanishi index
1-7t+21t^2-36t^3+41t^4-36t^5+21t^6-7t^7+t^8
Seifert matrix of 11a_314
1 0 0 0 1 0 0 1
-1 -1 -1 0 -1 -1 -1 -1
-1 0 -1 0 0 -1 0 -1
0 0 0 -1 0 0 0 0
0 0 0 -1 1 0 0 0
-1 0 0 0 0 -1 0 0
-1 0 -1 0 -1 -1 -1 -1
0 0 0 -1 1 0 0 1
2
171
First homology
of the double branched cover of 11a_314
Z/57+Z/3
-2 2
11a_315
1

detected by
an unknotting move
-1+6t-18t^2+33t^3-41t^4+33t^5-18t^6+6t^7-t^8
Seifert matrix of 11a_315
1 0 0 0 1 1 0 1
-1 -1 -1 0 -1 -1 -1 -1
-1 0 -1 0 0 -1 0 0
0 0 0 -1 0 0 0 0
0 0 0 -1 1 0 0 0
0 0 0 -1 1 1 0 1
-1 0 -1 0 -1 -1 -1 -1
0 0 0 -1 1 0 0 1
1
Generator of the Alexander module
(0,0,-2+t,0,0,0,-3+6t-4t^2+t^3,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
157
First homology
of the double branched cover of 11a_315
Z/157
0 0
11a_316
1

detected by
an unknotting move
1-5t+14t^2-25t^3+31t^4-25t^5+14t^6-5t^7+t^8
Seifert matrix of 11a_316
1 0 0 0 1 1 1 0
-1 -1 -1 0 0 -1 0 -1
-1 0 -1 0 0 -1 0 0
0 0 0 -1 0 0 0 0
0 0 0 -1 1 0 0 0
0 0 0 -1 1 1 1 0
0 0 0 -1 1 0 1 0
-1 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,2-2t+2t^2-t^3,0,0,1,-2+2t-2t^2+t^3,0)
the Blanchfield form on it
19t^-3-69t^-2+137t^-1-163+137t-69t^2+19t^3
121
First homology
of the double branched cover of 11a_316
Z/121
0 0
11a_317
2

detected by
the Nakanishi index
-3+14t-28t^2+35t^3-28t^4+14t^5-3t^6
Seifert matrix of 11a_317
-1 -1 0 -1 1 -1
0 -1 0 -1 1 0
0 0 2 1 1 0
0 0 0 1 0 0
0 0 1 0 2 0
0 -1 0 -1 1 -1
2
125
First homology
of the double branched cover of 11a_317
Z/25+Z/5
0 2
11a_318
3

detected by
the signature
5-16t+29t^2-35t^3+29t^4-16t^5+5t^6
Seifert matrix of 11a_318
-1 0 0 0 1 -1
0 -1 -1 -1 -1 0
0 0 -2 -1 -1 -1
0 0 -2 -2 -1 -1
0 0 0 0 -2 1
0 0 -1 -1 0 -2
1 or 2
135
First homology
of the double branched cover of 11a_318
Z/135
-6 6
11a_319
3

detected by
the signature
5-15t+25t^2-29t^3+25t^4-15t^5+5t^6
Seifert matrix of 11a_319
-2 -1 -1 -1 -2 -1
0 -2 1 0 0 1
-1 0 -2 -1 -1 -2
-2 -1 -1 -2 -2 -1
-1 -1 -1 -1 -2 -1
-1 0 -1 -1 -1 -2
1 or 2
119
First homology
of the double branched cover of 11a_319
Z/119
-6 6
11a_320
2

detected by
the signature
9-27t+37t^2-27t^3+9t^4
Seifert matrix of 11a_320
-3 1 1 1
0 -2 1 1
1 0 -2 -2
1 0 -1 -2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
6t^-1-11+6t
109
First homology
of the double branched cover of 11a_320
Z/109
-4 4
11a_321
2

detected by
the Nakanishi index
-3+15t-27t^2+31t^3-27t^4+15t^5-3t^6
Seifert matrix of 11a_321
-1 0 0 -1 1 0
0 2 1 1 1 1
0 2 2 1 1 2
0 0 0 1 0 0
0 1 1 0 2 1
0 2 1 1 1 2
2
121
First homology
of the double branched cover of 11a_321
Z/11+Z/11
4 4
11a_322
2

detected by
2-13t+36t^2-49t^3+36t^4-13t^5+2t^6
Seifert matrix of 11a_322
1 0 -1 0 1 0
-1 -1 0 0 0 -1
0 0 2 1 -1 1
0 0 0 -1 0 0
0 0 0 -1 1 0
0 0 0 0 0 1
2
151
First homology
of the double branched cover of 11a_322
Z/151
2 2
11a_323
1

detected by
an unknotting move
2-9t+19t^2-23t^3+19t^4-9t^5+2t^6
Seifert matrix of 11a_323
1 0 1 1 1 0
0 -1 0 0 0 0
0 -1 1 0 0 0
0 -1 1 1 1 0
0 -1 1 0 1 0
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,0,0,3-2t,0,-5+7t-2t^2)
the Blanchfield form on it
-55t^-3+248t^-2-524t^-1+634-524t+248t^2-55t^3
83
First homology
of the double branched cover of 11a_323
Z/83
2 2
11a_324
2

detected by
the Lickorish test
-5+25t-39t^2+25t^3-5t^4
Seifert matrix of 11a_324
-1 -1 1 0
0 1 0 0
0 0 2 -1
0 -1 -1 3
1
Generator of the Alexander module
(1,0,1,2)
the Blanchfield form on it
-4t^-1+5-4t
99
First homology
of the double branched cover of 11a_324
Z/99
2 2
11a_325
1

detected by
an unknotting move
-6+24t-35t^2+24t^3-6t^4
Seifert matrix of 11a_325
2 1 1 0
0 1 0 0
1 0 2 0
0 1 -1 -2
1
Generator of the Alexander module
(-2+3t-2t^2,4-20t+26t^2-16t^3,-2+6t-7t^2+4t^3,-1-2t^2+3t^3-2t^4)
the Blanchfield form on it
387t^-5-4097t^-4+18632t^-3-49320t^-2+85515t^-1-102232+85515t-49320t^2+18632t^3-4097t^4+387t^5
95
First homology
of the double branched cover of 11a_325
Z/95
2 2
11a_326
1

detected by
an unknotting move
1-6t+19t^2-36t^3+45t^4-36t^5+19t^6-6t^7+t^8
Seifert matrix of 11a_326
1 0 0 0 1 0 1 1
-1 -1 -1 0 0 -1 -1 -1
-1 0 -1 0 0 0 -1 0
0 0 0 -1 0 0 0 0
0 0 0 -1 1 0 0 0
-1 0 -1 0 0 -1 -1 -1
0 0 0 -1 1 0 1 1
0 0 0 -1 1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-3-5t^-2+12t^-1-15+12t-5t^2+t^3
169
First homology
of the double branched cover of 11a_326
Z/169
0 0
11a_327
1

detected by
an unknotting move
3-17t+44t^2-59t^3+44t^4-17t^5+3t^6
Seifert matrix of 11a_327
-1 0 0 0 -1 0
0 -2 0 0 -1 0
0 1 1 -1 1 1
0 1 0 -1 1 0
0 -1 0 0 -2 0
1 1 0 -1 1 1
1
Generator of the Alexander module
(-7-77t+301t^2-413t^3+147t^4,5+55t-215t^2+295t^3-105t^4,1+15t-121t^2+229t^3-58t^4-249t^5+126t^6,7+77t-301t^2+413t^3-147t^4,-8-93t+533t^2-941t^3+419t^4+435t^5-252t^6,-3-33t+129t^2-177t^3+63t^4)
the Blanchfield form on it
x
187
First homology
of the double branched cover of 11a_327
Z/187
-2 2
11a_328
2

detected by
the signature
-3+16t-34t^2+43t^3-34t^4+16t^5-3t^6
Seifert matrix of 11a_328
-1 0 0 0 -1 0
0 -2 0 0 -1 0
1 1 1 -1 1 0
0 1 0 -1 1 0
0 -1 0 0 -2 0
-1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,t,0,1,0)
the Blanchfield form on it
-3t^-2+10t^-1-14+10t-3t^2
149
First homology
of the double branched cover of 11a_328
Z/149
-4 4
11a_329
2

detected by
the signature
11-36t+51t^2-36t^3+11t^4
Seifert matrix of 11a_329
-3 0 -1 2
-1 -2 -1 1
-1 -1 -2 1
1 0 0 -2
2
145
First homology
of the double branched cover of 11a_329
Z/145
-4 4
11a_330
2

detected by
the signature
1-5t+12t^2-17t^3+19t^4-17t^5+12t^6-5t^7+t^8
Seifert matrix of 11a_330
1 0 1 0 1 1 1 1
-1 -1 -1 0 0 -1 -1 0
0 0 1 -1 1 1 0 1
0 0 0 -1 0 0 0 0
0 0 0 -1 1 0 0 0
0 0 0 -1 1 1 0 1
0 0 1 -1 1 1 1 1
0 0 0 -1 1 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+15-12t+5t^2-t^3
89
First homology
of the double branched cover of 11a_330
Z/89
4 4
11a_331
1

detected by
an unknotting move
2-11t+27t^2-35t^3+27t^4-11t^5+2t^6
Seifert matrix of 11a_331
1 0 -1 0 1 1
-1 -1 1 0 0 0
0 0 2 1 -1 -1
0 0 0 -1 0 0
0 0 0 -1 1 0
0 0 0 -1 1 1
1
Generator of the Alexander module
(0,-3+t,1,0,1,0)
the Blanchfield form on it
-2t^-2+9t^-1-14+9t-2t^2
115
First homology
of the double branched cover of 11a_331
Z/115
2 2
11a_332
2

detected by
the Nakanishi index
1-7t+22t^2-40t^3+49t^4-40t^5+22t^6-7t^7+t^8
Seifert matrix of 11a_332
1 0 -1 0 0 0 1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
1 -1 -1 1 1 0 1 0
1 0 -1 0 1 0 1 0
-1 0 0 -1 -1 -1 0 0
0 0 0 0 0 0 1 0
-1 0 0 0 -1 -1 0 -1
2
189
First homology
of the double branched cover of 11a_332
Z/63+Z/3
0 0
11a_333
2

detected by
the Lickorish test
4-16t+25t^2-16t^3+4t^4
Seifert matrix of 11a_333
-1 1 -1 0
0 2 0 0
0 1 -1 1
0 0 0 2
1 or 2
65
First homology
of the double branched cover of 11a_333
Z/65
0 0
11a_334
4

detected by
the signature
2-4t+6t^2-8t^3+9t^4-8t^5+6t^6-4t^7+2t^8
Seifert matrix of 11a_334
-1 -1 0 0 -1 -1 0 0
0 -1 0 0 0 -1 0 0
0 0 -1 -1 0 -1 0 -1
0 0 0 -1 0 -1 0 0
0 -1 0 0 -1 -1 0 0
0 0 0 0 0 -2 0 0
0 0 -1 -1 0 -1 -1 -1
0 0 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
2t^-3-4t^-2+6t^-1-7+6t-4t^2+2t^3
49
First homology
of the double branched cover of 11a_334
Z/49
-8 8
11a_335
3

detected by
the signature
4-10t+15t^2-17t^3+15t^4-10t^5+4t^6
Seifert matrix of 11a_335
-1 -1 0 0 -1 -1
0 -1 0 0 0 -1
0 0 -2 1 0 1
0 0 0 -1 0 -1
0 -1 0 0 -1 -1
0 0 0 0 0 -2
1 or 2
75
First homology
of the double branched cover of 11a_335
Z/75
-6 6
11a_336
3

detected by
the signature
4-9t+11t^2-11t^3+11t^4-9t^5+4t^6
Seifert matrix of 11a_336
-1 -1 0 -1 0 -1
0 -1 0 -1 0 0
0 0 -2 0 0 0
0 0 -1 -2 0 0
-1 -1 0 -1 -1 -1
0 -1 0 -1 0 -1
1 or 2
59
First homology
of the double branched cover of 11a_336
Z/59
-6 6
11a_337
2

detected by
the signature
8-22t+29t^2-22t^3+8t^4
Seifert matrix of 11a_337
-2 1 0 1
0 -1 0 -1
0 0 -2 0
0 0 -1 -2
1 or 2
89
First homology
of the double branched cover of 11a_337
Z/89
-4 4
11a_338
4

detected by
the signature
2-5t+9t^2-12t^3+13t^4-12t^5+9t^6-5t^7+2t^8
Seifert matrix of 11a_338
-1 -1 0 -1 -1 -1 -1 0
0 -1 0 -1 0 -1 -1 0
0 0 -1 -1 0 -1 -1 0
0 0 0 -2 0 -1 -2 0
0 -1 0 -1 -1 -1 -1 0
0 0 0 -2 0 -2 -2 0
0 0 0 -1 0 -1 -2 0
0 0 -1 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
2t^-3-4t^-2+6t^-1-7+6t-4t^2+2t^3
69
First homology
of the double branched cover of 11a_338
Z/69
-8 8
11a_339
3

detected by
the signature
3-7t+11t^2-13t^3+11t^4-7t^5+3t^6
Seifert matrix of 11a_339
-1 -1 0 1 -1 0
0 -1 0 1 0 0
0 0 -1 1 0 0
0 0 0 -3 0 0
0 -1 0 1 -1 0
0 0 -1 1 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
3t^-2-5t^-1+5-5t+3t^2
55
First homology
of the double branched cover of 11a_339
Z/55
-6 6
11a_340
3

detected by
the signature
4-11t+18t^2-21t^3+18t^4-11t^5+4t^6
Seifert matrix of 11a_340
-1 -1 0 -1 -1 0
0 -2 -1 -1 -2 0
0 0 -2 0 0 0
0 -2 -1 -2 -2 0
0 -1 -1 -1 -2 0
-1 -1 0 -1 -1 -1
2
87
First homology
of the double branched cover of 11a_340
Z/87
-6 6
11a_341
2

detected by
the signature
6-15t+19t^2-15t^3+6t^4
Seifert matrix of 11a_341
-1 1 0 0
0 -3 1 0
0 0 -2 0
-1 1 0 -1
1
Generator of the Alexander module
(0,1,0,-1+t)
the Blanchfield form on it
6t^-1-11+6t
61
First homology
of the double branched cover of 11a_341
Z/61
-4 4
11a_342
2

detected by
the signature
4-7t+7t^2-7t^3+4t^4
Seifert matrix of 11a_342
-1 -1 -1 -1
0 -1 0 -1
0 -1 -1 -1
0 0 0 -4
1
Generator of the Alexander module
(-t,1,2,1)
the Blanchfield form on it
8t^-1-13+8t
29
First homology
of the double branched cover of 11a_342
Z/29
-4 4
11a_343
1

detected by
an unknotting move
8-15t+8t^2
Seifert matrix of 11a_343
-2 0
-1 -4
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
-2t^-1+4-2t
31
First homology
of the double branched cover of 11a_343
Z/31
-2 2
11a_344
2

detected by
the signature
-3+15t-29t^2+35t^3-29t^4+15t^5-3t^6
Seifert matrix of 11a_344
-1 0 0 0 -1 0
0 -2 0 0 -1 0
0 1 1 -1 0 0
0 1 0 -1 1 0
0 -1 0 0 -2 0
-1 0 0 0 -1 -1
1 or 2
129
First homology
of the double branched cover of 11a_344
Z/129
-4 4
11a_345
1

detected by
an unknotting move
-5+23t-35t^2+23t^3-5t^4
Seifert matrix of 11a_345
-3 1 0 0
1 -2 0 0
0 1 1 -1
-1 1 0 -1
1
Generator of the Alexander module
(0,-1,t,3-2t)
the Blanchfield form on it
-30t^-1+53-30t
91
First homology
of the double branched cover of 11a_345
Z/91
-2 2
11a_346
2

detected by
the signature
-1+5t-12t^2+18t^3-21t^4+18t^5-12t^6+5t^7-t^8
Seifert matrix of 11a_346
-1 0 -1 -1 -1 0 -1 0
-1 -1 -1 -1 -1 0 -1 0
0 0 -1 -1 -1 -1 -1 0
0 0 0 -1 -1 -1 0 0
0 0 0 0 -1 -1 0 0
0 0 0 0 0 1 0 0
0 0 0 -1 -1 -1 -1 0
-1 0 -1 -1 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,-t)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
93
First homology
of the double branched cover of 11a_346
Z/93
-4 4
11a_347
2

detected by
the Lickorish test
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 11a_347
-1 0 -1 0 1 0
-1 -1 -1 0 1 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 0 1 1 -2 0
-1 0 0 0 1 1
2
111
First homology
of the double branched cover of 11a_347
Z/111
-2 2
11a_348
2

detected by
the signature
1-7t+19t^2-29t^3+33t^4-29t^5+19t^6-7t^7+t^8
Seifert matrix of 11a_348
1 0 0 0 0 -1 1 0
-1 -1 0 -1 -1 0 -1 -1
0 0 -1 0 0 -1 0 0
-1 0 0 -1 -1 0 0 -1
-1 0 0 0 -1 0 0 0
0 0 0 0 0 -1 0 0
0 0 -1 0 0 -1 1 0
-1 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,3+3t-t^2+6t^3-5t^4+t^5,-t+t^2-3t^3+t^4,-1+t-3t^2+t^3,2t-2t^2+6t^3-2t^4,0,0,-2t^2+2t^3-6t^4+2t^5)
the Blanchfield form on it
x
145
First homology
of the double branched cover of 11a_348
Z/145
-4 4
11a_349
1

detected by
an unknotting move
2-14t+37t^2-49t^3+37t^4-14t^5+2t^6
Seifert matrix of 11a_349
1 0 0 -1 1 0
-1 -1 0 0 -1 1
0 0 -1 -1 0 0
0 0 0 -1 0 0
0 0 -1 -1 1 0
1 0 0 0 0 -2
1
Generator of the Alexander module
(0,-5+4t+45t^2+102t^3-123t^4+40t^5-4t^6,3+8t+6t^2-39t^3+24t^4-4t^5,0,-5+4t+30t^2+38t^3-40t^4+8t^5,15t+15t^2-80t^3-72t^4+80t^5-16t^6)
the Blanchfield form on it
x
155
First homology
of the double branched cover of 11a_349
Z/155
-2 2
11a_350
1

detected by
an unknotting move
1-7t+21t^2-39t^3+49t^4-39t^5+21t^6-7t^7+t^8
Seifert matrix of 11a_350
1 0 0 1 0 -1 1 1
-1 -1 0 0 -1 0 0 -1
0 0 -1 0 0 -1 0 0
0 0 -1 1 0 -1 1 0
-1 0 0 0 -1 0 0 0
0 0 0 0 0 -1 0 0
0 0 -1 0 0 -1 1 0
0 0 -1 1 0 -1 1 1
1
Generator of the Alexander module
(0,-2+t,0,0,3-5t+4t^2-t^3,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-7t^-1+10-7t+4t^2-t^3
185
First homology
of the double branched cover of 11a_350
Z/185
0 0
11a_351
1

detected by
an unknotting move
1-7t+20t^2-34t^3+41t^4-34t^5+20t^6-7t^7+t^8
Seifert matrix of 11a_351
1 0 1 0 0 -1 1 1
-1 -1 -1 0 -1 0 -1 -1
0 0 1 -1 0 -1 1 0
0 0 0 -1 0 -1 0 0
-1 0 0 0 -1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 -1 0 -1 1 0
0 0 1 -1 0 -1 1 1
1
Generator of the Alexander module
(0,0,0,0,5-14t+14t^2-6t^3+t^4,0,2-t,0)
the Blanchfield form on it
3t^-3-14t^-2+22t^-1-17+22t-14t^2+3t^3
165
First homology
of the double branched cover of 11a_351
Z/165
0 2
11a_352
2

detected by
the Nakanishi index
2-13t+32t^2-41t^3+32t^4-13t^5+2t^6
Seifert matrix of 11a_352
1 0 -1 0 0 -1
-1 -1 1 0 -1 0
0 0 2 1 0 1
0 0 0 -1 0 -1
-1 0 0 0 -1 0
0 0 0 0 0 -1
2
135
First homology
of the double branched cover of 11a_352
Z/45+Z/3
-2 2
11a_353
3

detected by
the signature
5-15t+26t^2-31t^3+26t^4-15t^5+5t^6
Seifert matrix of 11a_353
-1 -1 0 0 -1 0
0 -2 1 0 0 1
0 0 -2 0 -1 -2
-1 -1 0 -1 -1 0
0 -1 -1 0 -2 -1
0 0 -1 0 -1 -2
1 or 2
123
First homology
of the double branched cover of 11a_353
Z/123
-6 6
11a_354
2

detected by
the signature
9-26t+35t^2-26t^3+9t^4
Seifert matrix of 11a_354
-3 0 1 1
-1 -1 1 1
1 0 -2 -1
1 0 0 -2
2
105
First homology
of the double branched cover of 11a_354
Z/105
-4 4
11a_355
4

detected by
the signature
2-4t+6t^2-7t^3+7t^4-7t^5+6t^6-4t^7+2t^8
Seifert matrix of 11a_355
-1 -1 -1 0 -1 -1 -1 0
0 -1 -1 0 0 -1 -1 0
0 0 -1 0 0 0 -1 0
0 0 0 -1 0 0 -1 0
0 -1 -1 0 -1 -1 -1 0
0 0 -1 0 0 -1 -1 0
0 0 0 0 0 0 -2 0
0 0 0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
2t^-3-4t^-2+6t^-1-7+6t-4t^2+2t^3
45
First homology
of the double branched cover of 11a_355
Z/45
-8 8
11a_356
3

detected by
the signature
4-10t+16t^2-19t^3+16t^4-10t^5+4t^6
Seifert matrix of 11a_356
-1 1 -1 0 -1 0
0 -2 1 0 1 0
0 0 -1 0 -1 0
0 0 0 -1 -1 0
0 0 0 0 -2 0
0 0 0 -1 -1 -1
1 or 2
79
First homology
of the double branched cover of 11a_356
Z/79
-6 6
11a_357
3

detected by
the signature
4-11t+19t^2-23t^3+19t^4-11t^5+4t^6
Seifert matrix of 11a_357
-1 0 -1 0 0 0
0 -1 0 0 -1 0
0 0 -2 0 0 0
-1 0 -1 -1 0 0
0 0 -1 0 -2 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
4t^-2-9t^-1+11-9t+4t^2
91
First homology
of the double branched cover of 11a_357
Z/91
-6 6
11a_358
3

detected by
the signature
3-5t+5t^2-5t^3+5t^4-5t^5+3t^6
Seifert matrix of 11a_358
-1 -1 -1 1 -1 -1
0 -1 -1 1 0 -1
0 0 -1 1 0 0
0 0 0 -3 0 0
0 -1 -1 1 -1 -1
0 0 -1 1 0 -1
1
Generator of the Alexander module
(t^2+t^3,t^2-5t^3,1-t-t^2,-t+t^2,-t-t^2,-t)
the Blanchfield form on it
-103t^-3+231t^-2-314t^-1+346-314t+231t^2-103t^3
31
First homology
of the double branched cover of 11a_358
Z/31
-6 6
11a_359
2

detected by
the signature
6-13t+15t^2-13t^3+6t^4
Seifert matrix of 11a_359
-1 1 -1 1
0 -2 1 -1
0 0 -1 1
0 0 0 -3
1
Generator of the Alexander module
(-1-2t-2t^2+57t^3-128t^4+122t^5-38t^6-164t^7+334t^8-328t^9+232t^10-96t^11,0,0,-2-7t-18t^2+78t^3-212t^4+334t^5-328t^6+232t^7-96t^8)
the Blanchfield form on it
x
53
First homology
of the double branched cover of 11a_359
Z/53
-4 4
11a_360
2

detected by
the signature
6-14t+17t^2-14t^3+6t^4
Seifert matrix of 11a_360
-1 0 -1 0
0 -3 1 0
0 0 -2 0
-1 0 -1 -1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-2t^-2+5t^-1-6+5t-2t^2
57
First homology
of the double branched cover of 11a_360
Z/57
-4 4
11a_361
2

detected by
the signature
7-17t+21t^2-17t^3+7t^4
Seifert matrix of 11a_361
-3 0 -1 0
1 -1 1 0
-2 0 -3 0
1 -1 1 -1
1 or 2
69
First homology
of the double branched cover of 11a_361
Z/69
-4 4
11a_362
1

detected by
an unknotting move
10-19t+10t^2
Seifert matrix of 11a_362
-3 -2
-1 -4
1
Generator of the Alexander module
(-2+3t,-3+4t)
the Blanchfield form on it
35t^-2-142t^-1+214-142t+35t^2
39
First homology
of the double branched cover of 11a_362
Z/39
-2 2
11a_363
2

detected by
the Lickorish test
9-17t+9t^2
Seifert matrix of 11a_363
-3 0
-1 -3
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
-3t^-1+6-3t
35
First homology
of the double branched cover of 11a_363
Z/35
-2 2
11a_364
4

detected by
the signature
2-3t+3t^2-3t^3+3t^4-3t^5+3t^6-3t^7+2t^8
Seifert matrix of 11a_364
-1 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -1 0 -1 -1 -1
0 0 -1 -1 0 0 -1 -1
0 0 0 -1 0 0 0 -1
0 -1 -1 -1 -1 -1 -1 -1
0 0 -1 -1 0 -1 -1 -1
0 0 0 -1 0 0 -1 -1
0 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
2t^-3-3t^-2+3t^-1-3+3t-3t^2+2t^3
25
First homology
of the double branched cover of 11a_364
Z/25
-8 8
11a_365
3

detected by
the signature
4-8t+9t^2-9t^3+9t^4-8t^5+4t^6
Seifert matrix of 11a_365
-1 -1 1 -1 -1 -1
0 -1 1 -1 0 -1
0 0 -2 1 0 1
0 0 0 -1 0 -1
0 -1 1 -1 -1 -1
0 0 0 0 0 -2
1 or 2
51
First homology
of the double branched cover of 11a_365
Z/51
-6 6
11a_366
2

detected by
the Nakanishi index
8-20t+25t^2-20t^3+8t^4
Seifert matrix of 11a_366
-2 1 1 1
0 -1 -1 -1
0 0 -2 0
0 0 -1 -2
2
81
First homology
of the double branched cover of 11a_366
Z/27+Z/3
-4 4
11a_367
5

detected by
the signature
1-t+t^2-t^3+t^4-t^5+t^6-t^7+t^8-t^9+t^10
Seifert matrix of 11a_367
-1 -1 -1 -1 -1 0 -1 -1 -1 -1
0 -1 -1 -1 -1 0 0 -1 -1 -1
0 0 -1 -1 -1 0 0 0 -1 -1
0 0 0 -1 -1 0 0 0 0 -1
0 0 0 0 -1 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -1 -1 0 -1 -1 -1 -1
0 0 -1 -1 -1 0 0 -1 -1 -1
0 0 0 -1 -1 0 0 0 -1 -1
0 0 0 0 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-4-t^-3+t^-2-t^-1+1-t+t^2-t^3+t^4
11
First homology
of the double branched cover of 11a_367
Z/11
-10 10
11n_1
1

detected by
an unknotting move
-1+7t-11t^2+7t^3-t^4
Seifert matrix of 11n_1
1 0 0 0
1 1 -1 1
1 -1 0 0
0 0 0 1
1
Generator of the Alexander module
(0,-2,1,0)
the Blanchfield form on it
t^-1-5+t
27
First homology
of the double branched cover of 11n_1
Z/27
2 2
11n_2
2

detected by
the signature
-2+8t-12t^2+13t^3-12t^4+8t^5-2t^6
Seifert matrix of 11n_2
1 0 0 0 0 0
-1 -1 0 -1 0 1
0 0 -1 0 0 0
-1 0 -1 -1 0 1
0 0 0 0 -1 -1
1 0 1 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,-t,1)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
57
First homology
of the double branched cover of 11n_2
Z/57
-4 4
11n_3
1

detected by
an unknotting move
-3+11t-15t^2+11t^3-3t^4
Seifert matrix of 11n_3
1 0 0 0
1 1 -1 1
1 -1 -2 0
0 0 0 1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-2t^-2+9t^-1-14+9t-2t^2
43
First homology
of the double branched cover of 11n_3
Z/43
2 2
11n_4
1

detected by
an unknotting move
-1+5t-11t^2+15t^3-11t^4+5t^5-t^6
Seifert matrix of 11n_4
1 0 0 0 0 0
-1 -1 0 1 1 1
0 0 -1 -1 -1 -1
1 0 0 0 -1 -1
1 0 0 -1 -2 -1
1 0 0 0 -1 0
1
Generator of the Alexander module
(0,0,-t,1,1,1)
the Blanchfield form on it
-t^-1+3-t
49
First homology
of the double branched cover of 11n_4
Z/49
0 0
11n_5
1

detected by
an unknotting move
1-7t+17t^2-21t^3+17t^4-7t^5+t^6
Seifert matrix of 11n_5
1 0 0 0 0 0
-1 -1 0 1 1 1
0 0 -1 -1 -1 -1
1 0 0 -2 -1 -2
1 0 0 -1 0 -1
1 0 0 -1 -1 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-1+3-t
71
First homology
of the double branched cover of 11n_5
Z/71
-2 2
11n_6
1

detected by
an unknotting move
-1+3t-3t^2+3t^3-3t^4+3t^5-t^6
Seifert matrix of 11n_6
1 0 0 0 0 0
-1 -1 0 1 1 1
0 0 -1 -1 -1 -1
1 0 0 0 -1 -1
1 0 0 -1 0 -1
1 0 0 0 -1 0
1
Generator of the Alexander module
(0,0,-t,-t,1,0)
the Blanchfield form on it
t^-1-2+t
17
First homology
of the double branched cover of 11n_6
Z/17
0 2
11n_7
1

detected by
an unknotting move
1-6t+16t^2-21t^3+16t^4-6t^5+t^6
Seifert matrix of 11n_7
1 0 0 0 0 0
-1 -1 0 1 1 1
0 0 1 0 0 0
1 0 1 -1 0 -1
1 0 1 0 -1 0
1 0 1 0 0 -1
1
Generator of the Alexander module
(0,0,0,-t,t,1)
the Blanchfield form on it
t^-2-5t^-1+10-5t+t^2
67
First homology
of the double branched cover of 11n_7
Z/67
-2 2
11n_8
2

detected by
the signature
-1+6t-12t^2+15t^3-12t^4+6t^5-t^6
Seifert matrix of 11n_8
1 0 0 0 0 0
-1 -1 0 1 1 1
0 0 1 0 0 0
1 0 1 1 0 0
1 0 1 0 1 0
1 0 1 1 0 1
1
Generator of the Alexander module
(0,2-2t+2t^2-t^3,0,-5+8t-9t^2+7t^3-3t^4+t^5,0,0)
the Blanchfield form on it
2t^-2-9t^-1+9-9t+2t^2
53
First homology
of the double branched cover of 11n_8
Z/53
4 4
11n_9
2

detected by
the signature
-1+3t-t^2-4t^3+7t^4-4t^5-t^6+3t^7-t^8
Seifert matrix of 11n_9
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 -1 -1 0 -1
0 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,1,-t,1)
the Blanchfield form on it
-t^-3+4t^-2-7t^-1+9-7t+4t^2-t^3
5
First homology
of the double branched cover of 11n_9
Z/5
-4 4
11n_10
2

detected by
the signature
-1+7t-15t^2+19t^3-15t^4+7t^5-t^6
Seifert matrix of 11n_10
1 1 0 -1 0 1
0 -2 2 1 0 -1
0 0 1 0 0 0
0 1 -1 0 0 0
1 1 0 -1 1 1
0 -2 1 1 0 0
1
Generator of the Alexander module
(0,1-2t-2t^2,-1-t,t+t^2,-t+2t^2,-1-3t-2t^2-t^3)
the Blanchfield form on it
2t^-2-11t^-1+12-11t+2t^2
65
First homology
of the double branched cover of 11n_10
Z/65
4 4
11n_11
2

detected by
the Lickorish test
1-5t+13t^2-17t^3+13t^4-5t^5+t^6
Seifert matrix of 11n_11
-2 -3 -1 -4 -1 -1
-1 -2 -1 -3 -1 -1
0 0 1 0 0 0
-2 -5 -1 -6 -2 -2
0 0 0 0 -1 0
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+8-4t+t^2
55
First homology
of the double branched cover of 11n_11
Z/55
-2 2
11n_12
1

detected by
an unknotting move
1-3t+5t^2-3t^3+t^4
Seifert matrix of 11n_12
-5 -3 -1 -7
-2 -1 -1 -3
0 0 1 0
-6 -4 -1 -9
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-1-1+t
13
First homology
of the double branched cover of 11n_12
Z/13
0 0
11n_13
3

detected by
the signature
-1+3t-2t^2+t^3-t^4+t^5-2t^6+3t^7-t^8
Seifert matrix of 11n_13
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 -1 0 -1 0 -1
0 -1 -1 0 -1 0 0 0
0 -1 0 0 -1 -1 0 0
0 0 0 -1 0 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-2t^-1+1-2t+3t^2-t^3
15
First homology
of the double branched cover of 11n_13
Z/15
-6 6
11n_14
2

detected by
the signature
-1+6t-10t^2+11t^3-10t^4+6t^5-t^6
Seifert matrix of 11n_14
0 2 -1 0 -1 0
1 1 1 0 0 0
0 0 1 0 0 0
1 1 0 1 0 1
0 1 -1 0 0 0
1 1 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-2-6t^-1+9-6t+t^2
45
First homology
of the double branched cover of 11n_14
Z/45
4 4
11n_15
2

detected by
the Lickorish test
1-4t+8t^2-9t^3+8t^4-4t^5+t^6
Seifert matrix of 11n_15
-1 0 0 -1 0 -1
0 0 0 0 -1 0
0 0 1 0 0 0
0 0 0 -1 0 -1
0 -1 1 0 -2 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-2-4t^-1+7-4t+t^2
35
First homology
of the double branched cover of 11n_15
Z/35
-2 2
11n_16
2

detected by
the signature
-2+7t-7t^2+5t^3-7t^4+7t^5-2t^6
Seifert matrix of 11n_16
-1 -1 -1 0 -1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 -2 0 1
0 -1 -1 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+5t^-1-4+5t-4t^2+t^3
37
First homology
of the double branched cover of 11n_16
Z/37
-4 4
11n_17
1

detected by
an unknotting move
-2+12t-19t^2+12t^3-2t^4
Seifert matrix of 11n_17
0 1 -1 0
1 -2 2 -1
0 0 1 0
1 -2 1 1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-t^-2+6t^-1-10+6t-t^2
47
First homology
of the double branched cover of 11n_17
Z/47
2 2
11n_18
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 11n_18
-5 -3 1 -7
-4 -2 1 -6
0 0 1 0
-8 -5 1 -12
1
Generator of the Alexander module
(1,1,0,2)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
33
First homology
of the double branched cover of 11n_18
Z/33
0 0
11n_19
2

detected by
the signature
-1+2t-t^3+2t^5-t^6
Seifert matrix of 11n_19
1 0 0 0 0 0
-1 0 1 0 -1 0
1 1 -2 1 1 1
-1 -1 1 0 -1 0
-1 0 1 0 0 0
-1 -1 1 -1 -1 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-2-2t^-1+1-2t+t^2
5
First homology
of the double branched cover of 11n_19
Z/5
4 4
11n_20
1

detected by
an unknotting move
-2+6t-7t^2+6t^3-2t^4
Seifert matrix of 11n_20
1 0 0 0
-1 0 1 0
1 1 -2 -1
1 1 -1 1
1
Generator of the Alexander module
(0,t,-t,1)
the Blanchfield form on it
t^-1-2+t
23
First homology
of the double branched cover of 11n_20
Z/23
2 2
11n_21
1

detected by
an unknotting move
-1+5t-11t^2+15t^3-11t^4+5t^5-t^6
Seifert matrix of 11n_21
1 0 0 0 0 0
0 -1 0 0 0 0
0 -1 -2 -1 -2 -2
0 -1 -1 0 -1 -1
0 -1 -1 -1 -2 -1
1 -1 -1 -1 -1 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-1-1+t
49
First homology
of the double branched cover of 11n_21
Z/49
0 0
11n_22
1

detected by
an unknotting move
1-5t+13t^2-17t^3+13t^4-5t^5+t^6
Seifert matrix of 11n_22
-1 0 0 0 0 -1
0 -1 0 0 0 0
0 -1 -2 1 1 0
0 0 1 0 0 1
0 0 1 -1 0 1
0 0 0 0 0 -1
1
Generator of the Alexander module
(-1,0,t,1,-1,-1)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
55
First homology
of the double branched cover of 11n_22
Z/55
-2 2
11n_23
2

detected by
the signature
-1+3t-5t^2+4t^3-3t^4+4t^5-5t^6+3t^7-t^8
Seifert matrix of 11n_23
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
-1 -1 0 -1 0 0 1 0
0 0 -1 -1 -1 -1 0 0
-1 -1 0 -1 0 -1 1 0
0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+2t^-2-3t^-1+3-3t+2t^2-t^3
29
First homology
of the double branched cover of 11n_23
Z/29
-4 4
11n_24
1

detected by
an unknotting move
1-3t+5t^2-5t^3+5t^4-3t^5+t^6
Seifert matrix of 11n_24
0 0 0 -1 0 1
0 -1 0 0 0 0
0 -1 -1 -2 -1 0
-1 -1 -1 0 -1 -1
0 -1 -1 -1 0 0
0 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-1+1-t
23
First homology
of the double branched cover of 11n_24
Z/23
-2 2
11n_25
1

detected by
an unknotting move
1-5t+11t^2-13t^3+11t^4-5t^5+t^6
Seifert matrix of 11n_25
0 0 0 -1 0 1
0 -1 0 0 0 0
0 -1 -2 -2 -1 0
-1 -1 -1 0 -1 -1
0 -1 -1 -1 0 0
0 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,1,0,1,0)
the Blanchfield form on it
-t^-1+2-t
47
First homology
of the double branched cover of 11n_25
Z/47
-2 2
11n_26
1

detected by
an unknotting move
-1+5t-9t^2+11t^3-9t^4+5t^5-t^6
Seifert matrix of 11n_26
0 0 1 0 0 -1
0 -1 0 0 0 0
1 -1 -2 0 1 1
-1 0 0 -1 -1 -1
-1 0 1 0 0 -1
0 0 1 0 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-2-6t^-1+9-6t+t^2
41
First homology
of the double branched cover of 11n_26
Z/41
0 2
11n_27
3

detected by
the signature
1-3t+3t^2-2t^3+t^4-2t^5+3t^6-3t^7+t^8
Seifert matrix of 11n_27
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 -1 -1
0 0 0 1 0 -1 -1 -1
0 0 -1 0 -1 -1 -1 -1
-1 -1 0 0 0 -1 -1 -1
-1 -1 0 0 0 0 -1 0
-1 -1 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+3t^-1-3+3t-2t^2+t^3
19
First homology
of the double branched cover of 11n_27
Z/19
-6 6
11n_28
1

detected by
an unknotting move
1-5t+9t^2-5t^3+t^4
Seifert matrix of 11n_28
-3 -2 -2 0
-3 -3 -2 0
-2 -2 -1 0
-1 -1 -1 1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-1
21
First homology
of the double branched cover of 11n_28
Z/21
0 0
11n_29
2

detected by
the Lickorish test
-3+13t-19t^2+13t^3-3t^4
Seifert matrix of 11n_29
1 0 -1 0
0 -1 0 0
-1 -1 -2 0
1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
2t^-1-3+2t
51
First homology
of the double branched cover of 11n_29
Z/51
-2 2
11n_30
2

detected by
the signature
-2+6t-6t^2+5t^3-6t^4+6t^5-2t^6
Seifert matrix of 11n_30
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 0 0 1
0 0 0 1 0 1
0 0 -1 0 -1 1
1 1 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
33
First homology
of the double branched cover of 11n_30
Z/33
-4 4
11n_31
1

detected by
an unknotting move
-1+2t+2t^2-5t^3+2t^4+2t^5-t^6
Seifert matrix of 11n_31
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 -1 0 0
-1 -1 0 -1 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,0,0,1,0)
the Blanchfield form on it
1
3
First homology
of the double branched cover of 11n_31
Z/3
-2 2
11n_32
1

detected by
an unknotting move
-1+6t-16t^2+23t^3-16t^4+6t^5-t^6
Seifert matrix of 11n_32
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 1 0 0
-1 -1 0 -1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,-1,0,1,0)
the Blanchfield form on it
-t^-2+3t^-1-6+3t-t^2
69
First homology
of the double branched cover of 11n_32
Z/69
0 0
11n_33
2

detected by
the Lickorish test
1-6t+12t^2-13t^3+12t^4-6t^5+t^6
Seifert matrix of 11n_33
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 1 0 0
-1 -1 0 -1 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
51
First homology
of the double branched cover of 11n_33
Z/51
-2 2
11n_34
0

detected by
1
Seifert matrix of 11n_34
trivial
0
1
First homology
of the double branched cover of 11n_34
trivial
0 0
11n_35
2

detected by
the signature
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 11n_35
-2 -1 -3 -1 -1 -1
-2 -2 -3 -1 -1 -1
-1 -1 -6 -2 -2 -3
0 0 -1 -1 0 -1
-1 -1 -4 -1 -2 -2
0 0 -3 -1 -1 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
89
First homology
of the double branched cover of 11n_35
Z/89
-4 4
11n_36
1

detected by
an unknotting move
1-4t+8t^2-13t^3+15t^4-13t^5+8t^6-4t^7+t^8
Seifert matrix of 11n_36
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 0
0 0 -1 1 0 1 -1 1
0 0 -1 0 -1 0 -1 0
0 0 0 0 0 1 0 0
-1 -1 0 0 0 0 -1 0
0 0 -1 0 0 1 0 1
1
Generator of the Alexander module
(0,0,0,1,1,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-6t^-1+6-6t+4t^2-t^3
67
First homology
of the double branched cover of 11n_36
Z/67
-2 2
11n_37
2

detected by
the Lickorish test
-1+3t-5t^2+7t^3-5t^4+3t^5-t^6
Seifert matrix of 11n_37
-1 -1 0 0 -1 0
0 0 0 0 -1 0
0 0 1 0 0 1
0 0 0 -1 -1 0
0 -1 1 0 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-1-1+t
25
First homology
of the double branched cover of 11n_37
Z/25
0 0
11n_38
1

detected by
an unknotting move
-1+t+t^2+t^3-t^4
Seifert matrix of 11n_38
-1 -1 1 0
0 0 1 0
0 1 1 0
0 0 1 -1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
1
3
First homology
of the double branched cover of 11n_38
Z/3
-2 2
11n_39
1

detected by
an unknotting move
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 11n_39
1 0 0 0
1 -2 -1 -2
0 0 0 -1
1 0 -1 -2
1
Generator of the Alexander module
(0,1,0,1)
the Blanchfield form on it
t^-1-2+t
25
First homology
of the double branched cover of 11n_39
Z/25
0 0
11n_40
1

detected by
an unknotting move
2-8t+18t^2-23t^3+18t^4-8t^5+2t^6
Seifert matrix of 11n_40
-2 -1 0 -1 0 0
-2 -2 0 -1 0 0
1 1 0 0 0 1
-1 -1 -1 -2 -1 0
0 0 -1 -1 0 0
-1 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,1,0)
the Blanchfield form on it
-t^-1+2-t
79
First homology
of the double branched cover of 11n_40
Z/79
-2 2
11n_41
2

detected by
the signature
-1+4t-8t^2+9t^3-9t^4+9t^5-8t^6+4t^7-t^8
Seifert matrix of 11n_41
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 1 0 0
0 0 -1 -1 -1 0 -1 0
-1 -1 -1 0 -1 1 0 1
0 0 0 0 0 1 0 1
-1 -1 -1 0 -1 1 -1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(-2+2t+2t^2+2t^3-2t^4,-1+2t^3-t^4,-1+t+t^2+t^3-t^4,-t^2-t^3+t^4,t+t^2-t^3,t^2+t^3-t^4,1+3t+t^2-2t^3,0)
the Blanchfield form on it
-14t^-3+123t^-2-286t^-1+361-286t+123t^2-14t^3
53
First homology
of the double branched cover of 11n_41
Z/53
-4 4
11n_42
0

detected by
1
Seifert matrix of 11n_42
trivial
0
1
First homology
of the double branched cover of 11n_42
trivial
0 0
11n_43
2

detected by
the signature
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 11n_43
-2 -1 0 -1 -1 0
-2 -2 0 -1 -1 0
0 0 0 -1 -1 0
-1 -1 -1 -2 -1 0
0 0 0 0 -1 0
-1 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,t)
the Blanchfield form on it
2t^-1-3+2t
89
First homology
of the double branched cover of 11n_43
Z/89
-4 4
11n_44
1

detected by
an unknotting move
1-4t+8t^2-13t^3+15t^4-13t^5+8t^6-4t^7+t^8
Seifert matrix of 11n_44
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 1 0 1
0 0 -1 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 1
-1 -1 -1 0 1 1 -1 1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+7t^-1-9+7t-4t^2+t^3
67
First homology
of the double branched cover of 11n_44
Z/67
-2 2
11n_45
1

detected by
an unknotting move
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 11n_45
0 1 0 1
0 -1 1 -1
0 0 1 -2
1 -2 -1 -2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-1-2+t
25
First homology
of the double branched cover of 11n_45
Z/25
0 0
11n_46
1

detected by
an unknotting move
2-8t+18t^2-23t^3+18t^4-8t^5+2t^6
Seifert matrix of 11n_46
-2 -1 0 0 0 1
-2 -2 0 0 0 1
0 0 2 1 0 2
0 0 1 0 0 1
0 0 1 1 -1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(-3+2t,0,0,0,-2+t,0)
the Blanchfield form on it
4t^-2-10t^-1+17-10t+4t^2
79
First homology
of the double branched cover of 11n_46
Z/79
-2 2
11n_47
2

detected by
the signature
-1+4t-8t^2+9t^3-9t^4+9t^5-8t^6+4t^7-t^8
Seifert matrix of 11n_47
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 -1
0 0 -1 1 0 1 -1 -1
0 0 -1 0 -1 0 -1 -1
0 0 -1 0 0 1 0 0
-1 -1 0 0 0 0 -1 0
-1 -1 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,-t,-t,1,0,0)
the Blanchfield form on it
t^-3-2t^-2+2t^-1-2+2t-2t^2+t^3
53
First homology
of the double branched cover of 11n_47
Z/53
-4 4
11n_48
1

detected by
an unknotting move
-1+3t-6t^2+9t^3-6t^4+3t^5-t^6
Seifert matrix of 11n_48
2 1 0 0 1 0
1 0 0 0 1 0
0 1 -1 0 0 1
1 1 0 1 1 1
0 0 0 0 1 0
1 0 0 0 1 -1
1
Generator of the Alexander module
(0,1,t,-t,0,1)
the Blanchfield form on it
-t^-1+2-t
29
First homology
of the double branched cover of 11n_48
Z/29
0 0
11n_49
2

detected by
A(F_2)
-1+3t^2-t^4
Seifert matrix of 11n_49
3 2 0 1
2 1 0 1
0 1 -1 1
2 1 0 0
2
1
First homology
of the double branched cover of 11n_49
0
0 0
11n_50
1

detected by
an unknotting move
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 11n_50
0 1 0 0
2 3 0 2
-1 0 -1 -1
0 0 0 1
1
Generator of the Alexander module
(0,-2,1,0)
the Blanchfield form on it
t^-1-2+t
25
First homology
of the double branched cover of 11n_50
Z/25
0 0
11n_51
1

detected by
an unknotting move
-1+4t-6t^2+7t^3-6t^4+4t^5-t^6
Seifert matrix of 11n_51
-1 -1 0 -1 -1 -1
0 0 0 -1 -1 -1
0 0 -1 0 0 0
0 -1 0 -2 -1 -1
0 0 -1 -1 0 -1
0 0 0 -1 0 0
1
Generator of the Alexander module
(t,0,0,1,0,0)
the Blanchfield form on it
-t^-2+2t^-1+2t-t^2
29
First homology
of the double branched cover of 11n_51
Z/29
0 2
11n_52
1

detected by
an unknotting move
1-6t+14t^2-17t^3+14t^4-6t^5+t^6
Seifert matrix of 11n_52
-1 -1 0 -1 -1 -1
0 -2 0 -1 -2 -2
0 0 1 0 0 0
0 -1 0 0 -1 -1
0 -1 -1 -1 -2 -2
0 -1 0 -1 -1 -2
1
Generator of the Alexander module
(-t,0,0,1,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
59
First homology
of the double branched cover of 11n_52
Z/59
-2 2
11n_53
1

detected by
an unknotting move
-1+4t-8t^2+11t^3-8t^4+4t^5-t^6
Seifert matrix of 11n_53
-1 -1 0 -1 -1 -1
0 0 0 -1 -1 -1
0 0 -1 0 0 0
0 -1 0 0 -1 -1
0 0 -1 -1 0 -1
0 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,0,-t,1,1)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
37
First homology
of the double branched cover of 11n_53
Z/37
0 0
11n_54
1

detected by
an unknotting move
1-4t+10t^2-13t^3+10t^4-4t^5+t^6
Seifert matrix of 11n_54
-1 -1 0 -1 0 -1
0 0 0 -1 0 -1
0 0 -1 0 -1 -1
0 -1 0 -2 0 -1
0 0 0 0 -1 -1
0 0 0 -1 0 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
t^-1-1+t
43
First homology
of the double branched cover of 11n_54
Z/43
-2 2
11n_55
1

detected by
an unknotting move
-1+6t-14t^2+19t^3-14t^4+6t^5-t^6
Seifert matrix of 11n_55
-1 -1 0 -1 0 -1
0 -2 0 -1 0 -2
0 0 1 0 0 -1
0 -1 0 0 0 -1
0 0 1 0 1 -1
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
t^-2-4t^-1+5-4t+t^2
61
First homology
of the double branched cover of 11n_55
Z/61
0 0
11n_56
1

detected by
an unknotting move
1-4t+8t^2-9t^3+8t^4-4t^5+t^6
Seifert matrix of 11n_56
-1 -1 0 -1 0 -1
0 0 0 -1 0 -1
0 0 -1 0 -1 -1
0 -1 0 0 0 -1
0 0 0 0 -1 -1
0 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-2-2t^-1+3-2t+t^2
35
First homology
of the double branched cover of 11n_56
Z/35
-2 2
11n_57
3

detected by
the signature
1-3t+2t^2+t^3-3t^4+t^5+2t^6-3t^7+t^8
Seifert matrix of 11n_57
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 -1 -1
-1 -1 0 -1 0 0 0 -1
0 0 0 0 1 0 0 -1
0 0 -1 -1 0 -1 -1 -1
-1 -1 0 -1 0 0 -1 -1
-1 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,t,0,0,1)
the Blanchfield form on it
t^-3-t^-2+1-t^2+t^3
7
First homology
of the double branched cover of 11n_57
Z/7
-6 6
11n_58
2

detected by
the Lickorish test
1-4t+8t^2-9t^3+8t^4-4t^5+t^6
Seifert matrix of 11n_58
1 0 0 1 0 0
0 -1 0 0 0 0
0 -1 -2 -2 0 -1
0 -1 -1 0 0 -1
1 0 0 1 1 0
0 -1 -1 -1 0 0
1
Generator of the Alexander module
(0,0,1,0,-1,1)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
35
First homology
of the double branched cover of 11n_58
Z/35
2 2
11n_59
2

detected by
the signature
-1+6t-12t^2+15t^3-12t^4+6t^5-t^6
Seifert matrix of 11n_59
-1 0 0 0 -1 -1
0 -1 0 0 0 0
0 -1 -2 0 0 1
-1 0 0 -1 -1 -1
0 0 0 0 -1 -1
0 0 1 0 0 0
1
Generator of the Alexander module
(0,1,-2t,0,0,t)
the Blanchfield form on it
-t^-2+4t^-1-4+4t-t^2
53
First homology
of the double branched cover of 11n_59
Z/53
-4 4
11n_60
1

detected by
an unknotting move
1-3t+4t^2-5t^3+5t^4-5t^5+4t^6-3t^7+t^8
Seifert matrix of 11n_60
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 0
0 0 0 1 0 0 -1 0
0 0 0 1 1 0 -1 1
0 0 -1 0 0 -1 -1 0
-1 -1 0 0 0 0 -1 0
0 0 0 1 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-2t^-1+1-2t+3t^2-t^3
31
First homology
of the double branched cover of 11n_60
Z/31
-2 2
11n_61
2

detected by
the signature
-1+3t-4t^2+t^3+t^4+t^5-4t^6+3t^7-t^8
Seifert matrix of 11n_61
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 -1
0 0 0 1 0 0 0 0
-1 -1 0 0 -1 0 0 0
0 0 -1 0 -1 -1 0 -1
0 0 0 1 0 0 1 0
-1 -1 0 1 -1 0 1 -1
1
Generator of the Alexander module
(0,0,1+t^2,0,0,t^2,0,0)
the Blanchfield form on it
-t^-3+2t^-2-2t^-1-2t+2t^2-t^3
17
First homology
of the double branched cover of 11n_61
Z/17
-4 4
11n_62
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 11n_62
1 2 2 2
1 1 2 2
3 3 2 3
2 2 2 3
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
-t^-1+2-t
33
First homology
of the double branched cover of 11n_62
Z/33
0 0
11n_63
1

detected by
an unknotting move
-2+10t-15t^2+10t^3-2t^4
Seifert matrix of 11n_63
-2 0 0 1
0 -1 0 0
0 -1 -2 1
0 0 1 0
1
Generator of the Alexander module
(1,0,1,0)
the Blanchfield form on it
-t^-1+2-t
39
First homology
of the double branched cover of 11n_63
Z/39
-2 2
11n_64
2

detected by
the signature
-2+5t-3t^2+t^3-3t^4+5t^5-2t^6
Seifert matrix of 11n_64
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 0 -1 0
0 0 -1 -1 -1 0
-1 -1 0 0 -1 0
0 0 0 0 1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+2t^-2-t^-1-t+2t^2-t^3
21
First homology
of the double branched cover of 11n_64
Z/21
-4 4
11n_65
1

detected by
an unknotting move
3-8t+11t^2-8t^3+3t^4
Seifert matrix of 11n_65
0 1 2 1
0 0 2 1
1 1 3 1
1 1 2 2
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
t^-1-2+t
33
First homology
of the double branched cover of 11n_65
Z/33
0 2
11n_66
1

detected by
an unknotting move
1-7t+18t^2-23t^3+18t^4-7t^5+t^6
Seifert matrix of 11n_66
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 1 0 0
1 1 0 -1 -1 0
-1 -1 0 1 -1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
75
First homology
of the double branched cover of 11n_66
Z/75
-2 2
11n_67
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 11n_67
0 -2
-1 -5
1
Generator of the Alexander module
(1,-3t+2t^2)
the Blanchfield form on it
-3t^-1+8-3t
9
First homology
of the double branched cover of 11n_67
Z/9
0 0
11n_68
2

detected by
the Lickorish test
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 11n_68
-5 -4 -6 -4
-5 -5 -6 -4
-5 -5 -8 -6
-4 -4 -7 -5
1 or 2
63
First homology
of the double branched cover of 11n_68
Z/63
-2 2
11n_69
2

detected by
the signature
-2+7t-9t^2+9t^3-9t^4+7t^5-2t^6
Seifert matrix of 11n_69
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 -1
0 0 0 -1 1 -1
1 1 0 0 -2 1
-1 -1 0 0 0 -1
1 or 2
45
First homology
of the double branched cover of 11n_69
Z/45
-4 4
11n_70
2

detected by
the signature
-1+2t-2t^2+3t^3-2t^4+2t^5-t^6
Seifert matrix of 11n_70
-1 0 -1 0 0 -1
0 -1 0 -1 0 0
0 0 0 0 0 -1
0 0 0 -1 0 -1
0 -1 0 -1 -1 0
0 0 -1 0 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
13
First homology
of the double branched cover of 11n_70
Z/13
-4 4
11n_71
2

detected by
the Nakanishi index
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 11n_71
-1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 -1
0 -1 -2 -1 -2 -1
0 -1 -1 -2 -1 -1
0 -1 -1 -1 -2 -1
0 0 -1 -1 -1 0
2
63
First homology
of the double branched cover of 11n_71
Z/21+Z/3
-2 2
11n_72
2

detected by
the Nakanishi index
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 11n_72
-1 -1 -1 -1 -1 -1
0 -2 -1 -1 -1 -2
0 -1 -2 -1 -2 -1
0 -1 -1 0 -1 -1
0 -1 -1 -1 -2 -1
0 -1 -1 -1 -1 -2
2
81
First homology
of the double branched cover of 11n_72
Z/27+Z/3
-4 4
11n_73
2

detected by
the Nakanishi index
1-2t+3t^2-2t^3+t^4
Seifert matrix of 11n_73
0 -1 0 1
-1 -2 1 1
0 0 0 -1
0 0 -1 0
2
9
First homology
of the double branched cover of 11n_73
Z/3+Z/3
0 0
11n_74
2

detected by
the Nakanishi index
1-2t+3t^2-2t^3+t^4
Seifert matrix of 11n_74
0 0 -1 1
0 0 0 -1
-1 1 -2 1
0 -1 0 0
2
9
First homology
of the double branched cover of 11n_74
Z/3+Z/3
0 0
11n_75
2

detected by
the Nakanishi index
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 11n_75
-1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 -1
0 -1 0 -1 -1 -1
0 -1 -1 0 -1 -1
0 -1 0 -1 0 -1
0 0 -1 -1 -1 0
2
63
First homology
of the double branched cover of 11n_75
Z/21+Z/3
2 2
11n_76
2

detected by
the Nakanishi index
-1+3t-6t^2+8t^3-9t^4+8t^5-6t^6+3t^7-t^8
Seifert matrix of 11n_76
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 1 0
-1 -1 1 1 1 1 1 0
0 0 0 0 1 0 0 0
-1 -1 1 0 1 1 1 0
0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 1
2
45
First homology
of the double branched cover of 11n_76
Z/15+Z/3
4 4
11n_77
3

detected by
the signature
-1+t+2t^2-8t^3+11t^4-8t^5+2t^6+t^7-t^8
Seifert matrix of 11n_77
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 1 0
-1 -1 0 -1 0 0 1 0
0 0 -1 -1 -1 -1 0 0
-1 -1 0 -1 0 -1 1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
27
First homology
of the double branched cover of 11n_77
Z/9+Z/3
-6 6
11n_78
2

detected by
the Nakanishi index
-1+3t-6t^2+8t^3-9t^4+8t^5-6t^6+3t^7-t^8
Seifert matrix of 11n_78
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 1 0
-1 -1 0 -1 0 0 1 0
0 0 -1 -1 -1 -1 0 0
-1 -1 0 -1 0 -1 1 0
0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 1
2
45
First homology
of the double branched cover of 11n_78
Z/15+Z/3
-4 4
11n_79
2

detected by
the Lickorish test
-2+4t-3t^2+4t^3-2t^4
Seifert matrix of 11n_79
-1 0 -1 -1
0 -2 0 1
0 0 0 -1
0 0 -1 0
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
15
First homology
of the double branched cover of 11n_79
Z/15
-2 2
11n_80
2

detected by
the Lickorish test
-1+t+5t^2-9t^3+5t^4+t^5-t^6
Seifert matrix of 11n_80
1 0 0 0 0 0
1 0 -1 0 -1 0
1 -1 -2 0 -1 0
0 1 0 1 1 0
1 0 -1 0 0 0
0 1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-2-2t^-1+1-2t+t^2
15
First homology
of the double branched cover of 11n_80
Z/15
2 2
11n_81
3

detected by
the signature
1-3t+4t^2-4t^3+3t^4-4t^5+4t^6-3t^7+t^8
Seifert matrix of 11n_81
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 -1 -1 -1 0 -1 -1
0 0 0 0 0 1 0 0
0 0 -1 -1 0 0 -1 -1
-1 -1 0 -1 0 -1 0 -1
2
27
First homology
of the double branched cover of 11n_81
Z/9+Z/3
-6 6
11n_82
1

detected by
an unknotting move
1-3t+4t^2-3t^3+4t^4-3t^5+t^6
Seifert matrix of 11n_82
0 0 0 0 -1 0
-1 -1 -1 0 -1 0
-1 0 0 0 -1 0
-1 -1 -1 -1 -1 0
-1 0 -1 0 0 0
0 -1 -1 -1 -1 -1
1
Generator of the Alexander module
(0,1,1,1,1,-t)
the Blanchfield form on it
1
19
First homology
of the double branched cover of 11n_82
Z/19
-2 2
11n_83
2

detected by
A(F_2)
3-12t+19t^2-12t^3+3t^4
Seifert matrix of 11n_83
-1 -3 1 -1
-2 -3 2 -2
1 1 0 0
-1 -3 1 -2
2
49
First homology
of the double branched cover of 11n_83
Z/49
0 0
11n_84
1

detected by
an unknotting move
-2+9t-13t^2+9t^3-2t^4
Seifert matrix of 11n_84
3 -1 2 0
0 1 -1 0
2 -1 1 0
1 0 1 1
1
Generator of the Alexander module
(0,1,0,-2+t)
the Blanchfield form on it
-1
35
First homology
of the double branched cover of 11n_84
Z/35
2 2
11n_85
1

detected by
an unknotting move
-1+5t-10t^2+13t^3-10t^4+5t^5-t^6
Seifert matrix of 11n_85
-1 -1 -1 -1 1 0
0 0 -1 -1 1 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 1 1 1 -2 1
0 -1 -1 0 1 0
1
Generator of the Alexander module
(1,0,0,0,-t,t)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
45
First homology
of the double branched cover of 11n_85
Z/45
0 0
11n_86
1

detected by
an unknotting move
-1+4t-7t^2+9t^3-7t^4+4t^5-t^6
Seifert matrix of 11n_86
-1 0 0 0 -1 -1
-1 -1 0 0 0 -1
0 0 0 0 0 -1
0 0 0 1 0 0
0 0 -1 0 0 -1
0 0 -1 1 -1 -2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
1
33
First homology
of the double branched cover of 11n_86
Z/33
0 2
11n_87
1

detected by
an unknotting move
1-5t+12t^2-15t^3+12t^4-5t^5+t^6
Seifert matrix of 11n_87
1 0 0 0 0 0
-1 -1 -1 0 -1 0
-1 0 0 -1 0 0
0 0 0 1 -1 0
-1 0 -1 -1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-1-2+t
51
First homology
of the double branched cover of 11n_87
Z/51
2 2
11n_88
3

detected by
the signature
-1+3t-2t^2+t^4-2t^6+3t^7-t^8
Seifert matrix of 11n_88
-1 -1 -1 -1 -1 -1 0 0
0 -1 -1 -1 0 -1 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 -1 -1 -1 -1 0 0
0 0 -1 -1 0 -1 0 0
0 -1 -1 0 -1 -1 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1+t^2-t^3,t^2+t^4-t^5,0,0,-t-t^4+t^5)
the Blanchfield form on it
x
11
First homology
of the double branched cover of 11n_88
Z/11
-6 6
11n_89
2

detected by
the signature
-1+7t-14t^2+17t^3-14t^4+7t^5-t^6
Seifert matrix of 11n_89
0 2 2 -1 -1 2
1 1 0 1 0 0
1 1 1 1 0 1
0 0 0 1 0 0
0 1 1 -1 0 1
1 1 0 1 0 1
1
Generator of the Alexander module
(2-2t-t^2+2t^3,0,-t^2+t^3,-t^2,-1+t+t^2-t^3,t)
the Blanchfield form on it
-209t^-2+344t^-1-365+344t-209t^2
61
First homology
of the double branched cover of 11n_89
Z/61
4 4
11n_90
2

detected by
the signature
-2+7t-8t^2+7t^3-8t^4+7t^5-2t^6
Seifert matrix of 11n_90
-1 1 -1 -1 0 0
0 -2 1 1 0 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 1 -1 0 -1 0
0 0 0 0 -1 -1
2
41
First homology
of the double branched cover of 11n_90
Z/41
-4 4
11n_91
2

detected by
A(F_2)
-1+8t-13t^2+8t^3-t^4
Seifert matrix of 11n_91
5 6 1 6
4 5 2 4
0 0 1 0
6 7 2 7
2
31
First homology
of the double branched cover of 11n_91
Z/31
2 2
11n_92
2

detected by
the Lickorish test
1-3t+3t^2-t^3+3t^4-3t^5+t^6
Seifert matrix of 11n_92
-1 -1 0 0 0 -1
0 0 -1 0 -1 -1
0 0 0 0 0 -1
0 0 0 1 0 0
0 0 -1 0 0 -1
0 -1 -1 1 -1 -2
1 or 2
15
First homology
of the double branched cover of 11n_92
Z/15
2 2
11n_93
3

detected by
the signature
3-7t+9t^2-9t^3+9t^4-7t^5+3t^6
Seifert matrix of 11n_93
-1 0 -1 -1 0 -1
0 -1 0 -1 -1 -1
0 0 -2 -1 0 -1
0 0 -2 -2 0 -1
0 0 -1 -1 -1 -1
0 0 -1 -1 0 -2
1 or 2
47
First homology
of the double branched cover of 11n_93
Z/47
-6 6
11n_94
1

detected by
an unknotting move
-1+6t-13t^2+17t^3-13t^4+6t^5-t^6
Seifert matrix of 11n_94
-1 0 -1 -1 0 -1
0 1 0 -1 0 -1
0 0 -2 -1 0 -1
0 0 -2 -2 0 -1
0 1 -1 -1 1 -1
0 0 -1 -1 0 0
1
Generator of the Alexander module
(1,0,0,0,1,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
57
First homology
of the double branched cover of 11n_94
Z/57
0 2
11n_95
2

detected by
the signature
-1+5t-7t^2+7t^3-7t^4+5t^5-t^6
Seifert matrix of 11n_95
-1 0 -1 -1 0 -1
0 -1 0 -1 -1 -1
0 0 -2 -1 0 -1
0 0 -2 -2 0 -1
0 0 -1 -1 -1 -1
0 0 -1 -1 0 0
1 or 2
33
First homology
of the double branched cover of 11n_95
Z/33
-4 4
11n_96
1

detected by
an unknotting move
1-2t+t^2+t^3+t^4-2t^5+t^6
Seifert matrix of 11n_96
-1 0 -1 -1 0 -1
0 -1 0 -1 -1 -1
0 0 0 0 0 -1
0 0 -1 0 0 -1
0 0 -1 -1 -1 -1
0 0 -1 -1 0 0
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
1
7
First homology
of the double branched cover of 11n_96
Z/7
-2 2
11n_97
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 11n_97
7 2
1 0
1
Generator of the Alexander module
(4-2t,1)
the Blanchfield form on it
-1
9
First homology
of the double branched cover of 11n_97
Z/9
0 0
11n_98
1

detected by
an unknotting move
-1+7t-16t^2+21t^3-16t^4+7t^5-t^6
Seifert matrix of 11n_98
1 0 0 0 0 0
0 1 0 0 0 0
1 0 1 1 1 1
-1 -1 0 -1 -1 -1
-1 -1 0 0 -1 0
-1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,-1-2t,1-t-3t^2,2+t+2t^2,-t+2t^2,1+t+2t^2)
the Blanchfield form on it
t^-1-2+t
69
First homology
of the double branched cover of 11n_98
Z/69
0 2
11n_99
1

detected by
an unknotting move
-3+10t-13t^2+10t^3-3t^4
Seifert matrix of 11n_99
-3 -4 -2 -4
-3 -2 -1 -3
-1 -1 0 -1
-3 -2 -1 -2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
39
First homology
of the double branched cover of 11n_99
Z/39
2 2
11n_100
1

detected by
an unknotting move
2-11t+19t^2-11t^3+2t^4
Seifert matrix of 11n_100
1 0 0 0
0 -1 0 0
1 0 -2 -1
1 1 0 1
1
Generator of the Alexander module
(0,0,-1,-1)
the Blanchfield form on it
t^-1-2+t
45
First homology
of the double branched cover of 11n_100
Z/45
0 0
11n_101
1

detected by
an unknotting move
-2+10t-15t^2+10t^3-2t^4
Seifert matrix of 11n_101
1 0 0 0
0 1 0 0
1 0 1 -1
1 1 0 -2
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-1
39
First homology
of the double branched cover of 11n_101
Z/39
2 2
11n_102
1

detected by
an unknotting move
-1+t+t^2+t^3-t^4
Seifert matrix of 11n_102
1 0 0 0
0 -1 0 0
1 0 1 -1
1 1 0 1
1
Generator of the Alexander module
(0,1,2t,1)
the Blanchfield form on it
3t^-1-7+3t
3
First homology
of the double branched cover of 11n_102
Z/3
2 2
11n_103
2

detected by
the signature
-1+7t-15t^2+19t^3-15t^4+7t^5-t^6
Seifert matrix of 11n_103
-1 0 -1 0 0 1
0 1 0 0 0 0
0 0 1 0 0 0
-1 0 0 1 1 0
0 0 0 0 1 0
0 1 1 0 0 1
1 or 2
65
First homology
of the double branched cover of 11n_103
Z/65
4 4
11n_104
3

detected by
the signature
-1+3t-2t^2-2t^3+5t^4-2t^5-2t^6+3t^7-t^8
Seifert matrix of 11n_104
-1 0 0 0 0 0 0 0
0 1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 -1
-1 0 -1 0 -1 0 0 0
0 0 0 -1 -1 -1 -1 -1
0 0 0 -1 -1 0 -1 -1
-1 0 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,1+2t-3t^2+t^3,1-t,0,0,0,0,0)
the Blanchfield form on it
-2t^-3+3t^-2+2t^-1-4+2t+3t^2-2t^3
3
First homology
of the double branched cover of 11n_104
Z/3
-6 6
11n_105
2

detected by
the signature
-1+7t-16t^2+21t^3-16t^4+7t^5-t^6
Seifert matrix of 11n_105
-2 0 -1 -1 0 -1
0 -1 0 0 -1 0
-2 0 -2 -1 0 -1
0 0 0 -1 0 0
0 0 0 0 -1 0
-1 1 -1 -1 1 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
69
First homology
of the double branched cover of 11n_105
Z/69
-4 4
11n_106
1

detected by
an unknotting move
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 11n_106
0 1 0 1 -1 1
0 0 -1 -1 0 -1
0 0 -1 0 0 0
1 -2 -1 -2 1 -2
0 1 0 1 0 1
0 0 -1 -1 0 0
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
27
First homology
of the double branched cover of 11n_106
Z/27
2 2
11n_107
2

detected by
the signature
1-3t+4t^2-2t^3+t^4-2t^5+4t^6-3t^7+t^8
Seifert matrix of 11n_107
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 -1
-1 0 -1 0 -1 0 0 0
0 1 0 0 0 1 0 0
0 1 0 -1 -1 1 -1 -1
-1 0 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-5+5t-3t^2+t^3
21
First homology
of the double branched cover of 11n_107
Z/21
-4 4
11n_108
2

detected by
the signature
-1+8t-17t^2+21t^3-17t^4+8t^5-t^6
Seifert matrix of 11n_108
2 1 1 1 1 1
1 2 1 1 2 1
0 0 1 0 0 0
0 0 0 1 0 0
1 1 1 1 2 1
0 1 0 1 1 0
1 or 2
73
First homology
of the double branched cover of 11n_108
Z/73
4 4
11n_109
2

detected by
the signature
-1+7t-13t^2+15t^3-13t^4+7t^5-t^6
Seifert matrix of 11n_109
1 0 0 1 0 0
-1 0 -1 0 -1 -1
-1 0 0 0 -1 0
0 0 0 1 0 0
-1 -1 -1 1 0 -1
-1 0 -1 0 -1 0
1 or 2
57
First homology
of the double branched cover of 11n_109
Z/57
4 4
11n_110
1

detected by
an unknotting move
-1+4t-9t^2+13t^3-9t^4+4t^5-t^6
Seifert matrix of 11n_110
2 0 2 1 0 2
0 -1 -1 0 -1 -1
1 0 2 1 0 2
0 0 1 0 0 1
1 0 2 1 1 2
1 0 3 1 0 2
1
Generator of the Alexander module
(0,3-2t,0,0,-1+t,0)
the Blanchfield form on it
t^-1-2+t
41
First homology
of the double branched cover of 11n_110
Z/41
0 0
11n_111
1

detected by
an unknotting move
-1+t+3t^2-5t^3+3t^4+t^5-t^6
Seifert matrix of 11n_111
0 0 0 0 -1 0
-1 -1 -1 0 -1 -1
-1 0 -1 0 -1 0
-1 0 0 -1 -1 0
-2 -1 -1 0 -1 -1
-1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,1,0,0,1,0)
the Blanchfield form on it
1
7
First homology
of the double branched cover of 11n_111
Z/7
-2 2
11n_112
1

detected by
an unknotting move
1-5t+13t^2-17t^3+13t^4-5t^5+t^6
Seifert matrix of 11n_112
-1 -1 -1 -1 0 -1
0 -2 -2 -1 0 -1
0 -1 -2 -1 0 -1
0 -2 -2 -2 0 -1
0 -1 0 -1 1 -1
0 -1 -1 -1 0 0
1
Generator of the Alexander module
(-t,0,0,0,0,1)
the Blanchfield form on it
-t^-1+2-t
55
First homology
of the double branched cover of 11n_112
Z/55
-2 2
11n_113
2

detected by
the Lickorish test
-1+9t-15t^2+9t^3-t^4
Seifert matrix of 11n_113
1 1 0 0
0 1 0 0
-1 1 0 -1
-1 0 -1 1
1 or 2
35
First homology
of the double branched cover of 11n_113
Z/35
2 2
11n_114
1

detected by
an unknotting move
3-13t+21t^2-13t^3+3t^4
Seifert matrix of 11n_114
2 1 1 1
1 1 2 1
2 2 1 2
1 2 2 1
1
Generator of the Alexander module
(0,1,3,t)
the Blanchfield form on it
15t^-1-27+15t
53
First homology
of the double branched cover of 11n_114
Z/53
0 0
11n_115
1

detected by
an unknotting move
-1+6t-18t^2+27t^3-18t^4+6t^5-t^6
Seifert matrix of 11n_115
1 0 0 0 0 0
-1 -1 0 -1 1 -1
0 0 1 0 0 0
-1 0 0 -1 1 0
0 0 -1 0 -1 -1
0 0 1 0 0 1
1
Generator of the Alexander module
(4+10t-2t^2+179t^3-32t^4-568t^5+527t^6-24t^7-178t^8+174t^9-96t^10+20t^11,-2+36t^2-160t^3+499t^4+807t^5-2575t^6+1780t^7+112t^8-1010t^9+808t^10-292t^11+40t^12,0,-8+16t-64t^2-78t^3+578t^4-666t^5+216t^6+164t^7-308t^8+192t^9-40t^10,-5+9t-53t^2+38t^3+181t^4-220t^5+1249t^6-2355t^7+1190t^8+504t^9-954t^10+65
the Blanchfield form on it
x
77
First homology
of the double branched cover of 11n_115
Z/77
0 0
11n_116
1

detected by
an unknotting move
-1+3t^2-t^4
Seifert matrix of 11n_116
1 1 0 0
0 1 0 0
-1 1 0 -1
-1 0 -1 -2
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
t^-1-2+t
1
First homology
of the double branched cover of 11n_116
0
0 0
11n_117
2

detected by
the Lickorish test
-3+9t-11t^2+9t^3-3t^4
Seifert matrix of 11n_117
0 0 -1 0
-1 -1 -1 0
-2 0 -1 -1
-1 0 -1 -2
1
Generator of the Alexander module
(0,-1+2t,0,3-2t)
the Blanchfield form on it
-16t^-3+80t^-2-171t^-1+214-171t+80t^2-16t^3
35
First homology
of the double branched cover of 11n_117
Z/35
-2 2
11n_118
2

detected by
the signature
-1+4t-4t^2+3t^3-4t^4+4t^5-t^6
Seifert matrix of 11n_118
-1 0 0 0 0 0
-1 -1 -1 0 0 0
-1 0 -1 0 0 0
1 1 1 -2 1 -1
0 -1 0 1 0 1
0 1 0 -2 1 -2
1 or 2
21
First homology
of the double branched cover of 11n_118
Z/21
-4 4
11n_119
1

detected by
an unknotting move
-1+6t-16t^2+23t^3-16t^4+6t^5-t^6
Seifert matrix of 11n_119
-1 0 0 0 0 0
0 0 0 -1 -1 0
-1 0 -1 0 0 0
1 -1 1 0 0 0
0 -1 0 -1 0 0
1 -1 1 0 0 1
1
Generator of the Alexander module
(0,0,0,1,1,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
69
First homology
of the double branched cover of 11n_119
Z/69
0 0
11n_120
1

detected by
an unknotting move
-1+4t-7t^2+8t^3-7t^4+8t^5-7t^6+4t^7-t^8
Seifert matrix of 11n_120
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 0 0 -1 0
0 1 0 -1 1 -1 -1 1
0 0 0 -1 0 -1 -1 0
-1 0 -1 0 0 0 -1 0
0 1 0 -1 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-1+1-t
47
First homology
of the double branched cover of 11n_120
Z/47
-2 2
11n_121
2

detected by
the signature
-1+6t-10t^2+11t^3-10t^4+6t^5-t^6
Seifert matrix of 11n_121
1 0 0 0 0 0
0 1 0 0 0 0
0 -1 1 0 0 0
1 0 1 1 1 1
-1 -1 0 0 -1 0
0 -1 1 0 0 1
1 or 2
45
First homology
of the double branched cover of 11n_121
Z/45
4 4
11n_122
1

detected by
an unknotting move
-2+7t-9t^2+7t^3-2t^4
Seifert matrix of 11n_122
5 4 0 2
2 1 0 1
2 1 1 1
1 1 0 1
1 or 2
27
First homology
of the double branched cover of 11n_122
Z/27
2 2
11n_123
1

detected by
an unknotting move
3-14t+23t^2-14t^3+3t^4
Seifert matrix of 11n_123
0 -1 0 -2
-2 -1 0 -3
1 1 -1 2
-4 -3 1 -6
1
Generator of the Alexander module
(30-12t-24t^2+12t^3,-20+8t+16t^2-8t^3,4-2t,-5+2t-8t^2+4t^3)
the Blanchfield form on it
-3712t^-4+14700t^-3-10166t^-2-35115t^-1+67282-35115t-10166t^2+14700t^3-3712t^4
57
First homology
of the double branched cover of 11n_123
Z/57
0 0
11n_124
1

detected by
an unknotting move
1-6t+14t^2-17t^3+14t^4-6t^5+t^6
Seifert matrix of 11n_124
1 0 0 0 0 0
-1 -1 0 -1 -1 -1
0 0 -1 1 0 1
0 0 0 -1 0 0
-1 0 0 -1 -1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,-4+t,1,0,-t,0)
the Blanchfield form on it
t^-2-4t^-1+5-4t+t^2
59
First homology
of the double branched cover of 11n_124
Z/59
-2 2
11n_125
1

detected by
an unknotting move
1-6t+15t^2-19t^3+15t^4-6t^5+t^6
Seifert matrix of 11n_125
-2 -1 -1 0 -1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
-1 0 0 -1 0 0
-1 -1 0 0 0 0
-1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
1
63
First homology
of the double branched cover of 11n_125
Z/63
-2 2
11n_126
3

detected by
the signature
3-6t+4t^2-t^3+4t^4-6t^5+3t^6
Seifert matrix of 11n_126
-1 0 0 0 0 0
0 -2 0 0 -1 1
-1 0 -1 0 0 0
-1 -1 -1 -1 0 0
0 -1 0 0 -2 1
-1 0 -1 0 0 -1
2
27
First homology
of the double branched cover of 11n_126
Z/3+Z/9
-6 6
11n_127
2

detected by
the Lickorish test
1-5t+13t^2-17t^3+13t^4-5t^5+t^6
Seifert matrix of 11n_127
0 0 -1 0 0 1
0 1 0 0 0 0
0 0 1 0 0 0
-1 1 0 0 0 0
0 0 0 0 1 1
1 -1 1 -1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-1+1-t
55
First homology
of the double branched cover of 11n_127
Z/55
2 2
11n_128
1

detected by
an unknotting move
1-5t+10t^2-11t^3+10t^4-5t^5+t^6
Seifert matrix of 11n_128
-1 0 -1 0 0 -1
0 0 0 0 0 -1
0 0 -1 0 -1 -1
-1 0 -1 -1 0 -1
0 -1 0 0 0 -1
0 -1 0 0 -1 0
1
Generator of the Alexander module
(0,0,0,-1,1,1)
the Blanchfield form on it
t^-2-5t^-1+9-5t+t^2
43
First homology
of the double branched cover of 11n_128
Z/43
-2 2
11n_129
1

detected by
an unknotting move
1-4t+10t^2-13t^3+10t^4-4t^5+t^6
Seifert matrix of 11n_129
0 -1 0 0 -1 -1
0 0 0 0 0 -1
0 0 -1 -1 0 -1
-1 -1 0 0 -1 -1
0 -1 0 0 0 -1
-1 -1 0 -1 -1 0
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+2t^-1-3+2t-t^2
43
First homology
of the double branched cover of 11n_129
Z/43
2 2
11n_130
1

detected by
an unknotting move
-1+5t-12t^2+17t^3-12t^4+5t^5-t^6
Seifert matrix of 11n_130
0 -1 0 -1 -1 -1
-1 0 0 0 -1 0
-1 -1 -1 -1 -1 -1
0 0 0 -1 0 0
-2 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 0
1
Generator of the Alexander module
(0,-3+2t,0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
53
First homology
of the double branched cover of 11n_130
Z/53
0 0
11n_131
1

detected by
an unknotting move
1-6t+16t^2-21t^3+16t^4-6t^5+t^6
Seifert matrix of 11n_131
1 0 0 0 0 0
-1 -1 1 0 0 0
1 0 1 0 0 0
0 -1 1 1 -1 1
-1 -1 1 0 -1 0
0 -1 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,-3+3t-t^2,0,-2+2t-t^2)
the Blanchfield form on it
t^-1-2+t
67
First homology
of the double branched cover of 11n_131
Z/67
2 2
11n_132
2

detected by
the Lickorish test
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 11n_132
-1 -1 0 -1
0 0 1 -1
0 0 1 1
0 -1 1 0
1
Generator of the Alexander module
(2-t,0,1,t)
the Blanchfield form on it
2t^-1-3+2t
25
First homology
of the double branched cover of 11n_132
Z/25
0 0
11n_133
3

detected by
the Stoimenow criterion
1-4t+6t^2-2t^3-t^4-2t^5+6t^6-4t^7+t^8
Seifert matrix of 11n_133
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 -1 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 0 -1 0 0
0 0 0 -1 -1 -1 0 0
-1 0 -1 0 0 -1 0 0
0 0 0 -1 -1 -1 -1 0
0 1 0 -1 -1 0 -1 1
2
25
First homology
of the double branched cover of 11n_133
Z/5+Z/5
-4 4
11n_134
1

detected by
an unknotting move
-3+12t-17t^2+12t^3-3t^4
Seifert matrix of 11n_134
1 -1 1 -1
0 0 1 -1
0 1 0 1
-1 -1 0 1
1
Generator of the Alexander module
(-1,0,0,1)
the Blanchfield form on it
-1
47
First homology
of the double branched cover of 11n_134
Z/47
2 2
11n_135
2

detected by
the signature
-1+2t-t^3+2t^5-t^6
Seifert matrix of 11n_135
1 0 0 0 0 0
-1 -1 0 -1 1 1
1 1 -2 1 -2 -2
-1 0 0 -1 1 1
1 1 -1 1 -2 -1
1 1 -1 1 -2 -2
1
Generator of the Alexander module
(0,0,0,t,0,1)
the Blanchfield form on it
-t^-2+t^-1+2+t-t^2
5
First homology
of the double branched cover of 11n_135
Z/5
-4 4
11n_136
3

detected by
the signature
3-8t+13t^2-15t^3+13t^4-8t^5+3t^6
Seifert matrix of 11n_136
-1 -1 -1 0 -1 0
0 -2 -1 0 -2 0
0 -1 -2 0 -1 0
0 1 1 -1 1 0
0 -1 -1 0 -2 0
0 1 0 -1 1 -1
1 or 2
63
First homology
of the double branched cover of 11n_136
Z/63
-6 6
11n_137
2

detected by
the signature
-1+7t-13t^2+15t^3-13t^4+7t^5-t^6
Seifert matrix of 11n_137
1 0 0 0 0 0
0 1 0 0 0 0
0 1 1 0 0 1
1 0 0 1 1 0
-1 -1 -1 0 -1 -1
0 1 0 0 0 1
1 or 2
57
First homology
of the double branched cover of 11n_137
Z/57
4 4
11n_138
1

detected by
an unknotting move
-2+4t-3t^2+4t^3-2t^4
Seifert matrix of 11n_138
-3 -2 0 -2
0 -1 0 0
-2 -1 -1 -1
-1 -1 0 0
1
Generator of the Alexander module
(2+2t^2,0,0,1)
the Blanchfield form on it
-t^-1+2-t
15
First homology
of the double branched cover of 11n_138
Z/15
-2 2
11n_139
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 11n_139
2 2
1 0
1
Generator of the Alexander module
(2,1)
the Blanchfield form on it
-2
9
First homology
of the double branched cover of 11n_139
Z/9
0 0
11n_140
2

detected by
the Lickorish test
-2+13t-21t^2+13t^3-2t^4
Seifert matrix of 11n_140
1 0 0 0
1 1 1 0
-1 0 -1 1
0 0 0 2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-2t^-1+3-2t
51
First homology
of the double branched cover of 11n_140
Z/51
2 2
11n_141
1

detected by
an unknotting move
-5+11t-5t^2
Seifert matrix of 11n_141
-7 -4
-3 -1
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
-t^-1+2-t
21
First homology
of the double branched cover of 11n_141
Z/21
0 0
11n_142
1

detected by
an unknotting move
1-8t+15t^2-8t^3+t^4
Seifert matrix of 11n_142
0 -1 0 -1
-1 -2 0 -1
-1 0 1 -1
-2 -2 0 -1
1
Generator of the Alexander module
(0,1,-t,0)
the Blanchfield form on it
4t^-1-9+4t
33
First homology
of the double branched cover of 11n_142
Z/33
0 0
11n_143
1

detected by
an unknotting move
-1+2t-t^2+t^3-t^4+2t^5-t^6
Seifert matrix of 11n_143
-1 -1 -1 0 0 -1
0 0 -1 1 0 -1
0 0 0 1 0 -1
0 0 0 1 0 0
0 -1 0 0 -1 -1
0 -1 -1 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
1
9
First homology
of the double branched cover of 11n_143
Z/9
0 2
11n_144
2

detected by
the signature
-1+7t-15t^2+19t^3-15t^4+7t^5-t^6
Seifert matrix of 11n_144
-1 -1 0 0 -1 -1
0 -2 -1 -1 0 -2
0 0 -1 0 0 0
0 -1 -1 -2 1 -1
0 -1 0 0 0 -1
0 -1 -1 -1 0 -2
1 or 2
65
First homology
of the double branched cover of 11n_144
Z/65
-4 4
11n_145
1

detected by
an unknotting move
1-t-3t^2+7t^3-3t^4-t^5+t^6
Seifert matrix of 11n_145
-1 0 0 0 0 0
0 1 -1 0 0 -1
1 0 0 1 1 1
-1 0 0 -1 0 0
1 0 0 1 0 1
0 0 1 0 1 2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-1
9
First homology
of the double branched cover of 11n_145
Z/9
0 0
11n_146
2

detected by
the Lickorish test
1-5t+15t^2-21t^3+15t^4-5t^5+t^6
Seifert matrix of 11n_146
-2 -1 0 0 -1 -2
0 -1 0 0 0 -1
-1 0 1 1 -1 -1
-1 -1 0 0 -1 -2
-2 -1 0 0 -2 -2
0 -1 0 -1 0 -1
1 or 2
63
First homology
of the double branched cover of 11n_146
Z/63
-2 2
11n_147
2

detected by
the signature
1-4t+7t^2-5t^3+3t^4-5t^5+7t^6-4t^7+t^8
Seifert matrix of 11n_147
-1 0 0 0 0 0 0 0
0 1 0 -1 0 0 -1 0
-1 0 -1 0 -1 0 0 0
0 0 -1 -1 0 -1 -1 0
-1 0 0 0 -1 0 0 0
-1 0 -1 0 -1 -1 0 0
0 0 -1 0 0 -1 -1 0
0 1 0 -1 0 -1 -1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
37
First homology
of the double branched cover of 11n_147
Z/37
-4 4
11n_148
3

detected by
the new u==2 criterion
-1+5t-10t^2+14t^3-15t^4+14t^5-10t^6+5t^7-t^8
Seifert matrix of 11n_148
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 -1 0
-1 0 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 1 -1 0 -1 1 -1 1
0 0 -1 0 -1 0 -1 0
0 1 0 0 -1 0 -1 1
2
75
First homology
of the double branched cover of 11n_148
Z/15+Z/5
-2 2
11n_149
2

detected by
the signature
-1+4t-6t^2+4t^3-3t^4+4t^5-6t^6+4t^7-t^8
Seifert matrix of 11n_149
-1 0 -1 -1 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 -1 -1 0 -1 0 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 -1 0
0 0 0 1 0 1 0 0
-1 0 -1 0 0 0 -1 0
0 0 0 0 -1 0 -1 -1
1 or 2
33
First homology
of the double branched cover of 11n_149
Z/33
-4 4
11n_150
2

detected by
the Lickorish test
2-9t+17t^2-19t^3+17t^4-9t^5+2t^6
Seifert matrix of 11n_150
-1 0 -1 -1 0 0
-1 -1 -1 -1 0 0
0 0 -1 -1 0 -1
0 0 0 1 0 0
1 0 1 0 -2 0
0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,1,0,-1+2t,0)
the Blanchfield form on it
2t^-2-9t^-1+15-9t+2t^2
75
First homology
of the double branched cover of 11n_150
Z/75
-2 2
11n_151
1

detected by
an unknotting move
-2+6t-7t^2+6t^3-2t^4
Seifert matrix of 11n_151
-2 1 0 0
0 0 -1 0
-2 0 -2 0
-1 1 0 -1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
1
23
First homology
of the double branched cover of 11n_151
Z/23
-2 2
11n_152
1

detected by
an unknotting move
-2+6t-7t^2+6t^3-2t^4
Seifert matrix of 11n_152
-1 -1 -2 -1
0 -2 -2 -1
0 -3 -4 -2
0 -1 -2 0
1
Generator of the Alexander module
(-t,0,1,0)
the Blanchfield form on it
1
23
First homology
of the double branched cover of 11n_152
Z/23
-2 2
11n_153
1

detected by
an unknotting move
-1+4t-7t^2+10t^3-13t^4+10t^5-7t^6+4t^7-t^8
Seifert matrix of 11n_153
-1 0 -1 -1 -1 -1 0 0
-1 -1 -1 -1 -1 -1 0 0
0 0 -1 -1 -1 -1 -1 0
0 0 0 1 0 0 0 0
0 0 0 1 1 1 0 0
0 0 0 1 0 1 0 0
0 0 0 1 1 1 1 0
-1 0 -1 0 0 0 0 -1
1
Generator of the Alexander module
(12t-20t^2-2t^3+31t^4-48t^5+55t^6-41t^7+22t^8-9t^9+2t^10,1+5t-20t^2+34t^3-40t^4+37t^5-25t^6+13t^7-5t^8+t^9,10t-20t^2+23t^3-24t^4+17t^5-9t^6+4t^7-t^8,0,20t-40t^2+46t^3-48t^4+34t^5-18t^6+8t^7-2t^8,0,-20t+40t^2-51t^3+58t^4-43t^5+25t^6-12t^7+3t^8,5t-10t^2-11t^3+33t^4-42t^5+47t^6-34t^7+18t^8-8t^9+2t^10)
the Blanchfield form on it
x
57
First homology
of the double branched cover of 11n_153
Z/57
0 0
11n_154
1

detected by
an unknotting move
1-7t+19t^2-25t^3+19t^4-7t^5+t^6
Seifert matrix of 11n_154
3 0 3 3 -1 3
1 -1 1 1 -1 1
2 0 1 2 -1 2
2 0 2 2 -1 2
0 0 0 -1 0 -1
2 0 2 3 -1 2
1
Generator of the Alexander module
(0,-2+t,5-4t+t^2,0,0,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
79
First homology
of the double branched cover of 11n_154
Z/79
-2 2
11n_155
2

detected by
the Lickorish test
2-8t+11t^2-9t^3+11t^4-8t^5+2t^6
Seifert matrix of 11n_155
-1 0 -1 1 0 0
-1 -1 -1 1 0 0
0 0 -1 1 -1 0
0 0 0 2 0 0
0 0 0 -1 1 0
-1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-2-10t^-1+17-10t+2t^2
51
First homology
of the double branched cover of 11n_155
Z/51
-2 2
11n_156
1

detected by
an unknotting move
-1+7t-18t^2+25t^3-18t^4+7t^5-t^6
Seifert matrix of 11n_156
1 1 1 1 0 1
0 -1 0 0 0 0
0 1 1 1 1 1
0 -1 0 -2 0 -1
0 -1 0 -1 -1 0
0 -1 0 -1 0 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-1
77
First homology
of the double branched cover of 11n_156
Z/77
0 0
11n_157
2

detected by
the Lickorish test
-1+6t-15t^2+21t^3-15t^4+6t^5-t^6
Seifert matrix of 11n_157
-1 0 0 0 0 0
0 1 0 0 -1 0
0 1 0 -1 -1 -2
1 0 -1 0 0 -1
-1 0 0 0 -1 0
1 1 -1 -1 -1 -2
2
65
First homology
of the double branched cover of 11n_157
Z/65
0 0
11n_158
2

detected by
the signature
-1+4t-7t^2+7t^3-7t^4+7t^5-7t^6+4t^7-t^8
Seifert matrix of 11n_158
-1 0 -1 -1 -1 0 -1 0
-1 -1 -1 -1 -1 0 -1 0
0 0 -1 -1 -1 -1 -1 0
0 0 0 -1 -1 -1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 0
0 0 0 -1 -1 -1 -1 0
-1 0 -1 -1 0 0 -1 -1
1 or 2
45
First homology
of the double branched cover of 11n_158
Z/45
-4 4
11n_159
1

detected by
an unknotting move
1-6t+17t^2-23t^3+17t^4-6t^5+t^6
Seifert matrix of 11n_159
1 0 -1 0 1 -1
0 -1 -1 -1 1 -1
0 0 0 -1 1 0
0 0 0 1 0 0
0 0 1 0 0 1
0 0 -1 -1 1 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-1
71
First homology
of the double branched cover of 11n_159
Z/71
2 2
11n_160
1

detected by
an unknotting move
1-6t+16t^2-21t^3+16t^4-6t^5+t^6
Seifert matrix of 11n_160
1 1 0 1 1 1
0 -1 0 0 0 0
0 -1 -1 -1 -1 0
0 -1 0 -2 0 -1
0 -1 0 -1 -1 0
0 -1 0 -1 0 0
1
Generator of the Alexander module
(-t,0,0,0,1,0)
the Blanchfield form on it
-t^-1+2-t
67
First homology
of the double branched cover of 11n_160
Z/67
-2 2
11n_161
1

detected by
an unknotting move
2-8t+14t^2-15t^3+14t^4-8t^5+2t^6
Seifert matrix of 11n_161
-1 0 -1 0 1 0
-1 -1 -1 0 1 0
0 0 1 0 0 0
0 0 1 1 0 0
0 0 1 1 -2 0
-1 0 0 0 1 -1
1
Generator of the Alexander module
(0,4-104t+182t^2-286t^3+471t^4-357t^5+293t^6-139t^7-4t^8+20t^9,-3+69t-108t^2+258t^3-408t^4+366t^5-444t^6+231t^7+6t^8-30t^9,-2+46t-60t^2+166t^3-244t^4+229t^5-302t^6+159t^7+4t^8-20t^9,1-23t+40t^2-34t^3+61t^4-36t^5-t^6+5t^7,1-29t+46t^2-51t^3+77t^4-41t^5-t^6+5t^7)
the Blanchfield form on it
x
63
First homology
of the double branched cover of 11n_161
Z/63
-2 2
11n_162
2

detected by
the Lickorish test
-3+14t-21t^2+14t^3-3t^4
Seifert matrix of 11n_162
-2 -1 1 0
0 0 -1 0
0 -1 0 -1
1 1 -1 -1
2
55
First homology
of the double branched cover of 11n_162
Z/55
-2 2
11n_163
2

detected by
the Lickorish test
1-8t+22t^2-29t^3+22t^4-8t^5+t^6
Seifert matrix of 11n_163
-1 0 -1 0 0 0
1 1 1 0 1 0
0 0 -1 0 0 0
1 1 1 -1 1 -1
1 0 0 0 1 0
1 0 1 -1 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
91
First homology
of the double branched cover of 11n_163
Z/91
-2 2
11n_164
2

detected by
the Nakanishi index
-1+5t-10t^2+13t^3-10t^4+5t^5-t^6
Seifert matrix of 11n_164
1 0 -1 0 0 -1
-1 -1 1 0 -1 1
0 0 -1 0 0 0
0 0 -1 -1 0 -1
-1 0 0 0 -1 1
0 0 0 0 0 -1
2
45
First homology
of the double branched cover of 11n_164
Z/15+Z/3
-4 4
11n_165
2

detected by
the Lickorish test
-1+7t-20t^2+29t^3-20t^4+7t^5-t^6
Seifert matrix of 11n_165
1 0 -1 0 0 -1
-1 -1 1 0 -1 1
0 0 1 0 0 0
0 0 -1 -1 0 -1
-1 0 0 0 -1 1
0 0 0 0 0 1
2
85
First homology
of the double branched cover of 11n_165
Z/85
0 0
11n_166
1

detected by
an unknotting move
1-4t+8t^2-11t^3+11t^4-11t^5+8t^6-4t^7+t^8
Seifert matrix of 11n_166
-1 0 0 -1 0 0 0 -1
-1 -1 0 -1 0 0 0 -1
-1 -1 1 0 0 0 1 0
0 0 0 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 1 0 0 1 1 -1
0 0 0 0 0 0 1 0
0 0 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-1-1+t
59
First homology
of the double branched cover of 11n_166
Z/59
-2 2
11n_167
2

detected by
the Nakanishi index
1-5t+15t^2-21t^3+15t^4-5t^5+t^6
Seifert matrix of 11n_167
-1 0 -1 0 0 -1
0 -1 0 0 0 0
0 1 0 1 0 -1
0 -1 0 -1 0 0
0 -1 1 -1 1 0
0 1 -1 1 0 -2
2
63
First homology
of the double branched cover of 11n_167
Z/21+Z/3
-2 2
11n_168
2

detected by
the Lickorish test
1-6t+18t^2-25t^3+18t^4-6t^5+t^6
Seifert matrix of 11n_168
-2 1 -1 0 0 -1
0 -1 0 0 0 0
-1 1 -1 0 0 -2
1 -1 0 1 -1 0
0 0 -1 0 -1 -1
-1 1 -1 0 0 -1
1 or 2
75
First homology
of the double branched cover of 11n_168
Z/75
-2 2
11n_169
3

detected by
the signature
3-6t+6t^2-5t^3+6t^4-6t^5+3t^6
Seifert matrix of 11n_169
-1 1 -1 -1 1 -1
0 -2 0 0 -1 0
0 0 -1 -1 1 -1
0 0 0 -1 1 0
0 -1 0 0 -2 0
0 0 0 -1 1 -1
1 or 2
35
First homology
of the double branched cover of 11n_169
Z/35
-6 6
11n_170
2

detected by
the Lickorish test
-3+16t-25t^2+16t^3-3t^4
Seifert matrix of 11n_170
-1 1 1 1
0 2 1 0
0 1 2 0
0 0 -1 1
1
Generator of the Alexander module
(-1,0,0,1)
the Blanchfield form on it
6t^-1-11+6t
63
First homology
of the double branched cover of 11n_170
Z/63
2 2
11n_171
2

detected by
the signature
6-16t+21t^2-16t^3+6t^4
Seifert matrix of 11n_171
-1 1 1 1
0 -2 -1 0
0 -1 -2 0
0 0 -1 -2
1
Generator of the Alexander module
(2t+4t^2-9t^3+11t^4-8t^5+2t^6,0,3t+t^2-9t^3+8t^4-2t^5,1+2t-9t^2+8t^3-2t^4)
the Blanchfield form on it
2553t^-3-10225t^-2+20602t^-1-25578+20602t-10225t^2+2553t^3
65
First homology
of the double branched cover of 11n_171
Z/65
-4 4
11n_172
1

detected by
an unknotting move
-1+5t-11t^2+15t^3-11t^4+5t^5-t^6
Seifert matrix of 11n_172
0 0 0 -1 -1 -1
1 0 1 -1 0 -1
1 0 0 -1 0 -1
-1 -1 -1 2 1 2
0 0 0 1 2 1
-1 0 -1 1 1 2
1
Generator of the Alexander module
(0,t,0,0,0,1-2t)
the Blanchfield form on it
t^-1-2+t
49
First homology
of the double branched cover of 11n_172
Z/49
0 0
11n_173
2

detected by
the signature
-1+4t-8t^2+7t^3-5t^4+7t^5-8t^6+4t^7-t^8
Seifert matrix of 11n_173
-1 0 -1 -1 0 0 -1 0
-1 -1 -1 -1 0 0 -1 0
0 0 -1 -1 -1 0 -1 0
0 0 0 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 0 -1 0 0 1 0 0
0 0 0 -1 -1 0 -1 0
-1 0 -1 -1 0 1 -1 1
1 or 2
45
First homology
of the double branched cover of 11n_173
Z/45
-4 4
11n_174
2

detected by
the signature
-2+11t-22t^2+27t^3-22t^4+11t^5-2t^6
Seifert matrix of 11n_174
2 0 1 -1 0 2
2 -1 1 -1 0 1
2 0 0 -1 -1 1
-1 0 0 0 0 -1
2 1 1 -1 -1 0
0 1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
4t^-1-7+4t
97
First homology
of the double branched cover of 11n_174
Z/97
-4 4
11n_175
2

detected by
the signature
-2+9t-14t^2+15t^3-14t^4+9t^5-2t^6
Seifert matrix of 11n_175
-1 0 0 0 -1 0
-1 -1 1 -1 0 0
1 0 -2 0 0 0
-1 0 0 -1 0 0
0 0 0 0 1 0
0 0 -1 0 -1 -1
2
65
First homology
of the double branched cover of 11n_175
Z/65
-4 4
11n_176
1

detected by
an unknotting move
1-6t+15t^2-19t^3+15t^4-6t^5+t^6
Seifert matrix of 11n_176
0 0 -1 -1 -1 -1
1 0 -1 -1 0 -1
-1 0 2 1 1 1
-1 -1 2 2 1 2
0 0 1 1 2 1
-1 -1 2 1 1 2
1
Generator of the Alexander module
(0,1,0,0,1,1)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
63
First homology
of the double branched cover of 11n_176
Z/63
2 2
11n_177
1

detected by
an unknotting move
1-5t+11t^2-16t^3+17t^4-16t^5+11t^6-5t^7+t^8
Seifert matrix of 11n_177
-1 0 0 -1 0 0 -1 0
-1 -1 0 -1 0 0 -1 0
-1 0 1 0 0 0 0 0
0 0 0 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 0 1 0 0 1 -1 0
0 0 0 -1 -1 0 -1 0
-1 0 1 -1 0 1 -1 1
1
Generator of the Alexander module
(-2-2t,-t^2-t^3,-3-3t,t+t^2+t^3+2t^4,1+t,-t^2,1+t,-t-t^2)
the Blanchfield form on it
395t^-3-989t^-2+1732t^-1-1761+1732t-989t^2+395t^3
83
First homology
of the double branched cover of 11n_177
Z/83
-2 2
11n_178
2

detected by
the Lickorish test
2-9t+22t^2-29t^3+22t^4-9t^5+2t^6
Seifert matrix of 11n_178
1 0 0 0 0 0
1 -1 0 0 -1 0
0 0 -1 0 -1 0
1 1 1 0 -1 1
0 1 0 0 -1 0
2 2 1 1 -2 2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
2t^-2-5t^-1+8-5t+2t^2
95
First homology
of the double branched cover of 11n_178
Z/95
-2 2
11n_179
1

detected by
an unknotting move
-1+7t-18t^2+25t^3-18t^4+7t^5-t^6
Seifert matrix of 11n_179
1 0 0 0 0 0
1 1 0 0 1 0
1 1 -1 0 1 0
0 -1 0 -1 -1 -1
1 0 0 0 1 0
1 1 0 0 1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
77
First homology
of the double branched cover of 11n_179
Z/77
0 0
11n_180
3

detected by
the signature
3-7t+11t^2-13t^3+11t^4-7t^5+3t^6
Seifert matrix of 11n_180
-1 1 1 -1 1 1
0 -2 -2 0 -1 -2
0 -1 -2 0 -1 -1
0 0 0 -1 1 0
0 -1 -1 0 -2 -1
0 -1 -2 0 -1 -2
1 or 2
55
First homology
of the double branched cover of 11n_180
Z/55
-6 6
11n_181
2

detected by
the signature
5-11t+13t^2-11t^3+5t^4
Seifert matrix of 11n_181
-1 -1 1 -1
0 -1 1 0
0 0 -2 1
0 0 1 -3
1 or 2
45
First homology
of the double branched cover of 11n_181
Z/45
-4 4
11n_182
1

detected by
an unknotting move
-1+5t-11t^2+18t^3-23t^4+18t^5-11t^6+5t^7-t^8
Seifert matrix of 11n_182
1 0 0 0 1 0 0 1
-1 -1 -1 0 -1 -1 -1 -1
-1 0 -1 0 0 -1 0 -1
0 0 0 1 0 0 0 0
0 0 0 -1 1 0 0 0
-1 0 0 0 0 -1 0 0
-1 0 -1 0 -1 -1 -1 -1
0 0 0 -1 1 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
93
First homology
of the double branched cover of 11n_182
Z/93
0 0
11n_183
2

detected by
the signature
1+t-6t^2+9t^3-6t^4+t^5+t^6
Seifert matrix of 11n_183
-1 -1 0 -2 -1 -1
0 -2 -1 -2 -1 -1
0 1 -1 0 0 0
0 0 -2 -2 -1 -1
0 0 -1 -1 -1 0
0 0 -1 0 0 -1
2
21
First homology
of the double branched cover of 11n_183
Z/21
-4 4
11n_184
1

detected by
an unknotting move
2-9t+20t^2-25t^3+20t^4-9t^5+2t^6
Seifert matrix of 11n_184
1 0 0 0 0 0
1 -1 -1 0 0 0
0 1 -1 0 0 0
2 2 -2 2 1 1
1 1 -1 1 0 1
1 1 -1 2 1 0
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
87
First homology
of the double branched cover of 11n_184
Z/87
-2 2
11n_185
2

detected by
the signature
-2+11t-24t^2+31t^3-24t^4+11t^5-2t^6
Seifert matrix of 11n_185
2 1 0 0 0 2
2 0 0 0 -1 1
-1 -1 -1 -1 0 0
0 0 0 -2 0 2
1 0 0 0 -1 0
0 0 0 0 0 -1
2
105
First homology
of the double branched cover of 11n_185
Z/105
-4 4
12a_0001
1

detected by
an unknotting move
1-7t+23t^2-46t^3+59t^4-46t^5+23t^6-7t^7+t^8
Seifert matrix of 12a_0001
-1 0 -1 -1 -1 -1 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 -1 -1 0 0
0 1 -1 0 -1 0 0 0
0 1 -1 0 -1 -1 0 0
0 0 0 0 -1 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,-1,1-t,t-t^2,-1+t)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
213
First homology
of the double branched cover of 12a_0001
Z/213
0 0
12a_0002
1

detected by
an unknotting move
-1+7t-21t^2+36t^3-41t^4+36t^5-21t^6+7t^7-t^8
Seifert matrix of 12a_0002
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 -1 -1 -1
0 0 1 0 0 0 0 0
-1 0 -1 -1 0 -1 -1 -1
0 0 0 0 1 0 0 0
-1 0 -1 0 -1 -1 -1 -1
-1 0 -1 0 -1 0 -1 0
-1 0 -1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
-t^-3+7t^-2-20t^-1+29-20t+7t^2-t^3
171
First homology
of the double branched cover of 12a_0002
Z/171
-2 2
12a_0003
2

detected by
the Lickorish test
-2+14t-40t^2+57t^3-40t^4+14t^5-2t^6
Seifert matrix of 12a_0003
1 0 0 0 0 0
-1 -1 0 -1 0 1
0 0 1 0 0 0
-1 0 -1 -1 0 1
0 0 0 0 1 0
1 0 1 0 1 -2
1
Generator of the Alexander module
(0,0,0,0,1,1)
the Blanchfield form on it
-t^-2+5t^-1-9+5t-t^2
169
First homology
of the double branched cover of 12a_0003
Z/169
0 0
12a_0004
1

detected by
an unknotting move
1-7t+23t^2-48t^3+63t^4-48t^5+23t^6-7t^7+t^8
Seifert matrix of 12a_0004
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 1 0 1 0
0 0 0 0 0 -1 0 -1
0 0 0 0 0 0 1 0
0 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,2,0,0)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+17-12t+5t^2-t^3
221
First homology
of the double branched cover of 12a_0004
Z/221
0 0
12a_0005
1

detected by
an unknotting move
3-19t+47t^2-61t^3+47t^4-19t^5+3t^6
Seifert matrix of 12a_0005
1 0 0 0 0 0
-1 -1 0 1 0 1
0 0 -1 -1 0 -1
1 0 0 -2 0 -1
0 0 0 0 1 -1
1 0 0 -1 0 -2
1
Generator of the Alexander module
(0,0,2-t,0,5-2t,0)
the Blanchfield form on it
6t^-2-23t^-1+31-23t+6t^2
199
First homology
of the double branched cover of 12a_0005
Z/199
-2 2
12a_0006
1

detected by
an unknotting move
-1+7t-23t^2+44t^3-53t^4+44t^5-23t^6+7t^7-t^8
Seifert matrix of 12a_0006
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 1 1 1 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+7t^-1-9+7t-4t^2+t^3
203
First homology
of the double branched cover of 12a_0006
Z/203
-2 2
12a_0007
1

detected by
an unknotting move
-1+8t-28t^2+55t^3-67t^4+55t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0007
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 0
0 0 1 0 0 0 0 0
-1 0 -1 -1 -1 0 -1 -1
0 0 0 0 1 1 0 1
0 0 0 0 0 1 0 0
-1 0 -1 0 -1 0 -1 0
0 0 0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
t^-1-1+t
251
First homology
of the double branched cover of 12a_0007
Z/251
2 2
12a_0008
1

detected by
an unknotting move
1-7t+21t^2-38t^3+47t^4-38t^5+21t^6-7t^7+t^8
Seifert matrix of 12a_0008
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 1 0 -1 0
0 -1 0 -1 1 1 -1 1
0 0 0 0 0 0 -1 0
0 -1 0 -1 1 0 -1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+7t^-2-18t^-1+23-18t+7t^2-t^3
181
First homology
of the double branched cover of 12a_0008
Z/181
0 0
12a_0009
2

detected by
the Lickorish test
2-12t+28t^2-35t^3+28t^4-12t^5+2t^6
Seifert matrix of 12a_0009
-1 -1 -1 -1 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 -1 -1 0 0
0 0 0 0 -1 0
0 1 0 1 1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-5t^-2+10t^-1-12+10t-5t^2+t^3
119
First homology
of the double branched cover of 12a_0009
Z/119
-2 2
12a_0010
2

detected by
the Lickorish test
3-19t+49t^2-65t^3+49t^4-19t^5+3t^6
Seifert matrix of 12a_0010
1 0 0 0 0 0
-1 -1 0 1 1 1
0 0 1 0 0 0
1 0 1 -2 -1 -2
1 0 1 -1 -2 -1
1 0 1 -1 -1 -2
1
Generator of the Alexander module
(0,0,0,-t,t,1)
the Blanchfield form on it
3t^-2-15t^-1+26-15t+3t^2
207
First homology
of the double branched cover of 12a_0010
Z/207
-2 2
12a_0011
2

detected by
the signature
1-7t+21t^2-34t^3+39t^4-34t^5+21t^6-7t^7+t^8
Seifert matrix of 12a_0011
-1 0 -1 -1 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 0 0
0 0 0 -1 1 0 1 0
0 0 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+7t^-2-20t^-1+27-20t+7t^2-t^3
165
First homology
of the double branched cover of 12a_0011
Z/165
4 4
12a_0012
1

detected by
an unknotting move
2-14t+40t^2-55t^3+40t^4-14t^5+2t^6
Seifert matrix of 12a_0012
-1 0 -1 -1 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 1 -1 -1 0 0
0 0 0 0 1 0
0 0 0 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,-1,1)
the Blanchfield form on it
-t^-2+5t^-1-9+5t-t^2
167
First homology
of the double branched cover of 12a_0012
Z/167
2 2
12a_0013
1

detected by
an unknotting move
1-8t+28t^2-55t^3+69t^4-55t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0013
-1 0 -1 -1 -1 0 -1 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 0 0
0 1 -1 -1 -1 0 0 0
0 0 0 -1 -1 1 -1 1
0 1 -1 -1 -1 0 -1 0
0 0 0 0 -1 0 -1 1
1
Generator of the Alexander module
(0,0,0,1+2t^2,0,2t,0,-2t^2)
the Blanchfield form on it
-t^-2+5t^-1-9+5t-t^2
253
First homology
of the double branched cover of 12a_0013
Z/253
0 0
12a_0014
1

detected by
an unknotting move
-1+8t-28t^2+55t^3-67t^4+55t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0014
-1 0 -1 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 0 0
0 0 0 0 1 0 -1 0
0 0 0 -1 1 1 -1 1
0 1 -1 -1 0 0 -1 0
0 0 0 -1 1 0 -1 1
1
Generator of the Alexander module
(0,0,0,-1-t^2,2+t^2,2+t^2,0,0)
the Blanchfield form on it
-t^-2+5t^-1-9+5t-t^2
251
First homology
of the double branched cover of 12a_0014
Z/251
2 2
12a_0015
1

detected by
an unknotting move
1-8t+28t^2-55t^3+69t^4-55t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0015
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 -1
0 0 1 0 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1
0 0 0 0 1 1 0 0
0 0 0 0 0 1 0 0
-1 0 -1 0 -1 0 -1 0
-1 0 -1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
t^-3-7t^-2+20t^-1-27+20t-7t^2+t^3
253
First homology
of the double branched cover of 12a_0015
Z/253
0 0
12a_0016
1

detected by
an unknotting move
1-7t+22t^2-43t^3+55t^4-43t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0016
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 -1 0 0 -1 0
0 -1 -1 0 -1 0 0 0
0 -1 0 0 -1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,-3+t,0,1,0,1)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+17-12t+5t^2-t^3
201
First homology
of the double branched cover of 12a_0016
Z/201
0 0
12a_0017
1

detected by
an unknotting move
-1+7t-24t^2+49t^3-61t^4+49t^5-24t^6+7t^7-t^8
Seifert matrix of 12a_0017
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 -1 0 0 -1 0
0 -1 -1 0 -1 0 0 0
0 -1 0 0 -1 1 0 1
0 0 0 0 0 0 -1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(-1-t+2t^2,0,-1-2t,-1,0,-t+2t^2,0,1-2t)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
223
First homology
of the double branched cover of 12a_0017
Z/223
-2 2
12a_0018
1

detected by
an unknotting move
-1+7t-20t^2+31t^3-33t^4+31t^5-20t^6+7t^7-t^8
Seifert matrix of 12a_0018
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 0 -1 -1
0 0 1 0 0 0 0 0
-1 0 -1 -1 -1 0 -1 -1
-1 0 -1 0 -1 0 0 -1
0 0 0 0 0 1 0 0
-1 0 -1 0 -1 0 -1 -1
-1 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,-1)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+11-10t+5t^2-t^3
151
First homology
of the double branched cover of 12a_0018
Z/151
-2 2
12a_0019
1

detected by
an unknotting move
-1+7t-22t^2+41t^3-49t^4+41t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0019
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 0
0 0 1 0 0 0 0 0
-1 0 -1 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 1
-1 0 -1 0 -1 -1 -1 -1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,-t,1+t,0)
the Blanchfield form on it
t^-3-7t^-2+20t^-1-29+20t-7t^2+t^3
191
First homology
of the double branched cover of 12a_0019
Z/191
2 2
12a_0020
1

detected by
an unknotting move
1-7t+22t^2-41t^3+51t^4-41t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0020
-1 0 -1 -1 0 -1 0 -1
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 -1 0 -1
0 0 0 0 1 0 0 -1
0 1 -1 0 0 -1 0 0
0 0 0 0 1 0 1 -1
0 1 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+11-10t+5t^2-t^3
193
First homology
of the double branched cover of 12a_0020
Z/193
0 0
12a_0021
2

detected by
the signature
-4+21t-45t^2+57t^3-45t^4+21t^5-4t^6
Seifert matrix of 12a_0021
1 0 0 0 0 0
-1 -1 0 0 1 0
0 0 -1 0 -1 0
0 0 0 -2 -1 -1
1 0 0 0 -2 0
0 0 0 -2 -1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
197
First homology
of the double branched cover of 12a_0021
Z/197
-4 4
12a_0022
1

detected by
an unknotting move
-2+13t-35t^2+49t^3-35t^4+13t^5-2t^6
Seifert matrix of 12a_0022
1 0 0 0 0 0
-1 -1 0 -1 -1 0
0 0 1 0 0 0
-1 0 -1 -1 -1 0
-1 0 -1 0 -1 1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,0,1,-1,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
149
First homology
of the double branched cover of 12a_0022
Z/149
0 0
12a_0023
1

detected by
an unknotting move
-2+15t-45t^2+65t^3-45t^4+15t^5-2t^6
Seifert matrix of 12a_0023
1 0 0 0 0 0
-1 -1 0 0 1 -1
0 0 1 0 0 0
0 0 0 1 0 0
1 0 1 0 -2 1
-1 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,1-t,t,t,t^2,5-6t+t^2)
the Blanchfield form on it
t^-2-6t^-1+11-6t+t^2
189
First homology
of the double branched cover of 12a_0023
Z/189
0 0
12a_0024
2

detected by
the signature
1-7t+20t^2-33t^3+39t^4-33t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0024
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 -1 0 0 -1 0
0 -1 -1 0 -1 0 0 0
0 -1 0 0 -1 1 -1 0
0 0 0 0 0 0 -1 0
0 0 0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-7t^-2+18t^-1-23+18t-7t^2+t^3
161
First homology
of the double branched cover of 12a_0024
Z/161
-4 4
12a_0025
1

detected by
an unknotting move
-2+15t-44t^2+63t^3-44t^4+15t^5-2t^6
Seifert matrix of 12a_0025
1 0 0 0 0 0
-1 -1 0 0 1 0
0 0 1 0 0 0
0 0 0 -1 0 -1
1 0 1 -1 -2 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,1-3t+t^2,1-2t,1,-2t,1)
the Blanchfield form on it
1
185
First homology
of the double branched cover of 12a_0025
Z/185
0 0
12a_0026
2

detected by
the signature
1-7t+20t^2-29t^3+31t^4-29t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0026
-1 0 -1 0 -1 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 1 0
0 1 -1 0 -1 0 0 0
0 0 0 1 -1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(1+2t,0,-4,0,0,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+7t^-1-7+7t-5t^2+t^3
145
First homology
of the double branched cover of 12a_0026
Z/145
4 4
12a_0027
1

detected by
an unknotting move
2-15t+45t^2-63t^3+45t^4-15t^5+2t^6
Seifert matrix of 12a_0027
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 2 0 0
0 1 -1 0 -1 0
0 0 0 -1 -1 1
1 or 2
187
First homology
of the double branched cover of 12a_0027
Z/187
2 2
12a_0028
1

detected by
an unknotting move
2-15t+42t^2-57t^3+42t^4-15t^5+2t^6
Seifert matrix of 12a_0028
-1 0 -1 1 0 0
0 -1 0 -1 0 0
0 0 1 0 0 0
0 0 1 -2 0 0
0 0 0 1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(1,-2t^2,0,0,3t,3)
the Blanchfield form on it
2t^-2-9t^-1+14-9t+2t^2
175
First homology
of the double branched cover of 12a_0028
Z/175
-2 2
12a_0029
2

detected by
the Lickorish test
-1+7t-24t^2+48t^3-59t^4+48t^5-24t^6+7t^7-t^8
Seifert matrix of 12a_0029
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 1 1 0 0
0 0 0 0 0 1 0 0
0 -1 0 -1 0 0 1 1
0 0 0 0 0 0 0 1
2
219
First homology
of the double branched cover of 12a_0029
Z/219
2 2
12a_0030
2

detected by
A(F_2)
1-7t+22t^2-40t^3+49t^4-40t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0030
-1 0 -1 -1 -1 -1 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 -1 -1 0 0
0 1 -1 0 -1 0 0 0
0 1 -1 0 -1 -1 0 0
0 0 0 -1 -1 -1 1 1
0 0 0 0 0 0 0 1
2
189
First homology
of the double branched cover of 12a_0030
Z/189
0 0
12a_0031
1

detected by
an unknotting move
2-13t+33t^2-43t^3+33t^4-13t^5+2t^6
Seifert matrix of 12a_0031
-1 -1 -1 0 -1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 -2 0 0
0 -1 -1 0 -1 0
0 -1 0 1 -1 1
1
Generator of the Alexander module
(0,0,0,0,1,1)
the Blanchfield form on it
2t^-2-9t^-1+15-9t+2t^2
139
First homology
of the double branched cover of 12a_0031
Z/139
-2 2
12a_0032
2

detected by
the Lickorish test
2-13t+34t^2-45t^3+34t^4-13t^5+2t^6
Seifert matrix of 12a_0032
-1 0 -1 1 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 -1 1 -2 0 0
0 0 0 1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(t,0,-1,1,0,0)
the Blanchfield form on it
2t^-1-3+2t
143
First homology
of the double branched cover of 12a_0032
Z/143
2 2
12a_0033
2

detected by
A(F_2)
1-7t+22t^2-40t^3+49t^4-40t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0033
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 0 0 -1
0 0 1 0 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1
-1 0 -1 0 -1 -1 -1 0
0 0 0 0 0 1 1 0
0 0 0 0 0 0 1 0
-1 0 -1 0 -1 -1 -1 -1
2
189
First homology
of the double branched cover of 12a_0033
Z/189
0 0
12a_0034
3

detected by
the signature
2-9t+16t^2-20t^3+21t^4-20t^5+16t^6-9t^7+2t^8
Seifert matrix of 12a_0034
1 0 0 0 0 0 0 0
-1 -1 0 0 0 1 0 0
0 0 -1 0 0 -1 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
1 0 0 -1 -1 -2 -1 -1
0 0 0 0 -1 0 -1 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1+t-t^2,0,1+t^2-t^3,0,0,0)
the Blanchfield form on it
2t^-3-7t^-2+9t^-1-11+9t-7t^2+2t^3
115
First homology
of the double branched cover of 12a_0034
Z/115
-6 6
12a_0035
2

detected by
the signature
-4+20t-40t^2+49t^3-40t^4+20t^5-4t^6
Seifert matrix of 12a_0035
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 -1 0 0 -1
0 0 0 -1 1 0
0 0 0 0 -2 0
1 0 0 -1 1 -2
1 or 2
177
First homology
of the double branched cover of 12a_0035
Z/177
-4 4
12a_0036
3

detected by
the signature
2-10t+21t^2-30t^3+33t^4-30t^5+21t^6-10t^7+2t^8
Seifert matrix of 12a_0036
1 0 0 0 0 0 0 0
-1 -1 0 0 1 1 1 0
0 0 -1 0 -1 -1 -1 0
0 0 0 -1 0 0 0 -1
1 0 0 -1 -2 -1 -2 -1
1 0 0 -1 -2 -2 -2 -1
1 0 0 -1 -1 -1 -2 -1
0 0 0 0 0 0 0 -1
2
159
First homology
of the double branched cover of 12a_0036
Z/159
-6 6
12a_0037
2

detected by
the signature
-3+15t-30t^2+37t^3-30t^4+15t^5-3t^6
Seifert matrix of 12a_0037
1 0 0 0 0 0
-1 -1 0 0 -1 0
0 0 -1 0 1 0
0 0 0 -1 0 -1
-1 0 0 1 -3 1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1+t-t^2,1-t,0,0)
the Blanchfield form on it
-3t^-2+12t^-1-16+12t-3t^2
133
First homology
of the double branched cover of 12a_0037
Z/133
-4 4
12a_0038
1

detected by
an unknotting move
-4+18t-27t^2+18t^3-4t^4
Seifert matrix of 12a_0038
1 0 0 0
-1 -1 0 1
0 0 -1 -1
1 0 0 -4
1
Generator of the Alexander module
(0,0,-t,1)
the Blanchfield form on it
-t^-1+3-t
71
First homology
of the double branched cover of 12a_0038
Z/71
-2 2
12a_0039
2

detected by
the Lickorish test
1-7t+21t^2-40t^3+49t^4-40t^5+21t^6-7t^7+t^8
Seifert matrix of 12a_0039
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
-1 -1 1 1 1 1 1 0
0 0 0 0 1 0 0 0
-1 -1 1 0 1 1 1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 1 1
1
Generator of the Alexander module
(0,2-5t+2t^2-8t^3+12t^4-7t^5+2t^6,4-10t+4t^2-16t^3+24t^4-14t^5+4t^6,-t-9t^2-2t^3+17t^4-12t^5+4t^6,1+7t-12t^2+7t^3-2t^4,-1-8t+3t^2-9t^3+19t^4-12t^5+4t^6,0,0)
the Blanchfield form on it
x
187
First homology
of the double branched cover of 12a_0039
Z/187
2 2
12a_0040
1

detected by
an unknotting move
1-7t+23t^2-46t^3+57t^4-46t^5+23t^6-7t^7+t^8
Seifert matrix of 12a_0040
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
0 0 0 -1 0 -1 0 0
0 0 0 0 1 0 0 0
-1 -1 1 0 1 1 1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,2-5t+3t^2-t^3,4-9t+13t^2-14t^3+7t^4-2t^5,2t+14t^2-24t^3+14t^4-4t^5,-1-7t+12t^2-7t^3+2t^4,0,1+7t-12t^2+7t^3-2t^4,0)
the Blanchfield form on it
x
211
First homology
of the double branched cover of 12a_0040
Z/211
-2 2
12a_0041
2

detected by
the signature
-2+9t-23t^2+37t^3-43t^4+37t^5-23t^6+9t^7-2t^8
Seifert matrix of 12a_0041
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 1
1 1 -1 1 -1 1 2 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,-1,0)
the Blanchfield form on it
t^-3-2t^-2+4t^-1-5+4t-2t^2+t^3
185
First homology
of the double branched cover of 12a_0041
Z/185
4 4
12a_0042
1

detected by
an unknotting move
3-13t+30t^2-39t^3+30t^4-13t^5+3t^6
Seifert matrix of 12a_0042
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 1 0
0 0 0 1 0 0
0 0 0 0 1 0
-1 -1 1 -1 1 3
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-5t^-2+12t^-1-16+12t-5t^2+t^3
131
First homology
of the double branched cover of 12a_0042
Z/131
2 2
12a_0043
3

detected by
the signature
6-23t+45t^2-55t^3+45t^4-23t^5+6t^6
Seifert matrix of 12a_0043
-1 -1 -1 0 -1 0
0 -2 -1 0 -2 0
0 -1 -2 0 -1 0
0 0 0 -1 0 -1
0 -1 -1 0 -2 0
0 1 0 0 1 -2
1
Generator of the Alexander module
(3-6t,0,2,-3t,2,3-4t)
the Blanchfield form on it
-382t^-3+1532t^-2-3059t^-1+3770-3059t+1532t^2-382t^3
203
First homology
of the double branched cover of 12a_0043
Z/203
-6 6
12a_0044
2

detected by
the signature
-4+22t-50t^2+65t^3-50t^4+22t^5-4t^6
Seifert matrix of 12a_0044
-1 -1 0 -1 -1 -1
0 -2 0 -1 -1 -1
0 0 1 -1 -1 -1
0 -1 0 -2 -1 -2
0 -1 0 -1 -2 -1
0 -1 0 -1 -1 -2
1
Generator of the Alexander module
(t,0,1,0,1,0)
the Blanchfield form on it
3t^-1-4+3t
217
First homology
of the double branched cover of 12a_0044
Z/217
-4 4
12a_0045
1

detected by
an unknotting move
1-8t+22t^2-37t^3+43t^4-37t^5+22t^6-8t^7+t^8
Seifert matrix of 12a_0045
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
-1 -1 0 -1 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(-1,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+7t^-2-19t^-1+26-19t+7t^2-t^3
179
First homology
of the double branched cover of 12a_0045
Z/179
2 2
12a_0046
1

detected by
an unknotting move
-2+15t-38t^2+51t^3-38t^4+15t^5-2t^6
Seifert matrix of 12a_0046
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 1 0
1 1 0 1 -1 2
1
Generator of the Alexander module
(0,-t,-1-t,0,0,1+t)
the Blanchfield form on it
-2t^-2+10t^-1-15+10t-2t^2
161
First homology
of the double branched cover of 12a_0046
Z/161
0 2
12a_0047
2

detected by
the signature
-3+19t-45t^2+59t^3-45t^4+19t^5-3t^6
Seifert matrix of 12a_0047
-1 -1 -1 -1 0 0
0 -2 -1 -2 0 0
0 -1 -2 -1 0 0
0 -1 -1 -2 0 0
0 1 0 1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(1+9t-15t^2+9t^3,-12t^2+6t^3,6t-3t^2,-2-12t+27t^2-18t^3,6t^2-3t^3,3+6t-27t^2+12t^3)
the Blanchfield form on it
620t^-5-9648t^-4+56392t^-3-172486t^-2+322604t^-1-394798+322604t-172486t^2+56392t^3-9648t^4+620t^5
193
First homology
of the double branched cover of 12a_0047
Z/193
-4 4
12a_0048
1

detected by
an unknotting move
-1+8t-28t^2+57t^3-73t^4+57t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0048
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
0 0 -1 -1 0 -1 -1 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
-1 -1 1 0 1 0 1 0
0 0 -1 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,-t,0,1,1,1-t)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
261
First homology
of the double branched cover of 12a_0048
Z/261
0 0
12a_0049
2

detected by
the Lickorish test
5-23t+53t^2-69t^3+53t^4-23t^5+5t^6
Seifert matrix of 12a_0049
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 -1 2 1 0
1 1 -1 1 2 1
1 1 -1 1 1 2
1 or 2
231
First homology
of the double branched cover of 12a_0049
Z/231
2 2
12a_0050 1 or 2
1-8t+20t^2-30t^3+33t^4-30t^5+20t^6-8t^7+t^8
Seifert matrix of 12a_0050
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 0 1 0 1 1
1
Generator of the Alexander module
(0,0,1+t-t^3,0,-t+t^4,0,0,0)
the Blanchfield form on it
-t^-3+7t^-2-13t^-1+17-13t+7t^2-t^3
151
First homology
of the double branched cover of 12a_0050
Z/151
2 2
12a_0051
1

detected by
an unknotting move
-2+17t-45t^2+61t^3-45t^4+17t^5-2t^6
Seifert matrix of 12a_0051
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 2 0
-1 -1 0 -1 -1 1
1
Generator of the Alexander module
(0,0,-t,0,1,t)
the Blanchfield form on it
t^-2-7t^-1+10-7t+t^2
189
First homology
of the double branched cover of 12a_0051
Z/189
0 2
12a_0052
4

detected by
the signature
-3+9t-15t^2+18t^3-19t^4+18t^5-15t^6+9t^7-3t^8
Seifert matrix of 12a_0052
-1 -1 -1 0 0 -1 0 0
0 -2 -1 0 0 -2 0 0
0 -1 -2 0 0 -1 0 0
0 -1 0 -1 -1 -1 0 -1
0 -1 0 0 -1 -1 0 0
0 -1 -1 0 0 -2 0 0
0 -1 0 -1 -1 -1 -1 -1
0 -1 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(-2t+3t^2-2t^3,-2t^3-2t^4,0,t-t^2+t^3,t,1,-t-t^2,t)
the Blanchfield form on it
2t^-8-6t^-7+28t^-6-101t^-5+295t^-4-617t^-3+949t^-2-1165t^-1+1230-1165t+949t^2-617t^3+295t^4-101t^5+28t^6-6t^7+2t^8
109
First homology
of the double branched cover of 12a_0052
Z/109
-8 8
12a_0053
3

detected by
the signature
6-21t+38t^2-45t^3+38t^4-21t^5+6t^6
Seifert matrix of 12a_0053
-1 -1 -1 0 0 -1
0 -2 -1 0 0 -2
0 -1 -2 0 0 -1
0 1 0 -2 1 1
0 -1 0 0 -1 -1
0 -1 -1 0 0 -2
1 or 2
175
First homology
of the double branched cover of 12a_0053
Z/175
-6 6
12a_0054
2

detected by
the Lickorish test
-3+17t-39t^2+51t^3-39t^4+17t^5-3t^6
Seifert matrix of 12a_0054
-1 -1 0 -1 0 0
0 -2 0 -1 0 0
0 0 1 -1 0 0
0 -1 0 -2 0 0
0 0 0 1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1-t,0,-1,0,2-t,0)
the Blanchfield form on it
-3t^-2+11t^-1-16+11t-3t^2
169
First homology
of the double branched cover of 12a_0054
Z/169
0 0
12a_0055
3

detected by
the signature
5-18t+34t^2-41t^3+34t^4-18t^5+5t^6
Seifert matrix of 12a_0055
-1 -1 0 1 0 0
0 -2 0 1 0 0
0 0 -1 1 0 0
0 1 0 -3 0 0
0 0 0 -1 -1 0
0 0 -1 1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,1)
the Blanchfield form on it
5t^-2-13t^-1+18-13t+5t^2
155
First homology
of the double branched cover of 12a_0055
Z/155
-6 6
12a_0056
2

detected by
the signature
7-22t+31t^2-22t^3+7t^4
Seifert matrix of 12a_0056
-1 -1 0 -1
0 -2 0 -1
0 0 -1 1
0 -1 0 -4
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
4t^-1-7+4t
89
First homology
of the double branched cover of 12a_0056
Z/89
-4 4
12a_0057
1

detected by
an unknotting move
-3+17t-41t^2+55t^3-41t^4+17t^5-3t^6
Seifert matrix of 12a_0057
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 -1 2 0 1
0 0 0 0 -1 0
1 1 -1 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,1,1)
the Blanchfield form on it
2t^-2-6t^-1+9-6t+2t^2
177
First homology
of the double branched cover of 12a_0057
Z/177
0 0
12a_0058
1

detected by
an unknotting move
-1+7t-23t^2+44t^3-55t^4+44t^5-23t^6+7t^7-t^8
Seifert matrix of 12a_0058
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 1 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 -1 -1 0 0
0 0 0 0 -1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,1-t,-1,0)
the Blanchfield form on it
-t^-3+4t^-2-9t^-1+11-9t+4t^2-t^3
205
First homology
of the double branched cover of 12a_0058
Z/205
0 0
12a_0059
2

detected by
the Lickorish test
1-8t+28t^2-57t^3+71t^4-57t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0059
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 0 1 1 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 -1 0
0 0 0 0 0 -1 0 0
-1 -1 0 1 0 1 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(4t^2+25t^3-63t^4+32t^5+89t^6-203t^7+218t^8-145t^9+62t^10-16t^11+2t^12,t^2+6t^3-20t^4+33t^5-31t^6+18t^7-6t^8+t^9,-1-6t+23t^2-14t^3-23t^4+60t^5-61t^6+36t^7-12t^8+2t^9,-1-7t+14t^2-12t^3+5t^4-t^5,4t+25t^2-63t^3+32t^4+89t^5-203t^6+218t^7-145t^8+62t^9-16t^10+2t^11,0,-2-11t+35t^2-8t^3-99t^4+205t^5-218t^6+
the Blanchfield form on it
x
259
First homology
of the double branched cover of 12a_0059
Z/259
-2 2
12a_0060
1

detected by
an unknotting move
-1+8t-28t^2+57t^3-73t^4+57t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0060
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 0 0 1 1
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 -1
0 0 0 0 0 1 0 0
-1 -1 0 1 1 0 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,-1-t,-1-2t,1,0,0,-t,1)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+17-12t+5t^2-t^3
261
First homology
of the double branched cover of 12a_0060
Z/261
0 0
12a_0061
1

detected by
an unknotting move
1-7t+21t^2-38t^3+45t^4-38t^5+21t^6-7t^7+t^8
Seifert matrix of 12a_0061
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 1 1 0 1
0 0 0 1 0 0 0 0
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
0 0 0 0 1 1 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,2,t)
the Blanchfield form on it
t^-3-4t^-2+9t^-1-11+9t-4t^2+t^3
179
First homology
of the double branched cover of 12a_0061
Z/179
-2 2
12a_0062
1

detected by
an unknotting move
-2+12t-30t^2+41t^3-30t^4+12t^5-2t^6
Seifert matrix of 12a_0062
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 1 0 -1
0 0 0 1 0 0
0 0 0 0 1 -1
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
129
First homology
of the double branched cover of 12a_0062
Z/129
0 0
12a_0063
2

detected by
the Lickorish test
1-8t+28t^2-57t^3+71t^4-57t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0063
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
0 0 -1 -1 0 0 0 -1
0 0 0 0 1 0 0 0
0 0 -1 -1 0 -1 0 0
0 0 0 0 0 0 -1 -1
-1 -1 1 0 1 0 0 1
1
Generator of the Alexander module
(0,2+3t-2t^3,-1+2t+t^2-2t^3,-3t+3t^2+8t^3-4t^5,-3-t+2t^2,0,1-3t-3t^2+t^3,1+8t+3t^2-4t^3)
the Blanchfield form on it
x
259
First homology
of the double branched cover of 12a_0063
Z/259
-2 2
12a_0064
2

detected by
the signature
-4+22t-50t^2+65t^3-50t^4+22t^5-4t^6
Seifert matrix of 12a_0064
-1 -1 -1 -1 0 -1
0 -2 -1 -1 0 -1
0 -1 -2 -1 0 -1
0 -1 -2 -2 0 -1
0 0 -1 -1 1 -1
0 -1 -1 -1 0 -2
1
Generator of the Alexander module
(t,0,1,1,t,2)
the Blanchfield form on it
3t^-1-4+3t
217
First homology
of the double branched cover of 12a_0064
Z/217
-4 4
12a_0065
1

detected by
an unknotting move
1-8t+22t^2-37t^3+43t^4-37t^5+22t^6-8t^7+t^8
Seifert matrix of 12a_0065
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,1,5t-5t^2+2t^3,0,-1-2t+2t^2,t+2t^2-2t^3,-1-2t+2t^2,t+2t^2-2t^3)
the Blanchfield form on it
-t^-3+6t^-2-13t^-1+17-13t+6t^2-t^3
179
First homology
of the double branched cover of 12a_0065
Z/179
2 2
12a_0066
1

detected by
an unknotting move
-1+7t-25t^2+52t^3-67t^4+52t^5-25t^6+7t^7-t^8
Seifert matrix of 12a_0066
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
-1 -1 1 1 1 0 1 1
0 0 0 0 1 0 0 0
0 0 -1 0 0 -1 0 -1
0 0 0 0 0 0 -1 0
-1 -1 1 0 1 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-9+8t-4t^2+t^3
237
First homology
of the double branched cover of 12a_0066
Z/237
0 0
12a_0067
2

detected by
the Lickorish test
1-8t+26t^2-47t^3+55t^4-47t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0067
1 0 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 -1
0 0 1 0 0 1 1 1
0 0 -1 -1 0 0 0 -1
-1 0 -1 0 -1 0 0 0
0 0 0 0 0 1 1 0
0 0 0 0 0 0 1 0
0 0 0 0 0 1 1 1
1
Generator of the Alexander module
(0,1,0,1,0,1,0,0)
the Blanchfield form on it
-t^-1+3-t
219
First homology
of the double branched cover of 12a_0067
Z/219
2 2
12a_0068
1

detected by
an unknotting move
-2+15t-44t^2+63t^3-44t^4+15t^5-2t^6
Seifert matrix of 12a_0068
1 0 0 0 0 0
-1 -1 0 0 -1 1
0 0 1 0 0 0
0 0 0 -1 0 1
-1 0 -1 0 -1 0
0 0 1 0 0 2
1
Generator of the Alexander module
(0,1,0,4-2t,-1,0)
the Blanchfield form on it
2t^-2-11t^-1+20-11t+2t^2
185
First homology
of the double branched cover of 12a_0068
Z/185
0 0
12a_0069
1

detected by
an unknotting move
1-8t+27t^2-52t^3+63t^4-52t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0069
1 0 0 0 0 0 0 0
-1 -1 -1 0 -1 0 -1 -1
0 0 1 1 0 0 1 0
0 0 0 1 0 0 0 0
-1 0 -1 0 -1 0 0 -1
0 0 0 0 0 1 0 0
0 0 0 1 0 0 1 0
-1 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,-1)
the Blanchfield form on it
t^-3-6t^-2+14t^-1-17+14t-6t^2+t^3
239
First homology
of the double branched cover of 12a_0069
Z/239
2 2
12a_0070
2

detected by
the signature
1-8t+27t^2-50t^3+61t^4-50t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0070
-1 1 -1 0 -1 1 0 0
0 1 0 1 0 1 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 1 -1 0 -1 0 0 0
0 0 0 1 0 1 0 0
0 0 0 0 -1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0,t,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+17-14t+6t^2-t^3
233
First homology
of the double branched cover of 12a_0070
Z/233
4 4
12a_0071
2

detected by
the Lickorish test
1-8t+25t^2-44t^3+51t^4-44t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_0071
1 0 0 0 0 0 0 0
-1 -1 -1 0 -1 -1 -1 -1
0 0 1 0 0 0 1 0
0 0 -1 -1 0 0 -1 0
-1 0 -1 0 -1 -1 0 -1
-1 0 -1 0 0 -1 0 0
0 0 0 0 0 0 1 0
-1 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-3-8t^-2+24t^-1-35+24t-8t^2+t^3
207
First homology
of the double branched cover of 12a_0071
Z/207
-2 2
12a_0072
1

detected by
an unknotting move
-2+16t-47t^2+67t^3-47t^4+16t^5-2t^6
Seifert matrix of 12a_0072
1 0 0 0 0 0
-1 -1 -1 0 -1 1
0 0 1 0 1 0
0 0 -1 -1 -1 0
0 0 0 0 1 0
1 0 1 0 0 -2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
2t^-2-8t^-1+13-8t+2t^2
197
First homology
of the double branched cover of 12a_0072
Z/197
0 0
12a_0073
1

detected by
an unknotting move
2-17t+51t^2-71t^3+51t^4-17t^5+2t^6
Seifert matrix of 12a_0073
-1 -1 0 0 0 0
0 1 0 0 0 0
1 1 -2 0 0 0
0 0 -1 -1 0 0
-1 0 0 -1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,1)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
211
First homology
of the double branched cover of 12a_0073
Z/211
-2 2
12a_0074
2

detected by
the Lickorish test
-1+7t-26t^2+57t^3-73t^4+57t^5-26t^6+7t^7-t^8
Seifert matrix of 12a_0074
-1 -1 -1 0 -1 1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 -1 0 -1 1 0 0
0 0 0 1 0 1 0 0
0 -1 0 0 -1 0 1 1
0 0 0 0 0 0 0 1
1 or 2
255
First homology
of the double branched cover of 12a_0074
Z/255
2 2
12a_0075
2

detected by
the signature
-5+24t-46t^2+55t^3-46t^4+24t^5-5t^6
Seifert matrix of 12a_0075
1 0 0 0 0 0
1 -2 0 -1 -1 0
0 0 -1 0 0 -1
1 -1 0 -2 -1 0
1 0 -1 -1 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(-2t-2t^2-4t^3-2t^4,4t^3+4t^4,t,-2t^3-2t^4,1-t-t^2-4t^3-2t^4,-t)
the Blanchfield form on it
6t^-7-36t^-6+15t^-5+52t^-4-164t^-3-21t^-2+450t^-1-604+450t-21t^2-164t^3+52t^4+15t^5-36t^6+6t^7
205
First homology
of the double branched cover of 12a_0075
Z/205
-4 4
12a_0076
1

detected by
an unknotting move
-8+36t-55t^2+36t^3-8t^4
Seifert matrix of 12a_0076
1 0 0 0
1 -2 1 -1
-1 0 -3 1
1 -1 1 -2
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
3t^-2-14t^-1+22-14t+3t^2
143
First homology
of the double branched cover of 12a_0076
Z/143
-2 2
12a_0077
2

detected by
the Lickorish test
-1+7t-24t^2+49t^3-63t^4+49t^5-24t^6+7t^7-t^8
Seifert matrix of 12a_0077
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
0 0 0 -1 0 0 -1 -1
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
-1 -1 1 0 0 1 1 0
0 0 0 0 1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+17-12t+5t^2-t^3
225
First homology
of the double branched cover of 12a_0077
Z/225
0 0
12a_0078
2

detected by
the signature
-2+8t-19t^2+29t^3-33t^4+29t^5-19t^6+8t^7-2t^8
Seifert matrix of 12a_0078
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
-1 -1 1 1 0 1 1 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
-1 -1 1 0 0 1 1 0
1 1 -1 -1 1 -1 -1 2
1
Generator of the Alexander module
(0,-t-t^2,-t^2,-t-t^2,-t,t,-t^2,1+3t^2)
the Blanchfield form on it
2t^-3-6t^-2+11t^-1-13+11t-6t^2+2t^3
149
First homology
of the double branched cover of 12a_0078
Z/149
4 4
12a_0079
1

detected by
an unknotting move
-1+7t-22t^2+43t^3-55t^4+43t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0079
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
0 0 0 -1 0 0 -1 0
0 0 0 0 -1 0 0 -1
0 0 0 0 0 1 0 0
-1 -1 1 0 0 1 1 0
-1 -1 1 0 0 1 1 1
1
Generator of the Alexander module
(0,-3+30t-28t^2+65t^3-70t^4+42t^5-10t^6,t-t^2+3t^3-3t^4+3t^5-t^6,1-10t+12t^2-31t^3+30t^4-30t^5+10t^6,1-7t+7t^2-15t^3+16t^4-9t^5+2t^6,-1+2t-4t^2+6t^3-6t^4+4t^5-t^6,-6+63t-59t^2+139t^3-149t^4+93t^5-23t^6,2t-5t^2+9t^3-15t^4+15t^5-11t^6+3t^7)
the Blanchfield form on it
x
201
First homology
of the double branched cover of 12a_0079
Z/201
0 0
12a_0080
1

detected by
an unknotting move
-1+7t-21t^2+36t^3-43t^4+36t^5-21t^6+7t^7-t^8
Seifert matrix of 12a_0080
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 0 0
0 0 0 -1 0 -1 -1 -1
0 0 0 0 -1 0 0 0
-1 -1 1 0 -1 1 0 0
-1 -1 1 0 -1 1 1 1
-1 -1 1 0 -1 1 0 1
1
Generator of the Alexander module
(0,0,1+t^2,2+t^2,0,0,0,0)
the Blanchfield form on it
t^-3-6t^-2+15t^-1-20+15t-6t^2+t^3
173
First homology
of the double branched cover of 12a_0080
Z/173
0 2
12a_0081
2

detected by
the Lickorish test
2-14t+38t^2-51t^3+38t^4-14t^5+2t^6
Seifert matrix of 12a_0081
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 -1 0
0 0 0 -1 0 1
0 0 0 0 -1 0
1 1 -1 0 1 2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
159
First homology
of the double branched cover of 12a_0081
Z/159
-2 2
12a_0082
3

detected by
the signature
6-22t+42t^2-51t^3+42t^4-22t^5+6t^6
Seifert matrix of 12a_0082
-1 -1 -1 -1 1 0
0 -2 -1 -2 2 0
0 -1 -2 -1 1 0
0 -1 -1 -2 2 0
0 1 1 1 -3 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-3t^-3+14t^-2-30t^-1+38-30t+14t^2-3t^3
191
First homology
of the double branched cover of 12a_0082
Z/191
-6 6
12a_0083
2

detected by
the signature
-3+20t-48t^2+63t^3-48t^4+20t^5-3t^6
Seifert matrix of 12a_0083
-1 -1 0 -1 -1 0
0 -2 0 -1 -2 0
0 0 -1 0 0 -1
0 -1 0 -2 -1 0
0 -1 0 -1 -2 -1
0 0 0 0 0 1
1 or 2
205
First homology
of the double branched cover of 12a_0083
Z/205
-4 4
12a_0084
1

detected by
an unknotting move
1-7t+22t^2-43t^3+53t^4-43t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0084
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
0 0 0 -1 0 -1 0 0
0 0 0 0 1 0 0 0
-1 -1 1 0 1 1 0 0
0 0 0 -1 0 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,t,0)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+17-12t+5t^2-t^3
199
First homology
of the double branched cover of 12a_0084
Z/199
2 2
12a_0085
2

detected by
the signature
-2+8t-19t^2+28t^3-31t^4+28t^5-19t^6+8t^7-2t^8
Seifert matrix of 12a_0085
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
0 0 0 1 0 0 0 0
0 0 0 1 1 0 1 0
0 0 0 0 0 1 0 0
0 0 0 1 0 0 1 0
1 1 -1 1 1 -1 1 2
1
Generator of the Alexander module
(0,-2t-t^2,-t-t^2,-1-t,-1-t,1+t,-1-t,-1+2t+3t^2)
the Blanchfield form on it
-2t^-3+4t^-2-6t^-1+7-6t+4t^2-2t^3
145
First homology
of the double branched cover of 12a_0085
Z/145
4 4
12a_0086
2

detected by
the Lickorish test
4-17t+39t^2-51t^3+39t^4-17t^5+4t^6
Seifert matrix of 12a_0086
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 1 0 0
0 0 0 1 0 0
0 0 0 0 2 1
1 1 -1 -1 0 2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-3-9t^-2+21t^-1-28+21t-9t^2+2t^3
171
First homology
of the double branched cover of 12a_0086
Z/171
2 2
12a_0087
2

detected by
the Lickorish test
1-7t+20t^2-37t^3+45t^4-37t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0087
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
0 0 0 1 0 0 0 0
-1 -1 1 0 1 1 1 0
0 0 0 0 0 1 0 0
-1 -1 1 0 0 1 1 0
0 0 0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-2t^-3+7t^-2-15t^-1+19-15t+7t^2-2t^3
175
First homology
of the double branched cover of 12a_0087
Z/175
2 2
12a_0088
2

detected by
the Lickorish test
1-8t+30t^2-65t^3+83t^4-65t^5+30t^6-8t^7+t^8
Seifert matrix of 12a_0088
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 1 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 0 -1 -1
-1 -1 1 -1 0 1 1 0
0 0 0 0 0 0 1 0
0 0 -1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,1-15t+34t^2-86t^3+138t^4-110t^5+58t^6-34t^7+12t^8,-7t+10t^2-5t^3+3t^4-2t^5,0,0,0,0,-35t^2+260t^3-890t^4+1519t^5-1523t^6+1075t^7-626t^8+288t^9-86t^10+12t^11)
the Blanchfield form on it
x
291
First homology
of the double branched cover of 12a_0088
Z/291
-2 2
12a_0089
1

detected by
an unknotting move
4-17t+38t^2-49t^3+38t^4-17t^5+4t^6
Seifert matrix of 12a_0089
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
1 1 0 -1 2 0
1 1 1 -1 1 2
1
Generator of the Alexander module
(0,8t-16t^2+12t^3-4t^4,0,0,2-10t+16t^2-12t^3+4t^4,-1+8t^2-10t^3+4t^4)
the Blanchfield form on it
-4t^-2+25t^-1-40+25t-4t^2
167
First homology
of the double branched cover of 12a_0089
Z/167
2 2
12a_0090
1

detected by
an unknotting move
1-7t+24t^2-49t^3+61t^4-49t^5+24t^6-7t^7+t^8
Seifert matrix of 12a_0090
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 1 0 0
0 0 0 -1 0 0 0 -1
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 -1 -1 0
-1 -1 1 0 1 0 0 1
1
Generator of the Alexander module
(0,-2t+t^2,-2t+t^2,1+4t-6t^2+2t^3,0,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-10t^-1+12-10t+4t^2-t^3
223
First homology
of the double branched cover of 12a_0090
Z/223
-2 2
12a_0091
2

detected by
the signature
-1+8t-26t^2+47t^3-57t^4+47t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0091
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 0 0
0 0 -1 -1 0 0 -1 0
0 0 0 0 -1 0 0 0
0 0 0 -1 0 -1 0 -1
-1 -1 1 0 -1 0 1 0
0 0 -1 -1 0 0 0 -1
1
Generator of the Alexander module
(0,1+10t-14t^2+20t^3-12t^4,-3t+4t^2-5t^3+3t^4,14t-21t^2+21t^3-13t^4-2t^5+3t^6,0,-3t^2+4t^3-2t^4-t^5+5t^6-3t^7,-6t+8t^2-10t^3+6t^4,-3t^3+4t^4-5t^5+3t^6)
the Blanchfield form on it
x
221
First homology
of the double branched cover of 12a_0091
Z/221
-4 4
12a_0092
1

detected by
an unknotting move
1-8t+23t^2-40t^3+47t^4-40t^5+23t^6-8t^7+t^8
Seifert matrix of 12a_0092
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 0 0
-1 -1 1 1 -1 1 0 0
0 0 0 0 -1 0 0 0
-1 -1 1 0 -1 1 0 0
-1 -1 0 0 -1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+8t^-2-20t^-1+27-20t+8t^2-t^3
191
First homology
of the double branched cover of 12a_0092
Z/191
2 2
12a_0093
4

detected by
the signature
-3+9t-16t^2+21t^3-23t^4+21t^5-16t^6+9t^7-3t^8
Seifert matrix of 12a_0093
-1 -1 -1 -1 0 -1 -1 0
0 -2 -2 -1 0 -2 -2 0
0 -1 -2 -1 0 -1 -2 0
0 -1 -1 -2 0 -1 -1 0
0 -1 -1 0 -1 -1 -1 0
0 -1 -2 -1 0 -2 -2 0
0 -1 -1 -1 0 -1 -2 0
0 -1 -1 0 -1 -1 -1 -1
1
Generator of the Alexander module
(2t+t^2-2t^3,0,1+2t+t^2,t^2,-t^2,1+t,1+2t+t^2,-t-2t^2)
the Blanchfield form on it
-15t^-3+24t^-2-32t^-1+37-32t+24t^2-15t^3
121
First homology
of the double branched cover of 12a_0093
Z/121
-8 8
12a_0094
3

detected by
the signature
6-20t+35t^2-41t^3+35t^4-20t^5+6t^6
Seifert matrix of 12a_0094
-1 -1 1 -1 0 0
0 -2 2 -1 0 0
0 1 -3 1 0 0
0 -1 1 -2 0 0
0 -1 1 0 -1 0
0 -1 1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-3t^-3+11t^-2-20t^-1+24-20t+11t^2-3t^3
163
First homology
of the double branched cover of 12a_0094
Z/163
-6 6
12a_0095
2

detected by
the Lickorish test
3-18t+46t^2-61t^3+46t^4-18t^5+3t^6
Seifert matrix of 12a_0095
-1 0 -1 0 0 -1
0 -1 0 0 -1 0
0 0 -2 0 0 -1
0 0 0 1 1 -1
0 0 0 0 1 0
0 0 -1 0 0 -2
1
Generator of the Alexander module
(0,-2,0,t,0,1)
the Blanchfield form on it
-3t^-2+12t^-1-17+12t-3t^2
195
First homology
of the double branched cover of 12a_0095
Z/195
-2 2
12a_0096
3

detected by
the signature
5-15t+24t^2-27t^3+24t^4-15t^5+5t^6
Seifert matrix of 12a_0096
-1 0 -1 1 0 0
0 -1 0 -1 0 -1
0 0 -2 1 0 0
0 0 1 -3 0 0
0 -1 0 -1 -1 -1
0 0 0 -1 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
3t^-2-5t^-1+5-5t+3t^2
115
First homology
of the double branched cover of 12a_0096
Z/115
-6 6
12a_0097
2

detected by
the signature
10-32t+45t^2-32t^3+10t^4
Seifert matrix of 12a_0097
-1 0 -1 1
0 -2 0 1
0 0 -2 1
0 0 1 -3
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-5t^-2+17t^-1-24+17t-5t^2
129
First homology
of the double branched cover of 12a_0097
Z/129
-4 4
12a_0098
1

detected by
an unknotting move
1-7t+22t^2-41t^3+49t^4-41t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0098
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 -1 0 1 1 1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 -1 0 0 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,t^2,0,1+t-t^3,1+t-t^3,0,0,0)
the Blanchfield form on it
t^-3-6t^-2+14t^-1-18+14t-6t^2+t^3
191
First homology
of the double branched cover of 12a_0098
Z/191
-2 2
12a_0099
1

detected by
an unknotting move
-1+7t-24t^2+47t^3-59t^4+47t^5-24t^6+7t^7-t^8
Seifert matrix of 12a_0099
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 -1
-1 -1 0 1 1 1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 1 0 0 0 1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,t,0,0,0,t,1)
the Blanchfield form on it
t^-3-5t^-2+12t^-1-15+12t-5t^2+t^3
217
First homology
of the double branched cover of 12a_0099
Z/217
0 0
12a_0100
2

detected by
the Nakanishi index
-3+21t-53t^2+71t^3-53t^4+21t^5-3t^6
Seifert matrix of 12a_0100
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 2 0 1 0
0 0 0 -1 0 0
1 1 1 1 2 0
-1 -1 -1 -1 -1 1
2
225
First homology
of the double branched cover of 12a_0100
Z/45+Z/5
0 0
12a_0101
1

detected by
an unknotting move
-1+7t-25t^2+50t^3-63t^4+50t^5-25t^6+7t^7-t^8
Seifert matrix of 12a_0101
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 1 0 1 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 1 -1 1 1 1 0
0 0 0 0 0 0 1 0
0 0 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,t-t^2-2t^3-3t^4+t^5+t^6,1+t+t^2-2t^3-4t^4+t^5+t^6,-2t^2-3t^3+t^4+t^5,t+2t^2-t^4,-t-t^2-3t^3-6t^4+2t^5+2t^6,t+2t^2-t^4,t-3t^3+t^5)
the Blanchfield form on it
x
229
First homology
of the double branched cover of 12a_0101
Z/229
0 0
12a_0102
3

detected by
the signature
7-27t+53t^2-65t^3+53t^4-27t^5+7t^6
Seifert matrix of 12a_0102
-1 -1 -1 -1 0 0
0 -2 -1 -1 0 -1
0 -1 -2 -1 0 0
0 -1 -1 -2 0 0
0 0 0 -1 -1 1
0 0 0 1 0 -2
1 or 2
239
First homology
of the double branched cover of 12a_0102
Z/239
-6 6
12a_0103
2

detected by
the Lickorish test
3-20t+52t^2-69t^3+52t^4-20t^5+3t^6
Seifert matrix of 12a_0103
-1 -1 0 -1 0 -1
0 -2 0 -1 0 -1
0 0 1 -1 0 0
0 -1 0 -2 0 -2
0 0 0 0 1 -1
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,3-t,0)
the Blanchfield form on it
3t^-2-11t^-1+16-11t+3t^2
219
First homology
of the double branched cover of 12a_0103
Z/219
-2 2
12a_0104
1

detected by
an unknotting move
4-17t+37t^2-47t^3+37t^4-17t^5+4t^6
Seifert matrix of 12a_0104
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
1 1 0 -1 2 -1
0 0 1 0 0 2
1
Generator of the Alexander module
(0,-t,0,0,1+t,0)
the Blanchfield form on it
4t^-2-11t^-1+15-11t+4t^2
163
First homology
of the double branched cover of 12a_0104
Z/163
2 2
12a_0105
3

detected by
the signature
1-7t+17t^2-26t^3+29t^4-26t^5+17t^6-7t^7+t^8
Seifert matrix of 12a_0105
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 1 1 0 1
0 0 0 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1+t^2,0,0,0,1-t-t^3,0)
the Blanchfield form on it
t^-3-6t^-2+11t^-1-14+11t-6t^2+t^3
131
First homology
of the double branched cover of 12a_0105
Z/131
-6 6
12a_0106
2

detected by
the signature
-2+14t-34t^2+45t^3-34t^4+14t^5-2t^6
Seifert matrix of 12a_0106
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 -1
0 0 0 -1 0 0
0 0 0 0 -1 1
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,t,1)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
145
First homology
of the double branched cover of 12a_0106
Z/145
-4 4
12a_0107
3

detected by
the signature
7-27t+53t^2-65t^3+53t^4-27t^5+7t^6
Seifert matrix of 12a_0107
-1 -1 -1 0 0 -1
0 -2 -1 -1 0 -1
0 -1 -2 0 0 -1
0 0 0 -2 0 1
0 -1 0 -1 -1 0
0 -1 -1 0 0 -2
1 or 2
239
First homology
of the double branched cover of 12a_0107
Z/239
-6 6
12a_0108
1

detected by
an unknotting move
1-8t+26t^2-51t^3+63t^4-51t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0108
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 1 1 1 0
0 0 0 -1 0 0 0 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 -1 0 0
-1 -1 0 -1 0 1 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,-t-t^2,1-4t-4t^2,-1+t+t^2+2t^3,2t,2+t,2t+t^2+2t^3,1)
the Blanchfield form on it
96t^-3-285t^-2+602t^-1-750+602t-285t^2+96t^3
235
First homology
of the double branched cover of 12a_0108
Z/235
-2 2
12a_0109
1

detected by
an unknotting move
-2+14t-35t^2+47t^3-35t^4+14t^5-2t^6
Seifert matrix of 12a_0109
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 0
1 1 1 2 0 0
-1 -1 -1 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
149
First homology
of the double branched cover of 12a_0109
Z/149
0 0
12a_0110
2

detected by
the signature
-3+18t-42t^2+55t^3-42t^4+18t^5-3t^6
Seifert matrix of 12a_0110
-1 -1 0 0 0 -1
0 -2 0 0 0 -1
0 0 1 -1 0 -1
0 0 0 -1 0 0
0 0 0 -1 -1 0
0 -1 0 0 0 -2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-2t^-2+9t^-1-13+9t-2t^2
181
First homology
of the double branched cover of 12a_0110
Z/181
-4 4
12a_0111
2

detected by
the signature
-1+8t-26t^2+47t^3-57t^4+47t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0111
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 1 1 1
0 0 0 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
2t^-2-5t^-1+7-5t+2t^2
221
First homology
of the double branched cover of 12a_0111
Z/221
-4 4
12a_0112
1

detected by
an unknotting move
1-7t+20t^2-35t^3+41t^4-35t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0112
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 1
-1 -1 0 1 1 1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 1 0 0 1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,t,0,1+t,0,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-11+9t-5t^2+t^3
167
First homology
of the double branched cover of 12a_0112
Z/167
2 2
12a_0113
2

detected by
the Lickorish test
1-7t+24t^2-48t^3+59t^4-48t^5+24t^6-7t^7+t^8
Seifert matrix of 12a_0113
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
0 0 0 -1 0 0 0 -1
0 0 -1 0 -1 0 0 -1
0 0 0 0 0 1 0 0
0 0 -1 0 -1 0 -1 -1
-1 -1 1 0 0 1 0 1
2
219
First homology
of the double branched cover of 12a_0113
Z/219
-2 2
12a_0114
2

detected by
the signature
-4+21t-46t^2+59t^3-46t^4+21t^5-4t^6
Seifert matrix of 12a_0114
-1 -1 -1 -1 0 -1
0 -2 -1 -2 0 -1
0 -1 -2 -1 0 -1
0 -1 -1 -2 0 -1
0 0 0 0 1 -1
0 -1 -1 -1 0 -2
2
201
First homology
of the double branched cover of 12a_0114
Z/201
-4 4
12a_0115
1

detected by
an unknotting move
-1+7t-25t^2+50t^3-63t^4+50t^5-25t^6+7t^7-t^8
Seifert matrix of 12a_0115
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 1 0
0 0 0 -1 0 0 0 0
0 0 -1 0 -1 0 -1 0
-1 -1 1 -1 0 1 1 1
0 0 0 0 0 0 1 0
-1 -1 1 -1 0 0 1 1
1
Generator of the Alexander module
(0,-2-2t+2t^2+t^3-12t^4+26t^5-26t^6+10t^7-2t^8,-4t+t^2+13t^3-38t^4+52t^5-36t^6+12t^7-2t^8,-4+t+13t^2-38t^3+52t^4-36t^5+12t^6-2t^7,-3+11t-14t^2+16t^4-8t^5+2t^6,-2-6t+3t^2+14t^3-50t^4+78t^5-62t^6+22t^7-4t^8,4-t-13t^2+38t^3-52t^4+36t^5-12t^6+2t^7,-4t+t^2+13t^3-38t^4+52t^5-36t^6+12t^7-2t^8)
the Blanchfield form on it
x
229
First homology
of the double branched cover of 12a_0115
Z/229
0 0
12a_0116
2

detected by
the Lickorish test
1-7t+20t^2-36t^3+43t^4-36t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0116
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 1 0
-1 -1 1 1 1 1 1 0
0 0 0 0 1 0 0 0
-1 -1 1 0 1 1 1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 1 1
2
171
First homology
of the double branched cover of 12a_0116
Z/171
2 2
12a_0117
2

detected by
the signature
-4+21t-46t^2+59t^3-46t^4+21t^5-4t^6
Seifert matrix of 12a_0117
-1 -1 -1 0 -1 -1
0 -2 -1 0 -1 -2
0 -1 -2 0 -1 -1
0 0 0 1 -1 0
0 -1 -1 0 -2 -1
0 -1 -1 0 -1 -2
2
201
First homology
of the double branched cover of 12a_0117
Z/201
-4 4
12a_0118
1

detected by
an unknotting move
-2+13t-32t^2+43t^3-32t^4+13t^5-2t^6
Seifert matrix of 12a_0118
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 -1 2 -1 0
0 0 0 0 -1 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,-3+t)
the Blanchfield form on it
-2t^-2+6t^-1-9+6t-2t^2
137
First homology
of the double branched cover of 12a_0118
Z/137
0 0
12a_0119
2

detected by
the Nakanishi index
-1+7t-22t^2+40t^3-49t^4+40t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0119
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 1 0 1 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 -1 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
189
First homology
of the double branched cover of 12a_0119
Z/63+Z/3
-4 4
12a_0120
1

detected by
an unknotting move
1-8t+26t^2-51t^3+63t^4-51t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0120
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 0 0
0 0 -1 -1 0 0 -1 -1
0 0 0 0 -1 0 0 0
0 0 -1 -1 0 -1 0 0
-1 -1 1 0 -1 0 1 1
-1 -1 1 0 -1 0 0 1
1
Generator of the Alexander module
(0,t+2t^2+t^3,0,-3t-5t^2-t^3+t^4,1+2t+t^2,-1-3t-t^2+t^3+t^4,1+2t+3t^2+3t^3+t^4,0)
the Blanchfield form on it
1345t^-3-5567t^-2+12442t^-1-15793+12442t-5567t^2+1345t^3
235
First homology
of the double branched cover of 12a_0120
Z/235
-2 2
12a_0121
1

detected by
an unknotting move
-2+13t-33t^2+45t^3-33t^4+13t^5-2t^6
Seifert matrix of 12a_0121
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 2 0 0 -1
-1 -1 0 1 1 1
0 0 0 0 1 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
141
First homology
of the double branched cover of 12a_0121
Z/141
0 0
12a_0122
2

detected by
the Lickorish test
1-7t+20t^2-36t^3+43t^4-36t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0122
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 1 0 0
-1 -1 1 1 0 1 0 1
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 -1 -1 1 0 -1 -1
-1 -1 1 0 0 1 0 1
2
171
First homology
of the double branched cover of 12a_0122
Z/171
2 2
12a_0123
2

detected by
the signature
1-7t+19t^2-30t^3+35t^4-30t^5+19t^6-7t^7+t^8
Seifert matrix of 12a_0123
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 0 1 0 0 0
0 0 0 -1 0 -1 -1 -1
0 0 0 0 1 0 0 0
-1 0 1 0 1 1 0 0
-1 0 1 0 1 1 1 1
-1 0 1 0 1 1 0 1
1
Generator of the Alexander module
(0,0,1+t^2,2+t^2,0,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-13t^-1+16-13t+6t^2-t^3
149
First homology
of the double branched cover of 12a_0123
Z/149
4 4
12a_0124
1

detected by
an unknotting move
2-14t+36t^2-47t^3+36t^4-14t^5+2t^6
Seifert matrix of 12a_0124
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 0 1 0
0 0 0 -1 0 1
0 0 0 0 1 0
1 0 -1 0 -1 2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
151
First homology
of the double branched cover of 12a_0124
Z/151
2 2
12a_0125
1

detected by
an unknotting move
-1+12t-44t^2+67t^3-44t^4+12t^5-t^6
Seifert matrix of 12a_0125
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 -1 0 0
0 0 0 -1 0 0
-1 0 0 -1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,6-2t,-2+t,0,3-t-2t^2+t^3,0)
the Blanchfield form on it
-687t^-2+3437t^-1-5647+3437t-687t^2
181
First homology
of the double branched cover of 12a_0125
Z/181
0 0
12a_0126
1

detected by
an unknotting move
1-8t+26t^2-49t^3+61t^4-49t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0126
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 0 1 0 0 0
0 0 -1 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 -1 0 -1 0 -1
-1 0 1 0 1 0 1 0
0 0 -1 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,-1+2t-t^2,0,-t+2t^2-t^3,-t+2t^2-2t^3+2t^4-t^5,1,0)
the Blanchfield form on it
229
First homology
of the double branched cover of 12a_0126
Z/229
0 0
12a_0127
2

detected by
the Lickorish test
3-17t+37t^2-45t^3+37t^4-17t^5+3t^6
Seifert matrix of 12a_0127
1 0 0 0 0 0
1 -2 0 0 -1 0
0 0 -1 0 0 -1
0 0 0 1 -1 0
1 -1 -1 0 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,-2+2t-t^2,-2t+2t^2-t^3,3-2t+t^2,-2t+2t^2-t^3,2-2t+t^2)
the Blanchfield form on it
-3t^-1+8-3t
159
First homology
of the double branched cover of 12a_0127
Z/159
-2 2
12a_0128
1

detected by
an unknotting move
5-25t+41t^2-25t^3+5t^4
Seifert matrix of 12a_0128
1 0 0 0
1 -2 1 0
-1 1 -3 0
0 0 1 1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
2t^-1-5+2t
101
First homology
of the double branched cover of 12a_0128
Z/101
0 0
12a_0129
2

detected by
the Lickorish test
-1+7t-19t^2+32t^3-37t^4+32t^5-19t^6+7t^7-t^8
Seifert matrix of 12a_0129
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 1 1 1 0 1
0 0 0 1 0 0 0 0
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,-1+t,-1+t,1,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-13t^-1+17-13t+6t^2-t^3
155
First homology
of the double branched cover of 12a_0129
Z/155
-2 2
12a_0130
1

detected by
an unknotting move
-2+14t-36t^2+49t^3-36t^4+14t^5-2t^6
Seifert matrix of 12a_0130
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 1 0 -1
0 0 0 1 0 0
0 0 0 0 -1 1
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
153
First homology
of the double branched cover of 12a_0130
Z/153
0 0
12a_0131
1

detected by
an unknotting move
-1+8t-26t^2+49t^3-59t^4+49t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0131
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 1 1 1 1 0
0 0 0 1 0 0 0 0
-1 0 0 1 1 1 1 1
0 0 0 0 0 -1 0 0
-1 0 0 1 0 1 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,1+5t-9t^2+27t^3-20t^4+19t^5-41t^6-36t^7+226t^8-457t^9+519t^10-354t^11+144t^12-27t^13,-17t^2+52t^3-133t^4+193t^5-279t^6+228t^7+252t^8-1394t^9+3182t^10-4634t^11+4864t^12-3699t^13+1947t^14-657t^15+108t^16,5t-18t^2+35t^3-53t^4+53t^5-40t^6-96t^7+452t^8-886t^9+1108t^10-924t^11+507t^12-171t^13+27t^14,-3
the Blanchfield form on it
x
227
First homology
of the double branched cover of 12a_0131
Z/227
2 2
12a_0132
1

detected by
an unknotting move
1-8t+26t^2-49t^3+61t^4-49t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0132
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 1 0 1 1 1
0 0 0 1 0 0 0 0
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
-1 0 0 1 1 1 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1+t-t^2,1-t)
the Blanchfield form on it
t^-3-7t^-2+18t^-1-24+18t-7t^2+t^3
229
First homology
of the double branched cover of 12a_0132
Z/229
0 0
12a_0133
1

detected by
an unknotting move
-1+8t-26t^2+49t^3-59t^4+49t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0133
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 0 1 0 0 0
0 0 -1 -1 0 0 -1 -1
0 0 0 0 1 0 0 0
0 0 -1 -1 0 -1 0 0
-1 0 1 0 1 0 1 1
-1 0 1 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,-5t+t^4+t^5+4t^7-t^8,1+t+t^2,-2-4t+2t^2-4t^3+5t^4-3t^5+5t^6-t^7,5t-5t^2+5t^3-6t^4+5t^5-5t^6+t^7,0)
the Blanchfield form on it
x
227
First homology
of the double branched cover of 12a_0133
Z/227
2 2
12a_0134
2

detected by
the Lickorish test
1-8t+26t^2-47t^3+57t^4-47t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0134
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 0 0 1 -1 -1 -1 1
-1 -1 1 0 -1 -1 -1 0
-1 -1 1 0 0 -1 0 0
-1 -1 1 0 0 -1 -1 0
0 0 0 0 -1 -1 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
221
First homology
of the double branched cover of 12a_0134
Z/221
0 2
12a_0135
1

detected by
an unknotting move
2-15t+42t^2-57t^3+42t^4-15t^5+2t^6
Seifert matrix of 12a_0135
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
-1 0 0 1 1 1
1 1 -1 0 -2 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,1,0,-3+t,1,-t)
the Blanchfield form on it
2t^-1-5+2t
175
First homology
of the double branched cover of 12a_0135
Z/175
2 2
12a_0136
2

detected by
the Lickorish test
-1+8t-26t^2+47t^3-55t^4+47t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0136
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 -1 0 0 0
0 0 0 -1 0 -1 -1 -1
-1 -1 0 0 -1 0 0 0
-1 0 1 0 -1 1 0 0
-1 0 1 0 -1 1 1 1
-1 0 1 0 -1 1 0 1
1
Generator of the Alexander module
(0,0,0,1,0,-t,0,0)
the Blanchfield form on it
t^-3-7t^-2+19t^-1-26+19t-7t^2+t^3
219
First homology
of the double branched cover of 12a_0136
Z/219
2 2
12a_0137
1

detected by
an unknotting move
1-8t+26t^2-46t^3+53t^4-46t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0137
1 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 -1
0 0 1 1 0 0 1 1
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 1 0
-1 0 -1 0 0 -1 0 0
0 0 0 1 0 0 1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
215
First homology
of the double branched cover of 12a_0137
Z/215
2 2
12a_0138
1

detected by
an unknotting move
1-8t+26t^2-48t^3+57t^4-48t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0138
1 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 -1
0 0 1 0 0 0 0 1
0 0 -1 -1 -1 0 -1 -1
0 0 -1 0 -1 0 0 -1
-1 0 -1 0 0 -1 0 0
0 0 -1 0 -1 0 -1 -1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,-1,t,t,t,t,0)
the Blanchfield form on it
t^-3-8t^-2+24t^-1-35+24t-8t^2+t^3
223
First homology
of the double branched cover of 12a_0138
Z/223
-2 2
12a_0139
1

detected by
an unknotting move
-1+8t-28t^2+56t^3-71t^4+56t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0139
1 0 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 -1
0 0 1 1 0 -1 0 1
0 0 0 1 0 -1 0 0
-1 0 -1 0 -1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 -1 -1 0
0 0 0 1 0 -1 0 1
1
Generator of the Alexander module
(0,1,0,0,4-3t+t^2,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
257
First homology
of the double branched cover of 12a_0139
Z/257
0 0
12a_0140
1

detected by
an unknotting move
-2+15t-43t^2+61t^3-43t^4+15t^5-2t^6
Seifert matrix of 12a_0140
1 0 0 0 0 0
-1 -1 -1 -1 0 -1
0 0 1 0 0 1
-1 0 -1 -1 0 0
0 0 1 0 -2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-7t^-2+19t^-1-26+19t-7t^2+t^3
181
First homology
of the double branched cover of 12a_0140
Z/181
0 0
12a_0141 1 or 2
-1+7t-20t^2+33t^3-39t^4+33t^5-20t^6+7t^7-t^8
Seifert matrix of 12a_0141
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 -1 0 0
-1 -1 1 1 0 -1 1 0
0 0 0 0 -1 0 0 -1
0 0 0 0 0 -1 0 0
-1 -1 1 0 0 -1 1 0
-1 -1 1 1 0 -1 1 1
1
Generator of the Alexander module
(0,1,-2t+3t^2-t^3,0,0,0,0,0)
the Blanchfield form on it
9t^-3-63t^-2+170t^-1-228+170t-63t^2+9t^3
161
First homology
of the double branched cover of 12a_0141
Z/161
0 2
12a_0142
2

detected by
the signature
-1+7t-22t^2+39t^3-47t^4+39t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0142
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 -1 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 -1 0
0 0 0 0 0 -1 0 0
-1 -1 1 0 0 -1 1 0
0 0 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+7t^-2-20t^-1+27-20t+7t^2-t^3
185
First homology
of the double branched cover of 12a_0142
Z/185
-4 4
12a_0143
4

detected by
the signature
-3+8t-12t^2+13t^3-13t^4+13t^5-12t^6+8t^7-3t^8
Seifert matrix of 12a_0143
-1 -1 -1 -1 -1 -1 -1 -1
0 -2 -2 -2 -1 -2 -2 -2
0 -1 -2 -2 -1 -1 -2 -2
0 -1 -1 -2 -1 -1 -1 -2
0 -1 -1 -1 -2 -1 -1 -1
0 -1 -2 -2 -1 -2 -2 -2
0 -1 -1 -2 -1 -1 -2 -2
0 -1 -1 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(t,0,0,0,1,0,0,0)
the Blanchfield form on it
-3t^-3+4t^-2-4t^-1+4-4t+4t^2-3t^3
85
First homology
of the double branched cover of 12a_0143
Z/85
-8 8
12a_0144
3

detected by
the signature
6-19t+32t^2-37t^3+32t^4-19t^5+6t^6
Seifert matrix of 12a_0144
-1 -1 -1 1 -1 -1
0 -2 -2 2 -1 -2
0 -1 -2 2 -1 -1
0 1 1 -3 1 1
0 -1 -1 1 -2 -1
0 -1 -2 2 -1 -2
1
Generator of the Alexander module
(2t-10t^2+10t^3+6t^4-32t^5+28t^6-8t^7,0,-1+6t^2+6t^3-12t^4-2t^5+4t^6,2t-4t^2-8t^3+6t^4+6t^5-4t^6,-2t+6t^2+4t^4-10t^5+4t^6,2t+2t^2-2t^3-6t^4+4t^5)
the Blanchfield form on it
x
151
First homology
of the double branched cover of 12a_0144
Z/151
-6 6
12a_0145
3

detected by
the signature
6-21t+39t^2-47t^3+39t^4-21t^5+6t^6
Seifert matrix of 12a_0145
-1 -1 1 1 -1 1
0 -2 2 2 -1 2
0 1 -3 -3 1 -3
0 1 -2 -3 1 -2
0 -1 1 1 -2 1
0 1 -2 -3 1 -3
1
Generator of the Alexander module
(0,0,2,1,0,0)
the Blanchfield form on it
11t^-2-29t^-1+40-29t+11t^2
179
First homology
of the double branched cover of 12a_0145
Z/179
-6 6
12a_0146
3

detected by
the signature
-1+3t-6t^2+7t^3-7t^4+7t^5-7t^6+7t^7-6t^8+3t^9-t^10
Seifert matrix of 12a_0146
-1 0 0 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0 0 0
-1 -1 1 0 0 0 1 0 0 0
-1 -1 1 1 0 0 1 1 0 0
-1 -1 1 1 1 0 1 1 1 0
-1 -1 1 1 1 1 1 1 1 1
0 0 0 0 0 0 1 0 0 0
-1 -1 1 0 0 0 1 1 0 0
-1 -1 1 1 0 0 1 1 1 0
-1 -1 1 1 1 0 1 1 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-3t^-3+6t^-2-7t^-1+7-7t+6t^2-3t^3+t^4
55
First homology
of the double branched cover of 12a_0146
Z/55
6 6
12a_0147
2

detected by
the signature
-2+7t-15t^2+20t^3-21t^4+20t^5-15t^6+7t^7-2t^8
Seifert matrix of 12a_0147
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 0 1 0
-1 -1 1 1 0 0 1 1
1 1 -1 -1 2 0 -1 -1
-1 -1 1 1 -1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 1 0 0 0 1 1
1
Generator of the Alexander module
(0,4-12t-2t^2-11t^3-7t^4+11t^5-t^6+10t^7+5t^8-4t^9,-2t+2t^2-4t^3+3t^4-t^5+t^6+2t^7-t^8,-2t+10t^2-8t^3+11t^4-13t^5+3t^6+2t^7+t^8+4t^9-2t^10,-7+10t-11t^2+17t^3-7t^4-7t^7+3t^8,3-8t+7t^2-11t^3+6t^4-t^6+5t^7-2t^8,2+2t-16t^2+13t^3-21t^4+25t^5-8t^6-3t^7-2t^8-8t^9+4t^10,2-6t+4t^2-11t^3+25t^4-15t^5+22t^6-24t
the Blanchfield form on it
x
109
First homology
of the double branched cover of 12a_0147
Z/109
4 4
12a_0148
2

detected by
the signature
-2+8t-20t^2+32t^3-37t^4+32t^5-20t^6+8t^7-2t^8
Seifert matrix of 12a_0148
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 0 1 0
1 1 -1 2 1 0 -1 1
1 1 -1 2 2 0 -1 2
-1 -1 1 -1 -1 1 1 -1
0 0 0 0 0 0 1 0
1 1 -1 2 1 0 -1 2
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
2t^-3-7t^-2+15t^-1-19+15t-7t^2+2t^3
161
First homology
of the double branched cover of 12a_0148
Z/161
4 4
12a_0149
1

detected by
an unknotting move
1-7t+22t^2-43t^3+53t^4-43t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0149
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 -1 0 0
0 0 0 -1 0 0 -1 0
-1 -1 1 0 1 -1 0 1
0 0 0 0 0 -1 0 0
0 0 0 0 0 0 -1 0
-1 -1 1 1 0 -1 1 1
1
Generator of the Alexander module
(0,0,-1-2t,-2,-2,0,0,-2t)
the Blanchfield form on it
t^-3-5t^-2+10t^-1-13+10t-5t^2+t^3
199
First homology
of the double branched cover of 12a_0149
Z/199
-2 2
12a_0150
2

detected by
the Lickorish test
4-16t+36t^2-47t^3+36t^4-16t^5+4t^6
Seifert matrix of 12a_0150
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 1 0
1 1 -1 2 -1 0
0 0 0 0 1 0
1 1 -1 1 -1 2
1 or 2
159
First homology
of the double branched cover of 12a_0150
Z/159
2 2
12a_0151
1

detected by
an unknotting move
2-13t+35t^2-47t^3+35t^4-13t^5+2t^6
Seifert matrix of 12a_0151
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
-1 -1 1 -1 1 0
0 0 0 0 1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
147
First homology
of the double branched cover of 12a_0151
Z/147
-2 2
12a_0152
2

detected by
the signature
9-28t+39t^2-28t^3+9t^4
Seifert matrix of 12a_0152
-1 -1 -1 -1
0 -2 -1 -2
0 -1 -2 -1
0 -1 -1 -4
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-3t^-2+10t^-1-14+10t-3t^2
113
First homology
of the double branched cover of 12a_0152
Z/113
-4 4
12a_0153
1

detected by
an unknotting move
3-11t+24t^2-31t^3+24t^4-11t^5+3t^6
Seifert matrix of 12a_0153
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 1 0
-1 -1 1 1 1 1
0 0 0 0 1 0
-1 -1 1 0 1 3
1
Generator of the Alexander module
(0,0,0,1,0,1)
the Blanchfield form on it
-4t^-2+12t^-1-17+12t-4t^2
107
First homology
of the double branched cover of 12a_0153
Z/107
2 2
12a_0154
2

detected by
the signature
-4+24t-56t^2+73t^3-56t^4+24t^5-4t^6
Seifert matrix of 12a_0154
-1 -1 0 -1 0 -1
0 -2 0 -1 0 -1
0 1 1 0 1 1
0 -1 0 -2 0 -1
0 -1 0 0 -1 0
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(t,0,-t,-1,2,0)
the Blanchfield form on it
-4t^-2+22t^-1-34+22t-4t^2
241
First homology
of the double branched cover of 12a_0154
Z/241
-4 4
12a_0155
2

detected by
the Lickorish test
2-15t+41t^2-55t^3+41t^4-15t^5+2t^6
Seifert matrix of 12a_0155
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 -1 0 0
1 1 0 1 2 0
-1 -1 0 -1 -1 1
1
Generator of the Alexander module
(8+30t-10t^2+74t^3-142t^4+98t^5-2t^6-12t^7,-5-15t+40t^2-35t^3+10t^4,1+2t-2t^2-6t^3+7t^4-2t^5,-2+12t+50t^2-95t^3-13t^4+124t^5-81t^6+8t^7+4t^8,1+3t-8t^2+7t^3-2t^4,2+18t+18t^2-70t^3+54t^4-6t^5-4t^6)
the Blanchfield form on it
x
171
First homology
of the double branched cover of 12a_0155
Z/171
-2 2
12a_0156
2

detected by
the signature
11-35t+49t^2-35t^3+11t^4
Seifert matrix of 12a_0156
-1 1 -1 1
0 -3 1 -1
0 1 -2 1
0 -2 1 -3
1 or 2
141
First homology
of the double branched cover of 12a_0156
Z/141
-4 4
12a_0157
2

detected by
A(F_2)
-1+7t-22t^2+40t^3-49t^4+40t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0157
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 -1 1 0
0 0 0 -1 0 0 0 -1
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 1 0 1 0
-1 -1 1 0 1 -1 1 1
2
189
First homology
of the double branched cover of 12a_0157
Z/189
0 0
12a_0158
3

detected by
the signature
1-7t+16t^2-23t^3+25t^4-23t^5+16t^6-7t^7+t^8
Seifert matrix of 12a_0158
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
0 0 -1 0 0 -1 0 -1
-1 -1 0 1 -1 1 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 0 -1 0 0
0 0 -1 0 0 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-3-7t^-2+16t^-1-21+16t-7t^2+t^3
119
First homology
of the double branched cover of 12a_0158
Z/119
-6 6
12a_0159
2

detected by
the signature
-2+15t-37t^2+49t^3-37t^4+15t^5-2t^6
Seifert matrix of 12a_0159
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -2 0 0 1
-1 -1 0 1 -1 1
0 0 0 0 -1 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
t^-3-8t^-2+21t^-1-28+21t-8t^2+t^3
157
First homology
of the double branched cover of 12a_0159
Z/157
-4 4
12a_0160
2

detected by
the signature
-2+7t-14t^2+18t^3-19t^4+18t^5-14t^6+7t^7-2t^8
Seifert matrix of 12a_0160
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
0 0 1 0 0 0 1 0
0 0 1 1 0 0 1 1
0 0 0 0 1 0 0 0
1 1 1 1 -1 2 1 1
0 0 0 0 0 0 1 0
0 0 1 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-4+4t^-3-8t^-2+11t^-1-12+11t-8t^2+4t^3-t^4
101
First homology
of the double branched cover of 12a_0160
Z/101
4 4
12a_0161
1

detected by
an unknotting move
4-16t+34t^2-43t^3+34t^4-16t^5+4t^6
Seifert matrix of 12a_0161
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 2 0 0 0
0 0 -1 1 0 0
0 0 0 0 1 0
1 1 -1 1 -1 2
1 or 2
151
First homology
of the double branched cover of 12a_0161
Z/151
2 2
12a_0162
2

detected by
the signature
-4+24t-56t^2+73t^3-56t^4+24t^5-4t^6
Seifert matrix of 12a_0162
-1 -1 0 0 -1 -1
0 -2 0 0 -1 -1
0 1 1 -1 0 0
0 0 0 -1 0 -1
0 -1 0 0 -2 -1
0 -1 0 0 -1 -2
1
Generator of the Alexander module
(-4t+8t^2-6t^3-4t^4+12t^5-8t^6,0,3t^2-4t^3+6t^5-4t^6,1-2t+4t^2-6t^3+4t^4,3t^4-4t^5+6t^7-4t^8,-4+6t-4t^2)
the Blanchfield form on it
x
241
First homology
of the double branched cover of 12a_0162
Z/241
-4 4
12a_0163
1

detected by
an unknotting move
4-22t+54t^2-71t^3+54t^4-22t^5+4t^6
Seifert matrix of 12a_0163
-1 -1 0 -1 -1 0
0 -2 0 -1 -1 0
0 1 1 0 1 1
0 -1 0 -2 -1 0
0 -1 0 -1 -2 0
0 0 0 0 1 1
1
Generator of the Alexander module
(-2,0,1,0,0,0)
the Blanchfield form on it
4t^-2-16t^-1+27-16t+4t^2
231
First homology
of the double branched cover of 12a_0163
Z/231
-2 2
12a_0164
2

detected by
the Nakanishi index
1-7t+20t^2-36t^3+43t^4-36t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0164
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 1 0
-1 -1 1 1 -1 1 1 0
0 0 0 0 -1 0 0 0
-1 -1 1 0 -1 1 1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
171
First homology
of the double branched cover of 12a_0164
Z/57+Z/3
-2 2
12a_0165
2

detected by
the signature
-2+11t-24t^2+31t^3-24t^4+11t^5-2t^6
Seifert matrix of 12a_0165
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 0
1 1 1 2 -1 0
0 0 0 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,-1+t)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
105
First homology
of the double branched cover of 12a_0165
Z/105
-4 4
12a_0166
2

detected by
the Nakanishi index
1-7t+20t^2-36t^3+43t^4-36t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0166
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 -1 -1 0
-1 -1 1 1 -1 -1 -1 1
0 0 0 0 -1 0 -1 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 0 -1 0
-1 -1 1 0 -1 -1 -1 1
2
171
First homology
of the double branched cover of 12a_0166
Z/57+Z/3
-2 2
12a_0167
2

detected by
the Nakanishi index
-2+8t-19t^2+30t^3-35t^4+30t^5-19t^6+8t^7-2t^8
Seifert matrix of 12a_0167
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 1
0 0 0 1 0 1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
1 1 1 1 -1 1 2 1
0 0 0 0 0 0 0 1
2
153
First homology
of the double branched cover of 12a_0167
Z/51+Z/3
4 4
12a_0168
1

detected by
an unknotting move
3-11t+22t^2-27t^3+22t^4-11t^5+3t^6
Seifert matrix of 12a_0168
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 1
-1 -1 -1 3 1 -1
0 0 0 0 1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,t,0,1+t,0,0)
the Blanchfield form on it
3t^-2-7t^-1+9-7t+3t^2
99
First homology
of the double branched cover of 12a_0168
Z/99
2 2
12a_0169
1

detected by
an unknotting move
4-12t+17t^2-12t^3+4t^4
Seifert matrix of 12a_0169
-1 0 0 0
-1 -1 0 0
0 0 1 0
1 1 -1 4
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
49
First homology
of the double branched cover of 12a_0169
Z/49
0 0
12a_0170
1

detected by
an unknotting move
3-18t+42t^2-53t^3+42t^4-18t^5+3t^6
Seifert matrix of 12a_0170
1 0 0 0 0 0
1 -2 0 -1 -2 -2
0 0 1 0 0 0
1 -1 0 -2 -1 -1
1 -1 -1 -1 -2 -2
1 -1 0 -1 -1 -2
1
Generator of the Alexander module
(0,-t,0,t,1,1)
the Blanchfield form on it
3t^-2-17t^-1+30-17t+3t^2
179
First homology
of the double branched cover of 12a_0170
Z/179
-2 2
12a_0171
1

detected by
an unknotting move
-3+18t-46t^2+63t^3-46t^4+18t^5-3t^6
Seifert matrix of 12a_0171
1 0 0 0 0 0
1 -2 0 -1 0 -2
0 0 1 0 0 -1
1 -1 0 -2 0 -1
0 0 1 0 1 -1
1 -1 0 -1 0 -2
1
Generator of the Alexander module
(0,-t,t,t,0,1)
the Blanchfield form on it
3t^-2-15t^-1+25-15t+3t^2
197
First homology
of the double branched cover of 12a_0171
Z/197
0 0
12a_0172
2

detected by
the signature
1-7t+18t^2-25t^3+27t^4-25t^5+18t^6-7t^7+t^8
Seifert matrix of 12a_0172
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 0 0 1 0 0
-1 0 1 1 0 1 1 0
0 0 0 0 -1 0 0 -1
0 0 0 0 0 1 0 0
-1 0 1 0 0 1 1 0
-1 0 1 1 0 1 1 1
1
Generator of the Alexander module
(0,5t+18t^2-3t^3-15t^4+24t^5-39t^6+10t^7,3t-10t^2-51t^3+27t^4+42t^5-87t^6+141t^7-69t^8+10t^9,-4-8t^2-26t^3+9t^4-2t^5-53t^6+102t^7-59t^8+10t^9,-8+2t^2+7t^3-6t^4-24t^5+t^6+2t^7,1+7t+4t^2-33t^3-t^4+37t^5-63t^6+49t^7-10t^8,-10t^2-31t^3+24t^4+27t^5-63t^6+102t^7-59t^8+10t^9,-10t^2-31t^3+24t^4+27t^5-63t^6+
the Blanchfield form on it
x
129
First homology
of the double branched cover of 12a_0172
Z/129
4 4
12a_0173
1

detected by
an unknotting move
1-7t+20t^2-35t^3+43t^4-35t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0173
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 0 0 1 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 -1 0
0 0 0 0 0 1 0 0
-1 0 1 0 0 1 1 0
0 0 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,2-2t+2t^2,0,0,0)
the Blanchfield form on it
t^-3-7t^-2+18t^-1-23+18t-7t^2+t^3
169
First homology
of the double branched cover of 12a_0173
Z/169
0 0
12a_0174
1

detected by
an unknotting move
-1+7t-20t^2+35t^3-41t^4+35t^5-20t^6+7t^7-t^8
Seifert matrix of 12a_0174
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 0 0 1 0 0
0 0 0 -1 0 0 -1 0
-1 0 1 0 1 1 0 1
0 0 0 0 0 1 0 0
0 0 0 0 0 0 -1 0
-1 0 1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,1+2t,4,0,0,2,0)
the Blanchfield form on it
-t^-3+5t^-2-8t^-1+9-8t+5t^2-t^3
167
First homology
of the double branched cover of 12a_0174
Z/167
2 2
12a_0175
2

detected by
the Lickorish test
2-16t+44t^2-59t^3+44t^4-16t^5+2t^6
Seifert matrix of 12a_0175
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 0 -1 0
0 0 0 1 0 0
0 0 0 0 -1 0
1 0 -1 1 1 2
1
Generator of the Alexander module
(-5t+11t^2-8t^3+2t^4,-9t+21t^2-16t^3+4t^4,10t-43t^2+62t^3-37t^4+8t^5,2+2t+26t^2-66t^3+50t^4-12t^5,-1-t+8t^2-53t^3+105t^4-77t^5+19t^6,10t-58t^2+109t^3-96t^4+41t^5-7t^6)
the Blanchfield form on it
x
183
First homology
of the double branched cover of 12a_0175
Z/183
2 2
12a_0176
1

detected by
an unknotting move
2-13t+31t^2-39t^3+31t^4-13t^5+2t^6
Seifert matrix of 12a_0176
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 1 0 0
0 0 0 1 0 0
-1 0 1 1 1 0
0 0 0 0 1 -2
1
Generator of the Alexander module
(0,0,-2+t,-2+t,0,1+4t-2t^2)
the Blanchfield form on it
-6t^-2+31t^-1-49+31t-6t^2
131
First homology
of the double branched cover of 12a_0176
Z/131
2 2
12a_0177
2

detected by
the Nakanishi index
2-15t+41t^2-55t^3+41t^4-15t^5+2t^6
Seifert matrix of 12a_0177
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 1 0 0
1 0 0 -1 2 0
-1 0 0 1 -1 1
2
171
First homology
of the double branched cover of 12a_0177
Z/57+Z/3
2 2
12a_0178
1

detected by
an unknotting move
3-16t+32t^2-37t^3+32t^4-16t^5+3t^6
Seifert matrix of 12a_0178
1 0 0 0 0 0
0 1 0 0 1 0
1 0 -2 0 0 -1
0 1 0 1 1 -1
0 0 0 0 1 0
1 0 -1 0 0 -2
1
Generator of the Alexander module
(0,t-t^4,1+t-t^3,0,0,-2-2t+2t^3)
the Blanchfield form on it
-3t^-2+13t^-1-19+13t-3t^2
139
First homology
of the double branched cover of 12a_0178
Z/139
2 2
12a_0179
2

detected by
the Lickorish test
-1+7t-18t^2+27t^3-29t^4+27t^5-18t^6+7t^7-t^8
Seifert matrix of 12a_0179
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 -1 0 0 -1 0 -1
-1 0 0 1 1 1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 -1 0 0 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,1,0,0,1+t^2)
the Blanchfield form on it
-t^-3+6t^-2-12t^-1+15-12t+6t^2-t^3
135
First homology
of the double branched cover of 12a_0179
Z/135
-2 2
12a_0180
1

detected by
an unknotting move
-2+15t-41t^2+57t^3-41t^4+15t^5-2t^6
Seifert matrix of 12a_0180
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 -2 0 0 1
-1 0 0 1 1 1
0 0 0 0 1 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1-2t,0,1,0)
the Blanchfield form on it
-t^-2+6t^-1-10+6t-t^2
173
First homology
of the double branched cover of 12a_0180
Z/173
0 0
12a_0181
1

detected by
an unknotting move
-1+11t-40t^2+61t^3-40t^4+11t^5-t^6
Seifert matrix of 12a_0181
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 -1 1 0
0 0 0 -1 0 0
0 0 0 0 -1 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,3-t)
the Blanchfield form on it
-t^-2+7t^-1-13+7t-t^2
165
First homology
of the double branched cover of 12a_0181
Z/165
0 0
12a_0182
2

detected by
the Lickorish test
-1+7t-20t^2+36t^3-43t^4+36t^5-20t^6+7t^7-t^8
Seifert matrix of 12a_0182
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 0 1 0 1 0
-1 0 1 1 1 1 1 0
0 0 0 0 1 0 0 0
-1 0 1 0 1 1 1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
171
First homology
of the double branched cover of 12a_0182
Z/171
2 2
12a_0183
1

detected by
an unknotting move
6-30t+49t^2-30t^3+6t^4
Seifert matrix of 12a_0183
1 0 0 0
0 2 0 1
1 0 -2 -1
1 0 -1 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
3t^-2-14t^-1+22-14t+3t^2
121
First homology
of the double branched cover of 12a_0183
Z/121
0 0
12a_0184
1

detected by
an unknotting move
1-8t+27t^2-52t^3+65t^4-52t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0184
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 0
-1 0 -1 1 0 -1 1 0
0 0 0 0 -1 0 0 -1
-1 -1 -1 0 0 -1 0 0
0 0 -1 0 0 -1 1 0
-1 0 -1 1 0 -1 1 1
1
Generator of the Alexander module
(0,0,0,1,2,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+19-14t+6t^2-t^3
241
First homology
of the double branched cover of 12a_0184
Z/241
0 0
12a_0185
1

detected by
an unknotting move
-1+8t-27t^2+54t^3-67t^4+54t^5-27t^6+8t^7-t^8
Seifert matrix of 12a_0185
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 0
-1 0 -1 1 -1 1 1 0
-1 -1 -1 0 -1 0 0 0
0 0 -1 0 -1 1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,1-t)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+19-14t+6t^2-t^3
247
First homology
of the double branched cover of 12a_0185
Z/247
-2 2
12a_0186
2

detected by
the signature
1-8t+25t^2-40t^3+45t^4-40t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_0186
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 0 0 1 0 -1 1 0
-1 0 0 1 1 -1 1 1
-1 -1 1 0 0 -1 0 0
0 0 0 0 0 -1 1 0
-1 0 0 1 0 -1 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+8t^-2-24t^-1+33-24t+8t^2-t^3
193
First homology
of the double branched cover of 12a_0186
Z/193
4 4
12a_0187
2

detected by
the Lickorish test
2-16t+49t^2-69t^3+49t^4-16t^5+2t^6
Seifert matrix of 12a_0187
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 1 0
1 0 0 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-8t^-2+25t^-1-36+25t-8t^2+t^3
203
First homology
of the double branched cover of 12a_0187
Z/203
2 2
12a_0188
2

detected by
the Lickorish test
-1+8t-26t^2+47t^3-57t^4+47t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0188
1 0 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 -1 -1
0 0 1 1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
-1 0 -1 0 -1 -1 -1 -1
-1 0 -1 0 -1 0 -1 0
-1 0 -1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
-t^-3+8t^-2-24t^-1+33-24t+8t^2-t^3
221
First homology
of the double branched cover of 12a_0188
Z/221
0 2
12a_0189
1

detected by
an unknotting move
1-8t+26t^2-48t^3+59t^4-48t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0189
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 0
0 0 0 1 0 0 0 0
-1 0 -1 0 1 -1 -1 1
-1 -1 -1 0 0 -1 -1 0
-1 -1 0 1 0 0 -1 0
0 0 -1 0 0 -1 -1 1
1
Generator of the Alexander module
(0,-3+7t-5t^2+t^3,3-10t+12t^2-6t^3+t^4,-2-2t+7t^2-5t^3+t^4,11t-25t^2+22t^3-8t^4+t^5,5-8t+5t^2-t^3,3-9t+3t^2+6t^3-5t^4+t^5,-3+12t-13t^2+6t^3-t^4)
the Blanchfield form on it
x
225
First homology
of the double branched cover of 12a_0189
Z/225
0 0
12a_0190
2

detected by
the signature
1-8t+26t^2-46t^3+55t^4-46t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0190
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 1 1 0 0 1 0
-1 0 0 0 1 -1 0 1
-1 -1 1 1 0 -1 1 0
0 0 1 0 0 0 1 0
0 0 0 0 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
217
First homology
of the double branched cover of 12a_0190
Z/217
4 4
12a_0191
1

detected by
an unknotting move
-1+8t-28t^2+58t^3-73t^4+58t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0191
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 -1 0
-1 -1 0 -1 0 0 0 0
-1 0 0 -1 1 0 -1 1
0 0 1 0 0 1 -1 0
-1 -1 0 -1 0 0 -1 0
0 0 0 -1 0 0 -1 1
1
Generator of the Alexander module
(0,1,0,1-t,-t,0,-t,0)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
263
First homology
of the double branched cover of 12a_0191
Z/263
2 2
12a_0192
1

detected by
an unknotting move
2-15t+43t^2-59t^3+43t^4-15t^5+2t^6
Seifert matrix of 12a_0192
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 -1 0 1
-1 -1 0 -1 -1 0
0 0 0 0 2 0
0 0 0 -1 0 1
1
Generator of the Alexander module
(0,0,4-3t+t^2,1,0,t)
the Blanchfield form on it
2t^-1-5+2t
179
First homology
of the double branched cover of 12a_0192
Z/179
2 2
12a_0193
2

detected by
the signature
1-7t+16t^2-19t^3+19t^4-19t^5+16t^6-7t^7+t^8
Seifert matrix of 12a_0193
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 0 0 -1 0 0
-1 0 1 1 0 -1 1 0
-1 0 1 1 1 -1 1 1
0 0 0 0 0 -1 0 0
-1 0 1 0 0 -1 1 0
-1 0 1 1 0 -1 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+7t^-2-16t^-1+19-16t+7t^2-t^3
105
First homology
of the double branched cover of 12a_0193
Z/105
4 4
12a_0194
1

detected by
an unknotting move
2-15t+39t^2-51t^3+39t^4-15t^5+2t^6
Seifert matrix of 12a_0194
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 0 0 -1
1 0 -1 2 0 1
-1 0 1 -1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,2t+2t^2,-2-6t^2-6t^3+2t^4,19-16t+16t^2+2t^3-2t^4,-4t^2-2t^3+2t^4,-2t+2t^2+2t^3)
the Blanchfield form on it
195t^-5-2095t^-4+9482t^-3-24957t^-2+43118t^-1-51456+43118t-24957t^2+9482t^3-2095t^4+195t^5
163
First homology
of the double branched cover of 12a_0194
Z/163
2 2
12a_0195
2

detected by
the signature
1-7t+18t^2-28t^3+33t^4-28t^5+18t^6-7t^7+t^8
Seifert matrix of 12a_0195
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 0 1 -1 1 0
-1 0 1 1 1 -1 1 1
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 1 0 1 0
-1 0 1 0 1 -1 1 1
2
141
First homology
of the double branched cover of 12a_0195
Z/141
4 4
12a_0196
1

detected by
an unknotting move
2-13t+30t^2-37t^3+30t^4-13t^5+2t^6
Seifert matrix of 12a_0196
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 1
0 0 0 -1 0 0
1 0 1 1 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,-t,0,-1-t,0)
the Blanchfield form on it
-2t^-2+12t^-1-21+12t-2t^2
127
First homology
of the double branched cover of 12a_0196
Z/127
2 2
12a_0197
1

detected by
an unknotting move
3-17t+29t^2-17t^3+3t^4
Seifert matrix of 12a_0197
-1 -1 0 0
0 1 0 0
-1 0 3 -1
0 0 0 -1
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
-t^-1+3-t
69
First homology
of the double branched cover of 12a_0197
Z/69
0 0
12a_0198
1

detected by
an unknotting move
-2+16t-50t^2+73t^3-50t^4+16t^5-2t^6
Seifert matrix of 12a_0198
1 0 0 0 0 0
-1 -1 0 -1 0 1
0 0 -1 1 0 -1
0 0 0 1 0 0
0 0 0 0 1 -1
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,-3+2t,9-9t+2t^2,0,5-10t+4t^2,0)
the Blanchfield form on it
-t^-1+3-t
209
First homology
of the double branched cover of 12a_0198
Z/209
0 0
12a_0199
2

detected by
the signature
-5+26t-56t^2+71t^3-56t^4+26t^5-5t^6
Seifert matrix of 12a_0199
1 0 0 0 0 0
0 -1 0 0 -1 0
1 0 -2 -1 0 -2
1 0 -1 -2 -1 -1
1 0 -1 -1 -2 -1
1 0 -1 -1 0 -2
1 or 2
245
First homology
of the double branched cover of 12a_0199
Z/245
-4 4
12a_0200
2

detected by
the Lickorish test
-1+7t-24t^2+47t^3-57t^4+47t^5-24t^6+7t^7-t^8
Seifert matrix of 12a_0200
-1 -1 -1 1 0 0 -1 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 0 0 1 0 -1 0
0 -1 0 0 1 1 -1 1
0 -1 -1 1 0 0 -1 0
0 -1 0 0 1 0 -1 1
1
Generator of the Alexander module
(2t^3+6t^4+6t^5-4t^6-12t^7-6t^8+2t^9+6t^10,0,-2-6t-t^2+8t^3+8t^4+14t^5+10t^6-2t^7-8t^8-6t^9,3+7t+2t^2-6t^3-11t^4-14t^5-10t^6+2t^7+8t^8+6t^9,-2t-6t^2-6t^3+4t^4+14t^5+12t^6+4t^7-8t^8-6t^9,-t^2-t^3+t^4+t^5-7t^6-10t^7+2t^9+6t^10,-1-3t-3t^2+t^3+3t^4,-2t-6t^2-6t^3+4t^4+12t^5+6t^6-2t^7-6t^8)
the Blanchfield form on it
x
215
First homology
of the double branched cover of 12a_0200
Z/215
2 2
12a_0201
1

detected by
an unknotting move
-2+13t-37t^2+53t^3-37t^4+13t^5-2t^6
Seifert matrix of 12a_0201
-1 -1 -1 1 -1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 -1 -1 1 -1 0
0 1 0 0 1 2
1
Generator of the Alexander module
(0,0,0,0,3-2t,1-3t+2t^2)
the Blanchfield form on it
9t^-3-58t^-2+164t^-1-234+164t-58t^2+9t^3
157
First homology
of the double branched cover of 12a_0201
Z/157
0 0
12a_0202
1

detected by
an unknotting move
1-8t+28t^2-58t^3+75t^4-58t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0202
-1 0 -1 -1 -1 0 0 -1
0 1 0 0 0 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 1 -1 -1 -1 1 0 -1
0 1 0 0 0 1 0 0
0 0 -1 0 0 0 1 -1
0 0 -1 -1 0 1 0 -1
1
Generator of the Alexander module
(9t+8t^2-16t^3+4t^4,0,0,-3+2t+12t^2-4t^3,-5-2t+12t^2-4t^3,0,5t+2t^2-12t^3+4t^4,0)
the Blanchfield form on it
t^-1-2+t
265
First homology
of the double branched cover of 12a_0202
Z/265
0 0
12a_0203
2

detected by
the Lickorish test
-1+7t-22t^2+39t^3-45t^4+39t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0203
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 0 0 0
0 0 1 0 0 0 0 0
0 0 0 -1 0 1 1 1
-1 0 -1 0 -1 -1 -1 -1
0 0 1 0 0 1 0 0
0 0 1 0 0 1 1 1
0 0 1 0 0 1 0 1
1
Generator of the Alexander module
(0,0,0,5t^2-5t^3+4t^4-4t^5+t^6,1+3t+2t^3-t^4,5-5t+4t^2-4t^3+t^4,2+t-3t^2+t^3-3t^4+t^5,0)
the Blanchfield form on it
-557t^-3+2372t^-2-2794t^-1+1784-2794t+2372t^2-557t^3
183
First homology
of the double branched cover of 12a_0203
Z/183
2 2
12a_0204
1

detected by
an unknotting move
-2+14t-41t^2+59t^3-41t^4+14t^5-2t^6
Seifert matrix of 12a_0204
1 0 0 0 0 0
-1 -1 0 0 -1 0
0 0 1 0 0 0
0 0 0 -1 0 -1
-1 0 -1 0 -1 1
0 0 -1 0 0 2
1
Generator of the Alexander module
(2-10t-53t^2+28t^3+30t^4-2t^5-8t^6,2+4t-3t^2+43t^3-41t^4+10t^5-14t^6+8t^7,-2-12t-7t^2+29t^3-12t^4,-3-2t+21t^2-24t^3-33t^4-17t^5+64t^6-10t^7-8t^8,2-12t-65t^2+21t^3+59t^4-14t^5-8t^6,-4-24t-12t^2+64t^3-35t^4+4t^5)
the Blanchfield form on it
x
173
First homology
of the double branched cover of 12a_0204
Z/173
0 0
12a_0205
3

detected by
the signature
-2+9t-18t^2+26t^3-29t^4+26t^5-18t^6+9t^7-2t^8
Seifert matrix of 12a_0205
1 0 0 0 0 0 0 0
-1 -1 -1 0 -1 0 1 0
-1 0 -1 0 0 0 1 0
0 0 0 -1 0 0 -1 0
-1 0 -1 0 -1 0 1 0
0 0 0 0 0 -1 0 -1
1 0 0 0 0 -1 -2 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-2t^-3+9t^-2-16t^-1+19-16t+9t^2-2t^3
139
First homology
of the double branched cover of 12a_0205
Z/139
-6 6
12a_0206
2

detected by
the signature
-3+13t-23t^2+27t^3-23t^4+13t^5-3t^6
Seifert matrix of 12a_0206
1 0 0 0 0 0
-1 -1 -1 0 -1 -1
-1 0 -1 0 0 -1
0 0 0 -1 0 1
-1 0 -1 0 -1 -1
-1 0 0 0 0 -3
1
Generator of the Alexander module
(0,0,0,t,0,1)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
105
First homology
of the double branched cover of 12a_0206
Z/105
-4 4
12a_0207
1

detected by
an unknotting move
-1+7t-20t^2+33t^3-37t^4+33t^5-20t^6+7t^7-t^8
Seifert matrix of 12a_0207
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 -1 -1 -1
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
-1 0 -1 0 -1 -1 -1 -1
-1 0 0 -1 0 -1 -1 -1
-1 0 0 -1 0 0 -1 0
-1 0 0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,2-46t+71t^2-80t^3+69t^4-37t^5+10t^6-t^7,0,0,11-44t+47t^2-49t^3+37t^4-15t^5+2t^6,17-16t+17t^2-15t^3+7t^4-t^5,-34t+32t^2-34t^3+30t^4-14t^5+2t^6,2-29t+72t^2-79t^3+71t^4-45t^5+16t^6-2t^7)
the Blanchfield form on it
x
159
First homology
of the double branched cover of 12a_0207
Z/159
-2 2
12a_0208
1

detected by
an unknotting move
-2+14t-39t^2+55t^3-39t^4+14t^5-2t^6
Seifert matrix of 12a_0208
1 0 0 0 0 0
-1 -1 0 0 -1 1
0 0 1 0 0 0
0 0 0 1 0 0
-1 0 -1 0 -1 1
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,0,1,0,-1,0)
the Blanchfield form on it
-2t^-2+10t^-1-17+10t-2t^2
165
First homology
of the double branched cover of 12a_0208
Z/165
0 0
12a_0209
1

detected by
an unknotting move
1-8t+29t^2-60t^3+77t^4-60t^5+29t^6-8t^7+t^8
Seifert matrix of 12a_0209
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 -1 0 0
0 0 1 0 0 0 0 0
0 0 1 1 0 0 -1 1
-1 0 -1 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 -1 0
0 0 1 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,0,0,1-7t+5t^2-t^3,0,3-8t+5t^2-t^3)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
273
First homology
of the double branched cover of 12a_0209
Z/273
0 0
12a_0210
2

detected by
the signature
-4+20t-43t^2+55t^3-43t^4+20t^5-4t^6
Seifert matrix of 12a_0210
-1 0 -1 0 0 0
0 1 0 0 0 0
0 0 -2 0 0 0
0 -1 -1 -1 0 1
0 0 0 0 -1 -1
0 1 1 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
189
First homology
of the double branched cover of 12a_0210
Z/189
-4 4
12a_0211
1

detected by
an unknotting move
2-8t+20t^2-34t^3+41t^4-34t^5+20t^6-8t^7+2t^8
Seifert matrix of 12a_0211
-1 0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 1 0 1 0
0 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
0 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+8t^-2-18t^-1+23-18t+8t^2-2t^3
169
First homology
of the double branched cover of 12a_0211
Z/169
0 0
12a_0212
1

detected by
an unknotting move
4-16t+33t^2-41t^3+33t^4-16t^5+4t^6
Seifert matrix of 12a_0212
-1 0 -1 0 0 0
0 -1 -1 0 0 0
0 0 -2 0 0 0
0 -1 -1 -1 0 0
0 0 0 0 1 0
0 1 0 1 -1 2
1
Generator of the Alexander module
(2-t,0,0,-2+t,0,3-t)
the Blanchfield form on it
-4t^-2+12t^-1-15+12t-4t^2
147
First homology
of the double branched cover of 12a_0212
Z/147
-2 2
12a_0213
2

detected by
the Lickorish test
-1+8t-28t^2+54t^3-65t^4+54t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0213
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 0 0 0
0 0 -1 -1 0 -1 -1 -1
0 0 0 1 0 0 1 0
-1 0 0 -1 -1 0 0 0
0 0 0 -1 0 -1 0 -1
0 0 0 0 0 0 1 0
0 0 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,2-t,0,0,0,0,1)
the Blanchfield form on it
t^-2-5t^-1+9-5t+t^2
247
First homology
of the double branched cover of 12a_0213
Z/247
-2 2
12a_0214
1

detected by
an unknotting move
1-8t+28t^2-56t^3+71t^4-56t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0214
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 0 0
0 0 1 0 -1 1 0 1
-1 0 -1 -1 0 0 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 -1 1 -1 0
0 0 0 0 -1 0 -1 0
0 0 0 0 -1 1 -1 1
1
Generator of the Alexander module
(0,0,1-t,-1,-1+t,1-t^2,t-t^2,2-t-t^2)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+17-14t+6t^2-t^3
257
First homology
of the double branched cover of 12a_0214
Z/257
0 0
12a_0215
2

detected by
the Lickorish test
-1+7t-22t^2+42t^3-51t^4+42t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0215
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 0 0 -1
0 0 1 0 0 0 0 0
0 0 1 1 0 0 1 0
-1 0 -1 -1 -1 0 -1 -1
0 0 0 0 0 1 0 0
0 0 1 0 0 0 1 0
-1 0 -1 -1 0 -1 -1 -1
2
195
First homology
of the double branched cover of 12a_0215
Z/195
2 2
12a_0216
2

detected by
the signature
1-7t+18t^2-24t^3+25t^4-24t^5+18t^6-7t^7+t^8
Seifert matrix of 12a_0216
-1 -1 -1 -1 -1 -1 0 0
0 -1 -1 -1 0 -1 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 -1 -1 -1 -1 0 0
0 0 -1 -1 0 -1 0 0
0 -1 -1 0 -1 -1 1 -1
0 0 0 0 0 0 0 -1
2
125
First homology
of the double branched cover of 12a_0216
Z/125
-4 4
12a_0217
1

detected by
an unknotting move
1-7t+22t^2-42t^3+53t^4-42t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0217
-1 -1 0 -1 -1 -1 0 0
0 -1 0 -1 0 -1 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 0 -1 -1 -1 0 0
0 0 1 -1 0 -1 0 0
0 -1 0 0 -1 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(5t-24t^2+52t^3-54t^4+35t^5-14t^6+3t^7,0,0,-2-3t-16t^2+27t^3-23t^4+11t^5-3t^6,-1+9t-12t^2+9t^3-4t^4+t^5,-3+t-7t^2+11t^3-9t^4+4t^5-t^6,3t-5t^2+19t^3-24t^4+18t^5-8t^6+2t^7,-3+5t-19t^2+24t^3-18t^4+8t^5-2t^6)
the Blanchfield form on it
x
197
First homology
of the double branched cover of 12a_0217
Z/197
0 0
12a_0218
2

detected by
the Lickorish test
2-15t+42t^2-57t^3+42t^4-15t^5+2t^6
Seifert matrix of 12a_0218
-1 1 -1 -1 0 0
0 -2 1 1 0 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 1 -1 0 1 -1
0 0 0 0 0 -1
2
175
First homology
of the double branched cover of 12a_0218
Z/175
-2 2
12a_0219
2

detected by
the signature
1-7t+22t^2-38t^3+45t^4-38t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0219
-1 0 0 -1 -1 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 1 0 0
0 0 0 1 0 0 0 0
0 1 1 -1 -1 1 0 0
0 1 0 0 0 1 0 0
0 0 0 0 -1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,t^2,0,1+t+t^4,0,t+t^2+t^5,0)
the Blanchfield form on it
x
181
First homology
of the double branched cover of 12a_0219
Z/181
4 4
12a_0220
1

detected by
an unknotting move
-1+7t-22t^2+40t^3-47t^4+40t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0220
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 -1 0 -1
0 0 1 0 0 0 0 0
0 0 0 -1 0 0 1 0
-1 0 -1 0 -1 -1 -1 -1
-1 0 -1 0 0 -1 -1 0
0 0 1 0 0 0 1 0
-1 0 -1 0 0 -1 -1 -1
1
Generator of the Alexander module
(8+10t^2+4t^4,2+2t,-1,t,-2-2t^2,2+t^2,-2-2t^2,2t+t^3)
the Blanchfield form on it
-853t^-3+4061t^-2-8951t^-1+10097-8951t+4061t^2-853t^3
187
First homology
of the double branched cover of 12a_0220
Z/187
-2 2
12a_0221
2

detected by
the Lickorish test
-2+14t-40t^2+57t^3-40t^4+14t^5-2t^6
Seifert matrix of 12a_0221
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 1 0 0 0
0 0 0 -1 1 0
0 0 1 0 1 0
1 0 1 0 1 -2
1
Generator of the Alexander module
(0,5t-16t^2+8t^3-t^4,-2t+6t^2-2t^3,-3t+t^2,-3-t+6t^2-2t^3,1-3t-3t^2+12t^3-4t^4)
the Blanchfield form on it
2t^-2-8t^-1+14-8t+2t^2
169
First homology
of the double branched cover of 12a_0221
Z/169
0 0
12a_0222
1

detected by
an unknotting move
1-8t+29t^2-62t^3+81t^4-62t^5+29t^6-8t^7+t^8
Seifert matrix of 12a_0222
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 0
0 0 1 0 0 1 0 1
-1 0 -1 -1 0 0 -1 -1
0 0 0 0 -1 0 0 0
0 0 0 0 -1 1 0 0
-1 0 -1 0 0 0 -1 0
0 0 0 0 -1 1 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+6t^-1-11+6t-t^2
281
First homology
of the double branched cover of 12a_0222
Z/281
0 0
12a_0223
1

detected by
an unknotting move
-3+18t-44t^2+59t^3-44t^4+18t^5-3t^6
Seifert matrix of 12a_0223
1 0 0 0 0 0
-1 -1 -1 0 -1 0
-1 0 -1 1 -1 1
0 0 0 2 0 1
-1 0 0 0 -1 1
0 0 0 1 0 2
1
Generator of the Alexander module
(0,0,0,0,-2t+3t^2-t^3,1-3t+t^2)
the Blanchfield form on it
3t^-2-12t^-1+17-12t+3t^2
189
First homology
of the double branched cover of 12a_0223
Z/189
0 0
12a_0224
2

detected by
the Lickorish test
-1+8t-27t^2+50t^3-59t^4+50t^5-27t^6+8t^7-t^8
Seifert matrix of 12a_0224
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 -1
0 0 1 0 0 1 0 0
-1 0 -1 -1 0 -1 -1 -1
0 0 0 0 -1 0 0 0
0 0 0 0 -1 1 0 0
-1 0 -1 0 0 0 -1 0
-1 0 -1 0 0 0 -1 -1
1
Generator of the Alexander module
(7-10t+7t^2+22t^3-46t^4-176t^5+24t^6,26-43t+40t^2+80t^3-180t^4-768t^5+112t^6+128t^7,-2+4t+4t^2-16t^3+16t^4,3-4t+25t^2-26t^3-38t^4-48t^5+24t^6,2-8t^2,4-16t^2,t+10t^2-20t^3+16t^5,2-2t+8t^2+4t^3-32t^4-48t^5)
the Blanchfield form on it
x
231
First homology
of the double branched cover of 12a_0224
Z/231
-2 2
12a_0225
1

detected by
an unknotting move
-1+7t-24t^2+50t^3-63t^4+50t^5-24t^6+7t^7-t^8
Seifert matrix of 12a_0225
-1 0 -1 -1 0 -1 0 0
0 1 0 0 0 -1 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 1 0 0 1 -1 0 0
0 0 -1 -1 0 -1 0 0
0 0 -1 0 0 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,1,t,0)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-15+11t-5t^2+t^3
227
First homology
of the double branched cover of 12a_0225
Z/227
2 2
12a_0226
2

detected by
the signature
-4+20t-41t^2+51t^3-41t^4+20t^5-4t^6
Seifert matrix of 12a_0226
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 -1 0 1 -1
0 0 0 -1 -1 0
0 0 0 0 -2 1
1 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
181
First homology
of the double branched cover of 12a_0226
Z/181
-4 4
12a_0227
2

detected by
the signature
-5+26t-56t^2+71t^3-56t^4+26t^5-5t^6
Seifert matrix of 12a_0227
1 0 0 0 0 0
-1 -1 0 1 1 1
0 0 -2 1 0 1
1 0 0 -2 -1 -2
1 0 -1 -1 -2 -1
1 0 0 -1 -1 -2
1
Generator of the Alexander module
(0,0,1,0,1,0)
the Blanchfield form on it
4t^-3-22t^-2+49t^-1-62+49t-22t^2+4t^3
245
First homology
of the double branched cover of 12a_0227
Z/245
-4 4
12a_0228
1

detected by
an unknotting move
-1+7t-24t^2+49t^3-61t^4+49t^5-24t^6+7t^7-t^8
Seifert matrix of 12a_0228
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 0 0
0 0 1 0 0 1 1 1
-1 0 -1 -1 0 0 -1 0
0 0 0 0 -1 0 0 0
0 0 0 0 -1 1 0 0
0 0 0 0 -1 1 1 1
0 0 0 0 -1 1 0 1
1
Generator of the Alexander module
(0,-3t+3t^2+87t^3-321t^4+312t^5-135t^6+27t^7,1+2t-32t^2+20t^3+217t^4-267t^5+126t^6-27t^7,-4t-30t^2+181t^3-416t^4+383t^5-251t^6+131t^7-45t^8+9t^9,1-4t+25t^2-117t^3+364t^4-422t^5+239t^6-72t^7+9t^8,0,4t-24t^2+111t^3-239t^4+513t^5-535t^6+284t^7-81t^8+9t^9,0)
the Blanchfield form on it
x
223
First homology
of the double branched cover of 12a_0228
Z/223
2 2
12a_0229
1

detected by
an unknotting move
-2+16t-48t^2+69t^3-48t^4+16t^5-2t^6
Seifert matrix of 12a_0229
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 1 0 0 0
0 0 0 1 0 0
0 0 1 -1 -1 -1
1 0 1 0 0 -2
1
Generator of the Alexander module
(0,9t-6t^2+t^3,-6t+2t^2,6t-2t^2,4+5t-8t^2+2t^3,3-t)
the Blanchfield form on it
6t^-2-26t^-1+42-26t+6t^2
201
First homology
of the double branched cover of 12a_0229
Z/201
0 0
12a_0230
2

detected by
the Lickorish test
3-20t+56t^2-77t^3+56t^4-20t^5+3t^6
Seifert matrix of 12a_0230
1 0 0 0 0 0
-1 -1 -1 0 0 0
-1 0 -1 0 -1 1
0 0 0 2 1 1
0 0 0 0 1 0
0 0 0 1 0 2
1 or 2
235
First homology
of the double branched cover of 12a_0230
Z/235
2 2
12a_0231
2

detected by
the signature
-5+24t-48t^2+59t^3-48t^4+24t^5-5t^6
Seifert matrix of 12a_0231
1 0 0 0 0 0
-1 -1 -1 1 1 1
-1 0 -1 1 1 1
1 0 0 -2 -1 -1
1 0 0 -1 -2 -1
1 0 0 0 -1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
3t^-3-16t^-2+35t^-1-44+35t-16t^2+3t^3
213
First homology
of the double branched cover of 12a_0231
Z/213
-4 4
12a_0232
2

detected by
the signature
-4+20t-42t^2+53t^3-42t^4+20t^5-4t^6
Seifert matrix of 12a_0232
1 0 0 0 0 0
-1 -1 0 0 1 1
0 0 -1 0 -1 0
0 0 0 -1 0 -1
1 0 0 0 -2 -1
1 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
185
First homology
of the double branched cover of 12a_0232
Z/185
-4 4
12a_0233
1

detected by
an unknotting move
1-8t+27t^2-54t^3+69t^4-54t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0233
-1 -1 -1 0 0 0 -1 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 1 1 0 -1 0
0 -1 0 0 1 1 -1 1
0 -1 -1 0 0 0 -1 0
0 -1 0 0 1 0 -1 1
1
Generator of the Alexander module
(1+13t-58t^2+73t^3-20t^4-22t^5+16t^6-3t^7,0,1+14t-44t^2+29t^3+9t^4-13t^5+3t^6,1+15t-28t^2+16t^3-3t^4,-3+15t-29t^2+16t^3+12t^4-13t^5+3t^6,1+28t-86t^2+89t^3-23t^4-22t^5+16t^6-3t^7,0,1+15t-29t^2+t^3+25t^4-16t^5+3t^6)
the Blanchfield form on it
x
249
First homology
of the double branched cover of 12a_0233
Z/249
0 0
12a_0234
1

detected by
an unknotting move
2-8t+18t^2-27t^3+31t^4-27t^5+18t^6-8t^7+2t^8
Seifert matrix of 12a_0234
-1 0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 0 0 1 0 0 1 0
0 -1 -1 0 -1 0 0 0
0 -1 0 1 -1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
141
First homology
of the double branched cover of 12a_0234
Z/141
0 2
12a_0235
1

detected by
an unknotting move
4-18t+40t^2-51t^3+40t^4-18t^5+4t^6
Seifert matrix of 12a_0235
-1 0 -1 0 0 0
0 -1 -1 0 0 0
0 0 -2 0 0 0
0 0 0 2 0 0
0 -1 -1 0 -1 0
0 -1 0 -1 -1 1
1 or 2
175
First homology
of the double branched cover of 12a_0235
Z/175
-2 2
12a_0236
3

detected by
the signature
-2+8t-14t^2+17t^3-17t^4+17t^5-14t^6+8t^7-2t^8
Seifert matrix of 12a_0236
-1 0 -1 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 0 -1 -1 0 -1
0 -1 -1 0 0 -1 0 0
0 -1 -1 0 -1 -1 -1 -1
0 -1 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-2t^-3+8t^-2-14t^-1+17-14t+8t^2-2t^3
99
First homology
of the double branched cover of 12a_0236
Z/99
-6 6
12a_0237
2

detected by
the signature
-4+18t-36t^2+45t^3-36t^4+18t^5-4t^6
Seifert matrix of 12a_0237
-1 0 -1 0 0 0
0 1 0 0 0 0
0 0 -2 0 0 0
0 -1 -1 -1 1 -1
0 1 1 0 -2 1
0 -1 -1 0 0 -1
1 or 2
161
First homology
of the double branched cover of 12a_0237
Z/161
-4 4
12a_0238
2

detected by
the signature
-4+17t-33t^2+41t^3-33t^4+17t^5-4t^6
Seifert matrix of 12a_0238
-1 0 -1 0 0 0
0 1 0 0 0 0
0 0 -2 0 0 0
0 0 0 -1 -1 0
0 1 1 0 -2 0
0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-4t^-2+15t^-1-21+15t-4t^2
149
First homology
of the double branched cover of 12a_0238
Z/149
-4 4
12a_0239
1

detected by
an unknotting move
-6+22t-31t^2+22t^3-6t^4
Seifert matrix of 12a_0239
-1 0 -1 0
0 1 0 0
0 0 -2 0
0 -1 -1 -3
1
Generator of the Alexander module
(0,1,0,1)
the Blanchfield form on it
-2t^-2+6t^-1-8+6t-2t^2
87
First homology
of the double branched cover of 12a_0239
Z/87
-2 2
12a_0240
2

detected by
the signature
-2+9t-22t^2+34t^3-39t^4+34t^5-22t^6+9t^7-2t^8
Seifert matrix of 12a_0240
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 -1 -1 0 -1
0 0 0 1 0 0 0 0
0 0 0 -1 2 1 1 1
0 0 0 -1 2 2 1 2
0 0 0 0 0 0 1 0
0 0 0 -1 2 1 1 2
1
Generator of the Alexander module
(0,1,1,0,0,0,0,0)
the Blanchfield form on it
-2t^-2+4t^-1-5+4t-2t^2
173
First homology
of the double branched cover of 12a_0240
Z/173
4 4
12a_0241
1

detected by
an unknotting move
3-13t+29t^2-37t^3+29t^4-13t^5+3t^6
Seifert matrix of 12a_0241
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 1 0 1
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 1 -1 3
1
Generator of the Alexander module
(0,t,1+t,0,0,0)
the Blanchfield form on it
3t^-2-7t^-1+9-7t+3t^2
127
First homology
of the double branched cover of 12a_0241
Z/127
2 2
12a_0242
1

detected by
an unknotting move
-1+7t-22t^2+41t^3-49t^4+41t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0242
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 1 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 -1
0 0 0 0 0 -1 -1 -1
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+7t^-2-19t^-1+27-19t+7t^2-t^3
191
First homology
of the double branched cover of 12a_0242
Z/191
-2 2
12a_0243
1

detected by
an unknotting move
-2+12t-31t^2+43t^3-31t^4+12t^5-2t^6
Seifert matrix of 12a_0243
-1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 1 1 0
0 0 0 0 1 0
0 1 0 0 1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-5t^-2+12t^-1-16+12t-5t^2+t^3
133
First homology
of the double branched cover of 12a_0243
Z/133
0 0
12a_0244
2

detected by
the Nakanishi index
5-24t+56t^2-73t^3+56t^4-24t^5+5t^6
Seifert matrix of 12a_0244
-1 0 0 0 0 0
0 2 0 0 1 1
-1 0 -1 0 0 0
-1 -1 -1 1 -1 -1
0 1 0 0 2 1
0 1 0 0 0 2
2
243
First homology
of the double branched cover of 12a_0244
Z/81+Z/3
2 2
12a_0245
2

detected by
the Nakanishi index
1-7t+24t^2-49t^3+63t^4-49t^5+24t^6-7t^7+t^8
Seifert matrix of 12a_0245
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 1 0 1 0
0 1 0 0 1 0 1 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 1 1 0
0 -1 0 0 -1 0 0 -1
2
225
First homology
of the double branched cover of 12a_0245
Z/75+Z/3
0 0
12a_0246
2

detected by
the signature
1-7t+20t^2-31t^3+35t^4-31t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0246
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 0 0
0 0 1 0 -1 -1 0 -1
-1 0 -1 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,2+t-2t^2-t^3-2t^4+t^5+t^6,-1-t+t^4,2-t-t^2-t^3-t^4+t^5,0,0,0)
the Blanchfield form on it
153
First homology
of the double branched cover of 12a_0246
Z/153
-4 4
12a_0247
1

detected by
an unknotting move
2-14t+39t^2-53t^3+39t^4-14t^5+2t^6
Seifert matrix of 12a_0247
1 0 0 0 0 0
-1 -1 0 -1 0 0
0 0 1 0 0 1
-1 0 -1 -1 0 0
0 0 0 0 -1 1
0 0 0 0 0 -2
1
Generator of the Alexander module
(4+46t-164t^2+298t^3-158t^4-420t^5+924t^6-892t^7+492t^8-120t^9,-10-115t+419t^2-775t^3+480t^4+842t^5-2064t^6+2108t^7-1210t^8+300t^9,3-2t-18t^2+78t^3-140t^4+142t^5-82t^6+20t^7,-3+2t+18t^2-114t^3+224t^4-146t^5-2t^6+20t^7,-18t^2+60t^3-62t^4+20t^5,11t^2+242t^3-788t^4+1280t^5-366t^6-2360t^7+4420t^8-4150t^
the Blanchfield form on it
x
163
First homology
of the double branched cover of 12a_0247
Z/163
-2 2
12a_0248
2

detected by
the Lickorish test
-2+13t-34t^2+47t^3-34t^4+13t^5-2t^6
Seifert matrix of 12a_0248
1 0 0 0 0 0
-1 -1 -1 0 0 -1
-1 0 -1 0 1 -1
0 0 0 1 0 0
0 0 0 0 2 0
-1 0 0 -1 1 -1
2
145
First homology
of the double branched cover of 12a_0248
Z/145
0 0
12a_0249
2

detected by
2-13t+36t^2-49t^3+36t^4-13t^5+2t^6
Seifert matrix of 12a_0249
-1 -1 -1 0 0 0
0 1 0 0 0 0
0 -1 -1 -1 0 0
0 0 0 2 0 0
0 0 -1 0 1 1
0 0 0 0 0 1
2
151
First homology
of the double branched cover of 12a_0249
Z/151
2 2
12a_0250
2

detected by
the signature
1-7t+20t^2-32t^3+37t^4-32t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0250
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 0 0 -1
0 0 1 0 0 -1 0 0
-1 0 -1 -1 -1 0 0 -1
-1 0 -1 0 -1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 -1 -1 0
-1 0 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-7t^-2+19t^-1-25+19t-7t^2+t^3
157
First homology
of the double branched cover of 12a_0250
Z/157
-4 4
12a_0251
2

detected by
the Lickorish test
2-14t+38t^2-51t^3+38t^4-14t^5+2t^6
Seifert matrix of 12a_0251
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 1 -1 0 0
0 0 0 -1 0 0
0 0 0 -1 -1 0
1 0 1 0 0 -2
1
Generator of the Alexander module
(0,0,1,0,1,1)
the Blanchfield form on it
t^-2-5t^-1+8-5t+t^2
159
First homology
of the double branched cover of 12a_0251
Z/159
-2 2
12a_0252
3

detected by
the signature
2-9t+17t^2-24t^3+27t^4-24t^5+17t^6-9t^7+2t^8
Seifert matrix of 12a_0252
1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 1 0
0 0 -1 -1 0 -1 -1 0
0 0 0 -1 0 0 -1 0
0 0 0 0 -1 0 0 -1
0 0 0 -1 0 -1 -1 0
1 0 0 0 -1 0 -2 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1+t-t^4,-t,0,0,0)
the Blanchfield form on it
4t^-3-16t^-2+23t^-1-24+23t-16t^2+4t^3
131
First homology
of the double branched cover of 12a_0252
Z/131
-6 6
12a_0253
2

detected by
the signature
-4+19t-36t^2+43t^3-36t^4+19t^5-4t^6
Seifert matrix of 12a_0253
1 0 0 0 0 0
-1 -1 0 0 1 0
0 0 -1 0 0 -1
0 0 0 -2 0 0
1 0 -1 -1 -2 -1
0 0 0 0 0 -1
2
161
First homology
of the double branched cover of 12a_0253
Z/161
-4 4
12a_0254
2

detected by
the signature
-3+13t-21t^2+23t^3-21t^4+13t^5-3t^6
Seifert matrix of 12a_0254
1 0 0 0 0 0
-1 -1 0 0 -1 0
0 0 -1 -1 1 -1
0 0 0 -1 1 0
-1 0 0 0 -3 0
0 0 0 -1 1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-3t^-2+13t^-1-19+13t-3t^2
97
First homology
of the double branched cover of 12a_0254
Z/97
-4 4
12a_0255
1

detected by
an unknotting move
-6+27t-41t^2+27t^3-6t^4
Seifert matrix of 12a_0255
1 0 0 0
-1 -1 -1 0
-1 0 -3 1
0 0 0 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
2t^-1-3+2t
107
First homology
of the double branched cover of 12a_0255
Z/107
-2 2
12a_0256
1

detected by
an unknotting move
3-20t+52t^2-69t^3+52t^4-20t^5+3t^6
Seifert matrix of 12a_0256
-1 -1 1 0 -1 1
0 1 0 0 0 0
0 1 -2 0 0 -1
0 0 1 1 -1 0
0 -1 1 0 -1 1
0 1 -1 0 0 -2
1
Generator of the Alexander module
(0,0,1,2,0,2)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
219
First homology
of the double branched cover of 12a_0256
Z/219
-2 2
12a_0257
1

detected by
an unknotting move
2-16t+46t^2-63t^3+46t^4-16t^5+2t^6
Seifert matrix of 12a_0257
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 -1 0 -1 0
0 0 0 -1 1 -1
0 0 0 0 1 0
1 0 0 0 1 -2
1
Generator of the Alexander module
(0,0,1,1,0,0)
the Blanchfield form on it
t^-2-7t^-1+14-7t+t^2
191
First homology
of the double branched cover of 12a_0257
Z/191
-2 2
12a_0258
2

detected by
the Lickorish test
1-7t+20t^2-35t^3+43t^4-35t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0258
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 0 0 0
0 0 -1 0 0 0 0 -1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 0 0 -1
0 0 0 0 0 1 1 0
0 0 0 0 0 0 1 0
0 0 0 0 0 1 1 1
1
Generator of the Alexander module
(0,0,3-t,-t,0,1,0,0)
the Blanchfield form on it
-t^-3+4t^-2-7t^-1+9-7t+4t^2-t^3
169
First homology
of the double branched cover of 12a_0258
Z/169
0 0
12a_0259
1

detected by
an unknotting move
2-12t+27t^2-33t^3+27t^4-12t^5+2t^6
Seifert matrix of 12a_0259
1 0 0 0 0 0
-1 -1 0 -1 -1 0
0 0 -1 0 0 1
-1 0 0 -1 0 0
-1 0 0 -1 -1 1
0 0 0 0 0 2
1 or 2
115
First homology
of the double branched cover of 12a_0259
Z/115
-2 2
12a_0260
2

detected by
the Lickorish test
-1+7t-22t^2+39t^3-45t^4+39t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0260
-1 -1 -1 -1 -1 0 -1 0
0 -1 -1 -1 -1 0 0 1
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 -1 -1 0 0 1
0 -1 0 0 0 1 -1 0
0 -1 -1 -1 -1 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+7t^-2-17t^-1+21-17t+7t^2-t^3
183
First homology
of the double branched cover of 12a_0260
Z/183
-2 2
12a_0261
1

detected by
an unknotting move
1-8t+27t^2-52t^3+65t^4-52t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0261
-1 0 -1 -1 -1 0 -1 0
0 1 0 0 0 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 0 -1 0 -1 1 -1 1
0 1 -1 -1 -1 0 -1 0
0 0 0 0 0 0 -1 1
1
Generator of the Alexander module
(2-2t+3t^2-3t^3+t^4,0,0,3-5t+6t^2-7t^3+4t^4-t^5,0,3-5t+6t^2-7t^3+4t^4-t^5,0,0)
the Blanchfield form on it
x
241
First homology
of the double branched cover of 12a_0261
Z/241
0 0
12a_0262
1

detected by
an unknotting move
-1+7t-22t^2+41t^3-49t^4+41t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0262
-1 0 -1 -1 -1 -1 0 -1
0 1 0 0 0 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 1 -1 -1 -1 -1 0 -1
0 0 -1 -1 0 -1 0 0
0 0 -1 0 0 -1 1 -1
0 1 -1 -1 0 -1 0 -1
1
Generator of the Alexander module
(-t^2,0,t,t,-t+2t^3-t^4,-t^2,1-2t^2+t^3,t^3)
the Blanchfield form on it
t^-3-13t^-2+50t^-1-46+50t-13t^2+t^3
191
First homology
of the double branched cover of 12a_0262
Z/191
-2 2
12a_0263
2

detected by
the Lickorish test
3-19t+48t^2-63t^3+48t^4-19t^5+3t^6
Seifert matrix of 12a_0263
1 0 0 0 0 0
-1 -1 0 0 1 1
0 0 1 0 0 0
0 0 0 -1 -1 0
1 0 0 0 -2 -1
1 0 1 0 -1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
2t^-2-10t^-1+17-10t+2t^2
203
First homology
of the double branched cover of 12a_0263
Z/203
-2 2
12a_0264
1

detected by
an unknotting move
-1+9t-33t^2+65t^3-79t^4+65t^5-33t^6+9t^7-t^8
Seifert matrix of 12a_0264
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 -1 0 0
0 0 1 0 0 0 -1 1
-1 0 -1 -1 0 -1 0 -1
0 0 0 0 -1 0 -1 0
-1 0 -1 0 0 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 -1 0 -1 1
1
Generator of the Alexander module
(0,5-3t+6t^2+46t^3-90t^4+34t^5-32t^6+44t^7-20t^8+5t^9,10-27t+22t^2+5t^3-5t^4+2t^5,6-13t+74t^2-112t^3+55t^4-15t^5+t^6,-15t^2+17t^3+6t^4+20t^5-43t^6+20t^7-5t^8,-10t+18t^2+17t^3-43t^4+20t^5-5t^6,0,0)
the Blanchfield form on it
x
295
First homology
of the double branched cover of 12a_0264
Z/295
-2 2
12a_0265
2

detected by
the Nakanishi index
1-8t+30t^2-66t^3+87t^4-66t^5+30t^6-8t^7+t^8
Seifert matrix of 12a_0265
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 0 0
0 0 1 0 0 1 -1 1
-1 0 -1 -1 0 -1 0 0
0 0 0 0 -1 0 -1 0
0 0 0 0 -1 1 -1 1
0 0 0 0 0 0 -1 0
0 0 0 0 -1 0 -1 1
2
297
First homology
of the double branched cover of 12a_0265
Z/99+Z/3
0 0
12a_0266
2

detected by
the signature
2-11t+28t^2-44t^3+51t^4-44t^5+28t^6-11t^7+2t^8
Seifert matrix of 12a_0266
-1 0 -1 0 0 0 -1 0
0 1 0 0 0 0 0 0
0 -1 -2 -1 0 0 -2 0
0 1 0 1 0 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -1 0 -1 -1 0
0 0 -1 -1 0 0 -2 0
0 -1 -1 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,14t-34t^2+48t^3-52t^4+42t^5-20t^6+4t^7,0,0,7-10t+7t^2-2t^3-5t^4+11t^5-8t^6+2t^7,-2+11t-22t^2+30t^3-30t^4+22t^5-10t^6+2t^7,7-17t+24t^2-26t^3+21t^4-10t^5+2t^6)
the Blanchfield form on it
x
221
First homology
of the double branched cover of 12a_0266
Z/221
-4 4
12a_0267
1

detected by
an unknotting move
4-22t+52t^2-67t^3+52t^4-22t^5+4t^6
Seifert matrix of 12a_0267
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 -1 -2 -1 -2 0
0 1 0 1 0 0
0 0 -1 -1 -2 0
0 1 1 1 1 -2
1
Generator of the Alexander module
(1-2t+2t^2,0,-2+2t,0,0,-1)
the Blanchfield form on it
6t^-2-26t^-1+42-26t+6t^2
223
First homology
of the double branched cover of 12a_0267
Z/223
-2 2
12a_0268
1

detected by
an unknotting move
-1+8t-30t^2+61t^3-77t^4+61t^5-30t^6+8t^7-t^8
Seifert matrix of 12a_0268
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 1 0 0
0 0 0 -1 0 0 0 0
0 0 0 -1 -1 0 0 0
0 0 0 -1 0 1 0 0
-1 -1 0 -1 -1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,1-t,2-2t,-1,0,0,1-t,0)
the Blanchfield form on it
t^-2-2t^-1+3-2t+t^2
277
First homology
of the double branched cover of 12a_0268
Z/277
0 0
12a_0269
2

detected by
the signature
-4+18t-34t^2+41t^3-34t^4+18t^5-4t^6
Seifert matrix of 12a_0269
1 0 0 0 0 0
0 -1 0 0 -1 0
1 0 -2 0 -1 0
0 0 0 -1 0 -1
1 0 0 -1 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-3-9t^-2+18t^-1-22+18t-9t^2+2t^3
153
First homology
of the double branched cover of 12a_0269
Z/153
-4 4
12a_0270
2

detected by
the Nakanishi index
-6+25t-37t^2+25t^3-6t^4
Seifert matrix of 12a_0270
1 0 0 0
0 -1 0 1
1 0 -2 1
-1 0 0 -3
2
99
First homology
of the double branched cover of 12a_0270
Z/33+Z/3
-2 2
12a_0271
2

detected by
the Lickorish test
1-7t+22t^2-39t^3+47t^4-39t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0271
-1 0 -1 0 0 -1 -1 -1
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 0 0 1 1 0 0 0
0 0 0 0 1 0 0 0
0 1 -1 0 0 -1 -1 -1
0 1 -1 0 0 0 -1 0
0 1 -1 0 0 0 -1 -1
1 or 2
185
First homology
of the double branched cover of 12a_0271
Z/185
0 2
12a_0272
1

detected by
an unknotting move
2-14t+39t^2-53t^3+39t^4-14t^5+2t^6
Seifert matrix of 12a_0272
-1 0 -1 0 0 1
0 1 0 0 0 0
0 0 1 0 0 0
-1 0 0 1 1 0
0 0 0 0 1 0
0 -1 1 0 0 -2
1
Generator of the Alexander module
(0,0,0,1,1,0)
the Blanchfield form on it
-2t^-2+10t^-1-17+10t-2t^2
163
First homology
of the double branched cover of 12a_0272
Z/163
2 2
12a_0273
1

detected by
an unknotting move
-4+21t-47t^2+61t^3-47t^4+21t^5-4t^6
Seifert matrix of 12a_0273
-1 0 -1 0 0 0
0 1 0 0 0 0
0 0 -2 0 0 1
0 0 0 1 0 0
0 -1 -1 0 -1 1
0 -1 0 1 0 2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-2-5t^-1+7-5t+2t^2
205
First homology
of the double branched cover of 12a_0273
Z/205
0 0
12a_0274
2

detected by
the signature
2-8t+18t^2-26t^3+29t^4-26t^5+18t^6-8t^7+2t^8
Seifert matrix of 12a_0274
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 0 1 1 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
1 -1 1 -1 1 -1 -1 2
1
Generator of the Alexander module
(0,0,-1,-1,0,0,1,1)
the Blanchfield form on it
-t^-3+3t^-2-6t^-1+7-6t+3t^2-t^3
137
First homology
of the double branched cover of 12a_0274
Z/137
4 4
12a_0275
1

detected by
an unknotting move
4-18t+41t^2-53t^3+41t^4-18t^5+4t^6
Seifert matrix of 12a_0275
-1 0 0 0 0 0
0 2 0 0 0 0
-1 0 -1 0 0 0
-1 -1 -1 1 0 0
0 0 0 0 1 0
1 1 1 -1 1 2
1 or 2
179
First homology
of the double branched cover of 12a_0275
Z/179
2 2
12a_0276
4

detected by
the signature
3-10t+20t^2-29t^3+33t^4-29t^5+20t^6-10t^7+3t^8
Seifert matrix of 12a_0276
-1 0 -1 -1 0 0 -1 0
0 -1 0 -1 0 0 0 0
0 0 -2 -1 0 0 -2 0
0 0 -1 -2 0 0 -1 0
0 -1 0 -1 -1 0 0 0
0 0 -1 0 0 -1 -1 0
0 0 -1 -1 0 0 -2 0
0 0 -1 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
3t^-3-9t^-2+16t^-1-19+16t-9t^2+3t^3
157
First homology
of the double branched cover of 12a_0276
Z/157
-8 8
12a_0277
3

detected by
the signature
5-17t+31t^2-37t^3+31t^4-17t^5+5t^6
Seifert matrix of 12a_0277
-1 0 -1 0 1 0
0 -1 -1 0 0 0
0 0 -2 0 1 0
0 -1 -1 -1 0 0
0 0 1 0 -3 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(1,0,0,1,0,0)
the Blanchfield form on it
10t^-2-29t^-1+40-29t+10t^2
143
First homology
of the double branched cover of 12a_0277
Z/143
-6 6
12a_0278
1

detected by
an unknotting move
-1+7t-18t^2+28t^3-31t^4+28t^5-18t^6+7t^7-t^8
Seifert matrix of 12a_0278
-1 0 0 0 0 0 0 0
0 1 0 0 1 0 0 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 1 1 1 0
0 0 0 0 1 0 0 0
0 1 0 0 1 1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+3t^-2-5t^-1+5-5t+3t^2-t^3
139
First homology
of the double branched cover of 12a_0278
Z/139
2 2
12a_0279
2

detected by
-2+15t-40t^2+55t^3-40t^4+15t^5-2t^6
Seifert matrix of 12a_0279
-1 0 0 0 0 0
0 2 0 0 0 0
-1 0 -1 0 0 0
-1 -1 -1 1 1 0
0 0 0 0 -1 0
0 0 0 0 1 1
2
169
First homology
of the double branched cover of 12a_0279
Z/169
0 0
12a_0280
1

detected by
an unknotting move
-1+7t-22t^2+42t^3-51t^4+42t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0280
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 1 1 1 0
0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,-t,1+t,t-t^2+t^3,0,-1+t-2t^2+t^3,0,-t)
the Blanchfield form on it
-t^-1+2-t
195
First homology
of the double branched cover of 12a_0280
Z/195
-2 2
12a_0281
2

detected by
the signature
1-7t+24t^2-46t^3+57t^4-46t^5+24t^6-7t^7+t^8
Seifert matrix of 12a_0281
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 1 1 0
0 0 0 0 -1 0 0 0
0 1 0 0 1 1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,1,0,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
213
First homology
of the double branched cover of 12a_0281
Z/213
-4 4
12a_0282
1

detected by
an unknotting move
1-8t+26t^2-50t^3+63t^4-50t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0282
-1 0 0 0 -1 -1 0 -1
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 1 0 1 0
0 0 0 0 1 0 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 1 0 1 0
0 0 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(-1,0,0,0,1,0,0,-t)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
233
First homology
of the double branched cover of 12a_0282
Z/233
0 0
12a_0283
1

detected by
an unknotting move
-1+8t-26t^2+48t^3-57t^4+48t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0283
-1 0 0 0 0 -1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 1 0 1 1
0 0 0 0 1 1 1 0
0 0 0 0 0 -1 0 0
1 0 0 0 0 1 1 0
0 0 0 0 1 1 1 1
1
Generator of the Alexander module
(0,7-8t-t^2+4t^3-t^4,0,-3+t+12t^2-16t^3+7t^4-t^5,-3-2t+16t^2-8t^3-5t^4+2t^5,0,-3+4t-t^2,3t+5t^2-11t^3+3t^4)
the Blanchfield form on it
x
223
First homology
of the double branched cover of 12a_0283
Z/223
2 2
12a_0284
2

detected by
the Lickorish test
1-8t+25t^2-43t^3+49t^4-43t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_0284
1 0 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 -1 -1
-1 0 -1 -1 0 0 -1 -1
0 0 0 1 0 0 0 1
0 0 0 -1 -1 0 0 -1
-1 0 -1 -1 0 -1 -1 -1
-1 0 0 -1 0 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,-1+33t-80t^2+80t^3-40t^4+10t^5-t^6,4-8t+5t^2-t^3,1-12t+20t^2-11t^3+2t^4,0)
the Blanchfield form on it
x
203
First homology
of the double branched cover of 12a_0284
Z/203
-2 2
12a_0285
1

detected by
an unknotting move
1-8t+27t^2-49t^3+57t^4-49t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0285
1 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 -1 -1
0 0 1 0 1 0 0 1
0 0 0 -1 0 0 1 0
0 0 0 0 1 0 0 0
-1 0 -1 0 0 -1 -1 0
0 0 1 0 1 0 1 1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,t-2t^3+8t^4-4t^5,0,-3-3t+8t^2-2t^3,3t^2+3t^3-8t^4+2t^5,-2+2t^2-4t^3+22t^4-20t^5+4t^6,-2t+t^2+4t^3-21t^4+13t^5+4t^6-2t^7,0)
the Blanchfield form on it
x
227
First homology
of the double branched cover of 12a_0285
Z/227
2 2
12a_0286
1

detected by
an unknotting move
-3+20t-55t^2+77t^3-55t^4+20t^5-3t^6
Seifert matrix of 12a_0286
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 -2 0 -1 -1
0 0 0 1 0 0
1 -1 -1 -1 -2 -1
0 0 0 1 0 1
1
Generator of the Alexander module
(-1,0,1,0,0,0)
the Blanchfield form on it
-2t^-2+7t^-1-10+7t-2t^2
233
First homology
of the double branched cover of 12a_0286
Z/233
0 0
12a_0287
1

detected by
an unknotting move
1-8t+27t^2-53t^3+65t^4-53t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0287
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 -1 -1 -1
0 0 1 0 0 0 0 0
0 0 0 1 1 0 0 1
0 0 0 0 1 0 0 0
-1 0 -1 -1 0 -1 -1 -1
-1 0 0 -1 0 0 -1 0
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(-4-28t+42t^2-12t^3-6t^4-10t^5+20t^6-24t^7+8t^8,2+14t-21t^2+6t^3+3t^4+5t^5-10t^6+12t^7-4t^8,-3-t+18t^2-26t^3+4t^4+46t^5-72t^6+51t^7-23t^8+7t^9-t^10,-6t+9t^2-6t^3-11t^4+7t^5+32t^6-77t^7+79t^8-53t^9+22t^10-6t^11+t^12,5-6t+4t^3-t^4-2t^5+3t^6-t^7,-1+28t-18t^2-6t^3+4t^4+65t^5-166t^6+201t^7-130t^8+65t^9-1
the Blanchfield form on it
x
243
First homology
of the double branched cover of 12a_0287
Z/243
2 2
12a_0288
1

detected by
an unknotting move
1-8t+28t^2-56t^3+69t^4-56t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0288
1 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 -1 -1
0 0 1 0 1 0 1 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
-1 0 -1 0 0 -1 0 -1
0 0 0 0 1 0 1 0
-1 0 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,6+11t-17t^2+11t^3-3t^4,-9+3t+5t^2-5t^3+2t^4,-3+14t-12t^2+6t^3-t^4,0,-3+2t-t^2,0,1+9t-15t^2+12t^3-5t^4+t^5)
the Blanchfield form on it
x
255
First homology
of the double branched cover of 12a_0288
Z/255
2 2
12a_0289
2

detected by
the signature
-5+23t-43t^2+51t^3-43t^4+23t^5-5t^6
Seifert matrix of 12a_0289
1 0 0 0 0 0
0 -1 0 -1 0 0
1 -1 -2 -1 -1 -1
0 0 0 -1 0 0
1 -1 -1 -1 -2 -1
1 0 0 0 -1 -2
1 or 2
193
First homology
of the double branched cover of 12a_0289
Z/193
-4 4
12a_0290
1

detected by
an unknotting move
-2+9t-21t^2+34t^3-39t^4+34t^5-21t^6+9t^7-2t^8
Seifert matrix of 12a_0290
-1 0 -1 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 -2 -1 0 0 -1 0
0 1 0 1 0 0 1 0
0 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -1 0 -1 -1 0
0 1 0 0 0 0 1 0
0 -1 -1 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,-t,0,-1-t+t^4,0,0)
the Blanchfield form on it
2t^-2-7t^-1+10-7t+2t^2
171
First homology
of the double branched cover of 12a_0290
Z/171
-2 2
12a_0291
2

detected by
-4+17t-34t^2+43t^3-34t^4+17t^5-4t^6
Seifert matrix of 12a_0291
-1 0 -1 0 0 0
0 1 0 0 0 0
0 0 -2 -1 -1 0
0 1 0 1 1 0
0 1 0 0 1 0
0 1 1 1 1 -2
2
153
First homology
of the double branched cover of 12a_0291
Z/153
0 0
12a_0292
1

detected by
an unknotting move
-1+8t-25t^2+47t^3-57t^4+47t^5-25t^6+8t^7-t^8
Seifert matrix of 12a_0292
-1 0 0 0 0 0 0 0
0 1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 -1 1 0 0
0 0 0 0 -1 0 0 0
0 1 0 0 -1 1 0 0
-1 0 -1 0 -1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,3-t-14t^2+20t^3+23t^4-72t^5+22t^6+32t^7-29t^8+6t^9,1+3t+2t^2-7t^3-40t^4+28t^5+61t^6-37t^7-9t^8+23t^9-6t^10,1-t^2+15t^3-37t^4-9t^5+74t^6-26t^7-22t^8+26t^9-6t^10,-t+15t^2-37t^3-9t^4+74t^5-26t^6-22t^7+26t^8-6t^9,7t-2t^2+5t^3-19t^4-17t^5+21t^6-2t^7-10t^8+3t^9,-2t^2+30t^3-74t^4-18t^5+148t^6-52t^7-44t^
the Blanchfield form on it
x
219
First homology
of the double branched cover of 12a_0292
Z/219
2 2
12a_0293
3

detected by
the signature
7-26t+50t^2-61t^3+50t^4-26t^5+7t^6
Seifert matrix of 12a_0293
-1 0 -1 1 0 0
0 -1 0 -1 0 -1
0 0 -2 1 0 0
0 0 2 -3 0 -1
0 0 0 -1 -1 0
0 0 1 -1 0 -2
1 or 2
227
First homology
of the double branched cover of 12a_0293
Z/227
-6 6
12a_0294
2

detected by
the signature
-2+9t-24t^2+40t^3-47t^4+40t^5-24t^6+9t^7-2t^8
Seifert matrix of 12a_0294
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 0 1 0
-1 -1 0 1 1 -1 0 0
0 0 0 0 1 0 0 0
0 0 1 0 -1 2 1 1
0 0 0 0 0 0 1 0
-1 -1 1 0 0 0 1 1
1
Generator of the Alexander module
(0,4+2t-t^2+t^3+t^5,0,5t-3t^2+6t^3-4t^4+3t^5-t^6+t^7,-1+t-5t^2+3t^3-2t^4+t^5-t^6,1+6t^2-12t^3+8t^4-4t^5+3t^6-2t^7,0,0)
the Blanchfield form on it
x
197
First homology
of the double branched cover of 12a_0294
Z/197
4 4
12a_0295
3

detected by
the signature
6-23t+46t^2-57t^3+46t^4-23t^5+6t^6
Seifert matrix of 12a_0295
-1 0 -1 -1 0 -1
0 -1 0 0 -1 0
0 0 -2 -1 0 -2
0 0 -1 -2 0 -1
0 0 0 1 -2 0
0 0 -1 -1 0 -2
2
207
First homology
of the double branched cover of 12a_0295
Z/69+Z/3
-6 6
12a_0296
2

detected by
the Lickorish test
3-21t+55t^2-73t^3+55t^4-21t^5+3t^6
Seifert matrix of 12a_0296
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 0 -2 -1 0 -1
0 -1 -2 -2 0 -1
0 0 0 -1 1 -1
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(2t-3t^2+5t^3-5t^4+3t^5,0,-2+3t-5t^2+5t^3-3t^4,0,-1+6t-15t^2+20t^3-14t^4+3t^5,0)
the Blanchfield form on it
-25t^-2+106t^-1-141+106t-25t^2
231
First homology
of the double branched cover of 12a_0296
Z/231
-2 2
12a_0297
2

detected by
the Nakanishi index
-2+8t-19t^2+30t^3-35t^4+30t^5-19t^6+8t^7-2t^8
Seifert matrix of 12a_0297
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 -1 0 0
-1 -1 1 1 1 -1 0 1
0 0 0 0 1 0 0 0
0 0 0 0 -1 2 1 0
0 0 0 0 0 0 1 0
-1 -1 1 0 1 -1 0 1
2
153
First homology
of the double branched cover of 12a_0297
Z/51+Z/3
4 4
12a_0298
2

detected by
the Nakanishi index
-1+7t-20t^2+36t^3-43t^4+36t^5-20t^6+7t^7-t^8
Seifert matrix of 12a_0298
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 1 0 0
-1 0 -1 1 1 1 0 1
0 0 0 0 0 1 0 0
0 -1 0 0 0 -1 -1 0
-1 0 -1 1 0 1 0 1
2
171
First homology
of the double branched cover of 12a_0298
Z/57+Z/3
2 2
12a_0299
2

detected by
the signature
1-7t+20t^2-33t^3+39t^4-33t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0299
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 -1 0 0 -1 -1 -1 -1
0 -1 0 0 -1 0 -1 0
0 -1 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,-1,1,3,0,t,0,0)
the Blanchfield form on it
2t^-3-8t^-2+14t^-1-17+14t-8t^2+2t^3
161
First homology
of the double branched cover of 12a_0299
Z/161
-4 4
12a_0300
1

detected by
an unknotting move
2-14t+37t^2-49t^3+37t^4-14t^5+2t^6
Seifert matrix of 12a_0300
-1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 1 -1 0
0 0 0 0 -1 0
0 1 0 0 1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+7t^-2-18t^-1+24-18t+7t^2-t^3
155
First homology
of the double branched cover of 12a_0300
Z/155
-2 2
12a_0301
1

detected by
an unknotting move
-3+20t-52t^2+71t^3-52t^4+20t^5-3t^6
Seifert matrix of 12a_0301
-1 0 0 0 0 0
0 2 0 1 0 1
-1 0 -1 0 0 0
-1 0 -1 1 0 0
0 0 0 -1 -1 -1
0 1 0 1 0 2
1
Generator of the Alexander module
(0,1,0,0,-2,2)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
221
First homology
of the double branched cover of 12a_0301
Z/221
0 0
12a_0302
1

detected by
an unknotting move
4-16t+33t^2-41t^3+33t^4-16t^5+4t^6
Seifert matrix of 12a_0302
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
0 0 -1 2 1 0
0 0 0 0 1 0
1 1 -1 1 0 2
1
Generator of the Alexander module
(0,-t,0,0,0,1+t)
the Blanchfield form on it
4t^-2-10t^-1+13-10t+4t^2
147
First homology
of the double branched cover of 12a_0302
Z/147
2 2
12a_0303
1

detected by
an unknotting move
-2+14t-36t^2+49t^3-36t^4+14t^5-2t^6
Seifert matrix of 12a_0303
-1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 0 0 0
0 0 0 1 0 0
0 -1 0 -1 -1 0
1 0 1 -1 0 2
1
Generator of the Alexander module
(0,0,0,0,4-t,1)
the Blanchfield form on it
4t^-2-13t^-1+19-13t+4t^2
153
First homology
of the double branched cover of 12a_0303
Z/153
0 0
12a_0304
2

detected by
the signature
1-7t+18t^2-27t^3+31t^4-27t^5+18t^6-7t^7+t^8
Seifert matrix of 12a_0304
-1 0 0 0 -1 -1 -1 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 1 1 1 1
0 0 0 0 1 0 0 0
0 0 0 0 1 1 1 0
0 0 0 0 1 0 1 0
0 0 0 0 1 1 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0,1,0)
the Blanchfield form on it
-t^-3+6t^-2-12t^-1+14-12t+6t^2-t^3
137
First homology
of the double branched cover of 12a_0304
Z/137
4 4
12a_0305
1

detected by
an unknotting move
-1+7t-20t^2+35t^3-41t^4+35t^5-20t^6+7t^7-t^8
Seifert matrix of 12a_0305
-1 0 0 0 0 -1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 0 0 0 1
-1 0 0 0 -1 -1 0 0
0 0 0 0 0 -1 0 0
-1 0 0 0 -1 -1 -1 0
1 0 0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,0,1,t,0,0,1)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
167
First homology
of the double branched cover of 12a_0305
Z/167
-2 2
12a_0306
2

detected by
the Lickorish test
2-14t+35t^2-45t^3+35t^4-14t^5+2t^6
Seifert matrix of 12a_0306
-1 0 0 0 1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 0 1 -1 1
0 0 0 0 2 0
0 0 0 0 -1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
147
First homology
of the double branched cover of 12a_0306
Z/147
2 2
12a_0307
1

detected by
an unknotting move
-2+14t-37t^2+51t^3-37t^4+14t^5-2t^6
Seifert matrix of 12a_0307
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 0 0 1
0 0 0 -2 0 0
0 0 0 -1 -1 0
0 0 0 -1 0 1
1 or 2
157
First homology
of the double branched cover of 12a_0307
Z/157
0 0
12a_0308
1

detected by
an unknotting move
-2+16t-48t^2+69t^3-48t^4+16t^5-2t^6
Seifert matrix of 12a_0308
1 0 0 0 0 0
-1 -1 0 -1 1 -1
0 0 -1 0 1 -1
-1 0 0 -1 1 0
0 0 0 0 2 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,1-t,0,1,0,0)
the Blanchfield form on it
-8t^-2+36t^-1-58+36t-8t^2
201
First homology
of the double branched cover of 12a_0308
Z/201
0 0
12a_0309
1

detected by
an unknotting move
-3+21t-58t^2+81t^3-58t^4+21t^5-3t^6
Seifert matrix of 12a_0309
1 0 0 0 0 0
0 1 0 0 0 1
1 0 -2 1 -1 0
-1 -1 0 -1 0 0
1 1 -1 1 -2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,-3t+41t^2-40t^3+170t^4+185t^5+122t^6-198t^7+52t^8+51t^9+116t^10-135t^11+30t^12,-1+27t-80t^2-501t^3+647t^4-615t^5-520t^6+675t^7-150t^8,2-37t+82t^2+743t^3-854t^4+488t^5-135t^6+879t^7-1375t^8-769t^9+964t^10-105t^11-30t^12,21t-166t^2-321t^3-316t^4+201t^5-554t^6+540t^7-120t^8,-3+25t+42t^2-8t^3+51t^4+1
the Blanchfield form on it
x
245
First homology
of the double branched cover of 12a_0309
Z/245
0 0
12a_0310
1

detected by
an unknotting move
-1+8t-27t^2+53t^3-67t^4+53t^5-27t^6+8t^7-t^8
Seifert matrix of 12a_0310
1 0 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 -1
0 0 1 1 0 -1 0 1
0 0 0 1 0 0 0 0
-1 0 -1 0 -1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 -1 -1 0
0 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,-2+t,0,0,1,0,2-3t+t^2,0)
the Blanchfield form on it
t^-3-5t^-2+10t^-1-14+10t-5t^2+t^3
245
First homology
of the double branched cover of 12a_0310
Z/245
0 0
12a_0311
3

detected by
the new u==2 criterion
-5+23t-42t^2+49t^3-42t^4+23t^5-5t^6
Seifert matrix of 12a_0311
1 0 0 0 0 0
1 -2 -1 -1 -2 -1
1 -1 -2 -1 -1 -1
1 -2 -1 -2 -2 -1
1 -1 -1 -1 -2 -1
1 -1 0 -1 -1 -2
2
189
First homology
of the double branched cover of 12a_0311
Z/63+Z/3
-4 4
12a_0312
2

detected by
the Lickorish test
-9+40t-61t^2+40t^3-9t^4
Seifert matrix of 12a_0312
1 0 0 0
-1 -3 1 1
1 1 -2 -1
1 1 0 -2
2
159
First homology
of the double branched cover of 12a_0312
Z/159
-2 2
12a_0313
2

detected by
the Lickorish test
4-20t+48t^2-63t^3+48t^4-20t^5+4t^6
Seifert matrix of 12a_0313
-1 -1 0 0 0 0
0 -2 0 -1 0 0
0 0 -1 1 0 0
0 0 0 -2 0 0
0 1 -1 1 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-2-7t^-1+11-7t+2t^2
207
First homology
of the double branched cover of 12a_0313
Z/207
-2 2
12a_0314
2

detected by
the signature
-3+21t-51t^2+67t^3-51t^4+21t^5-3t^6
Seifert matrix of 12a_0314
-1 -1 -1 0 0 -1
0 -2 -1 0 0 -2
0 -1 -2 0 0 -1
0 0 0 -1 0 0
0 0 -1 1 1 -1
0 -1 -1 0 0 -2
1 or 2
217
First homology
of the double branched cover of 12a_0314
Z/217
-4 4
12a_0315
2

detected by
the signature
-5+24t-50t^2+63t^3-50t^4+24t^5-5t^6
Seifert matrix of 12a_0315
-1 0 -1 -1 -1 0
0 1 0 0 0 0
0 0 -2 -1 -2 -1
0 0 -1 -2 -1 0
0 0 -1 -1 -2 -1
0 1 0 1 0 -2
1
Generator of the Alexander module
(1-6t+2t^2+12t^3-10t^4+2t^5,20t-4t^2-36t^3+24t^4-4t^5,-2-4t+8t^2-2t^3,-2+6t+6t^2-20t^3+12t^4-2t^5,10-22t-48t^2+64t^3-32t^4+15t^5+2t^6-26t^7+8t^8+6t^9-2t^10,6+46t-38t^2-58t^3+45t^4-2t^5-2t^6-12t^7+10t^8-2t^9)
the Blanchfield form on it
x
221
First homology
of the double branched cover of 12a_0315
Z/221
-4 4
12a_0316
1

detected by
an unknotting move
1-8t+29t^2-62t^3+81t^4-62t^5+29t^6-8t^7+t^8
Seifert matrix of 12a_0316
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 1 0 0
0 -1 0 -1 -1 -1 -1 0
0 0 0 0 0 1 0 0
-1 0 -1 1 0 1 1 0
0 -1 0 -1 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
1
281
First homology
of the double branched cover of 12a_0316
Z/281
0 0
12a_0317
2

detected by
the Lickorish test
5-25t+60t^2-79t^3+60t^4-25t^5+5t^6
Seifert matrix of 12a_0317
-1 0 0 0 0 0
0 2 0 1 1 0
-1 0 -1 0 0 0
-1 0 -1 1 0 0
0 1 0 1 2 1
1 1 1 0 1 2
1
Generator of the Alexander module
(0,2t^2+8t^3-6t^4,1+t-t^2,4t+3t^2-3t^3,1+2t-t^2,-1-4t+3t^2)
the Blanchfield form on it
-3t^-6-105t^-5+469t^-4-53t^-3-3576t^-2+10035t^-1-13534+10035t-3576t^2-53t^3+469t^4-105t^5-3t^6
259
First homology
of the double branched cover of 12a_0317
Z/259
2 2
12a_0318
1

detected by
an unknotting move
-1+7t-22t^2+43t^3-53t^4+43t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0318
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 1 0 0
-1 0 -1 1 1 1 1 0
0 0 0 0 0 1 0 0
-1 0 -1 1 0 1 1 0
0 -1 0 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,2+t^3-t^4,2t-2t^2+2t^3-t^4,2+2t-2t^2+3t^3-2t^4,-2+2t-2t^2+t^3,2t-2t^2+2t^3-t^4,1-2t+t^2)
the Blanchfield form on it
t^-3-6t^-2+15t^-1-21+15t-6t^2+t^3
199
First homology
of the double branched cover of 12a_0318
Z/199
2 2
12a_0319
3

detected by
the signature
7-23t+39t^2-45t^3+39t^4-23t^5+7t^6
Seifert matrix of 12a_0319
-1 1 -1 0 0 0
0 -3 1 0 -1 0
0 1 -2 0 -1 0
0 0 -1 -1 -1 0
0 -1 0 0 -2 0
0 0 -1 -1 -1 -1
1 or 2
183
First homology
of the double branched cover of 12a_0319
Z/183
-6 6
12a_0320
2

detected by
the signature
12-39t+55t^2-39t^3+12t^4
Seifert matrix of 12a_0320
-1 1 1 1
0 -3 -1 -2
0 -1 -3 -1
0 -2 -2 -3
1 or 2
157
First homology
of the double branched cover of 12a_0320
Z/157
-4 4
12a_0321
3

detected by
the signature
-2+10t-22t^2+33t^3-37t^4+33t^5-22t^6+10t^7-2t^8
Seifert matrix of 12a_0321
-1 0 -1 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 -1 -2 -2 0 0 -2 0
0 0 -1 -2 0 0 -1 0
0 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -1 0 -1 -1 0
0 -1 -1 -2 0 0 -2 0
0 -1 -1 -1 0 -1 -1 -1
1
Generator of the Alexander module
(4+8t-15t^2-14t^3+15t^4+50t^5-74t^6+19t^7+19t^8-10t^9-t^10+t^11,0,-1+t+2t^2-2t^3-5t^4+6t^5+7t^6-13t^7+4t^8+2t^9-t^10,3-6t^2-4t^3+14t^4+2t^5-14t^6+5t^7+2t^8-t^9,1-t-3t^2+t^3+7t^4+2t^5-20t^6+17t^7-2t^8-3t^9+t^10,-2+2t+6t^2-2t^3-14t^4-4t^5+40t^6-34t^7+4t^8+6t^9-2t^10,4+8t-15t^2-14t^3+15t^4+50t^5-74t^6+
the Blanchfield form on it
x
171
First homology
of the double branched cover of 12a_0321
Z/171
-6 6
12a_0322
2

detected by
the signature
-4+20t-42t^2+53t^3-42t^4+20t^5-4t^6
Seifert matrix of 12a_0322
-1 0 -1 -1 -1 0
0 1 0 0 0 0
0 -1 -2 -2 -2 0
0 0 -1 -2 -1 0
0 -1 -1 -2 -2 0
0 1 1 1 1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-3-10t^-2+22t^-1-28+22t-10t^2+2t^3
185
First homology
of the double branched cover of 12a_0322
Z/185
-4 4
12a_0323
1

detected by
an unknotting move
-1+8t-28t^2+55t^3-69t^4+55t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0323
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 1 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 0 0 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,-1+3t-t^2,-1+3t-t^2,0,0,2-3t^2+t^3,2-3t^2+t^3,0)
the Blanchfield form on it
t^-3-6t^-2+15t^-1-19+15t-6t^2+t^3
253
First homology
of the double branched cover of 12a_0323
Z/253
0 0
12a_0324
1

detected by
an unknotting move
1-8t+26t^2-49t^3+59t^4-49t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0324
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 0 0 0 1
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 0 0 1 1 1 0
0 0 0 0 0 0 1 0
-1 -1 0 1 1 0 0 1
1
Generator of the Alexander module
(-4-4t+6t^2+2t^3,4+20t-52t^2-10t^3+40t^4,2+4t-2t^2-4t^3,-2+2t^2,-2+12t+10t^2-16t^3-4t^4,3+10t-22t^2-6t^3+16t^4,0,4t-4t^3)
the Blanchfield form on it
25803t^-3-107221t^-2+228021t^-1-271835+228021t-107221t^2+25803t^3
227
First homology
of the double branched cover of 12a_0324
Z/227
2 2
12a_0325
1

detected by
an unknotting move
1-8t+27t^2-53t^3+65t^4-53t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0325
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 -1 0
-1 -1 0 1 0 0 0 1
0 0 0 0 1 0 -1 0
-1 -1 1 0 1 1 -1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+19-14t+6t^2-t^3
243
First homology
of the double branched cover of 12a_0325
Z/243
2 2
12a_0326
2

detected by
the Lickorish test
3-19t+51t^2-69t^3+51t^4-19t^5+3t^6
Seifert matrix of 12a_0326
-1 -1 0 0 0 -1
0 -2 0 0 0 -1
0 0 1 0 0 -1
0 0 0 -1 0 0
0 -1 1 1 1 -1
0 -1 0 0 0 -2
1 or 2
215
First homology
of the double branched cover of 12a_0326
Z/215
-2 2
12a_0327
3

detected by
the new u==2 criterion
4-18t+40t^2-51t^3+40t^4-18t^5+4t^6
Seifert matrix of 12a_0327
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 -1 2 0 0
0 0 0 0 1 0
1 1 0 1 -1 2
2
175
First homology
of the double branched cover of 12a_0327
Z/35+Z/5
2 2
12a_0328
1

detected by
an unknotting move
-1+8t-27t^2+52t^3-63t^4+52t^5-27t^6+8t^7-t^8
Seifert matrix of 12a_0328
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 1 0 0
0 -1 0 -1 -1 -1 0 0
0 0 0 0 0 1 0 0
0 -1 0 -1 -1 -1 -1 0
0 -1 0 0 -1 -1 -1 -1
1
Generator of the Alexander module
(0,-3+7t-4t^2+t^3,0,8-6t+2t^2,9-14t+8t^2-2t^3,-3+7t-4t^2+t^3,-3-5t+5t^2-2t^3,3t-7t^2+4t^3-t^4)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-9+8t-4t^2+t^3
239
First homology
of the double branched cover of 12a_0328
Z/239
-2 2
12a_0329
2

detected by
the signature
-4+17t-31t^2+37t^3-31t^4+17t^5-4t^6
Seifert matrix of 12a_0329
1 0 0 0 0 0
0 -2 -1 1 -1 1
1 0 -2 0 0 0
0 0 0 -1 0 -1
0 -2 -1 1 -2 1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,1+t-t^2,0,1-t,0,0)
the Blanchfield form on it
-4t^-2+13t^-1-16+13t-4t^2
141
First homology
of the double branched cover of 12a_0329
Z/141
-4 4
12a_0330
1

detected by
an unknotting move
-6+24t-35t^2+24t^3-6t^4
Seifert matrix of 12a_0330
1 0 0 0
0 -1 0 -1
1 0 -2 0
0 0 1 -3
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-2t^-1+5-2t
95
First homology
of the double branched cover of 12a_0330
Z/95
-2 2
12a_0331
2

detected by
the signature
1-7t+22t^2-37t^3+43t^4-37t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0331
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 -1 0 0 0 0
-1 -1 0 -1 0 0 0 0
-1 0 0 0 1 0 1 0
-1 0 0 0 1 1 1 1
0 0 0 0 0 0 1 0
-1 0 0 0 1 0 1 1
1 or 2
177
First homology
of the double branched cover of 12a_0331
Z/177
4 4
12a_0332
2

detected by
the Nakanishi index
2-14t+41t^2-57t^3+41t^4-14t^5+2t^6
Seifert matrix of 12a_0332
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 1 -1 0 0
-1 -1 0 -1 0 0
0 0 0 0 1 0
1 0 0 0 -1 2
2
171
First homology
of the double branched cover of 12a_0332
Z/57+Z/3
2 2
12a_0333
1

detected by
an unknotting move
-1+8t-27t^2+52t^3-65t^4+52t^5-27t^6+8t^7-t^8
Seifert matrix of 12a_0333
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 -1 0 -1
0 0 -1 0 0 0 -1 0
0 0 0 1 1 0 0 1
0 0 0 0 1 0 0 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 -1 0
0 0 -1 0 1 0 -1 1
1
Generator of the Alexander module
(0,-3t+6t^2-2t^3-t^4,1-2t,-t^2,t,4-4t+2t^2+t^3,-t,0)
the Blanchfield form on it
-407t^-3+2084t^-2-4486t^-1+5955-4486t+2084t^2-407t^3
241
First homology
of the double branched cover of 12a_0333
Z/241
0 0
12a_0334
1

detected by
an unknotting move
1-8t+28t^2-54t^3+67t^4-54t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0334
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 -1 0 0 0 0
-1 -1 0 -1 -1 0 -1 0
-1 -1 0 0 -1 0 0 0
-1 0 0 0 -1 1 -1 1
-1 -1 0 0 -1 0 -1 0
0 0 0 0 -1 0 -1 1
1 or 2
249
First homology
of the double branched cover of 12a_0334
Z/249
0 2
12a_0335
1

detected by
an unknotting move
-1+9t-30t^2+59t^3-73t^4+59t^5-30t^6+9t^7-t^8
Seifert matrix of 12a_0335
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 -1 0 -1 1 -1 1
0 -1 0 0 -1 0 -1 0
0 -1 0 0 0 0 -1 1
1
Generator of the Alexander module
(0,2-2t-2t^2,-1-4t-2t^2,-8t-2t^2+2t^3,0,-1-6t-6t^2-2t^3,1-6t-4t^2,0)
the Blanchfield form on it
t^-3-7t^-2+13t^-1-16+13t-7t^2+t^3
271
First homology
of the double branched cover of 12a_0335
Z/271
-2 2
12a_0336
2

detected by
the signature
-4+22t-49t^2+63t^3-49t^4+22t^5-4t^6
Seifert matrix of 12a_0336
-1 0 -1 0 1 0
0 1 0 0 0 0
0 0 -2 0 1 0
0 -1 -1 -1 1 0
0 1 2 0 -3 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(t+29t^2-44t^3+33t^4-8t^5,2t^2+58t^3-88t^4+66t^5-16t^6,0,1+6t-10t^2+8t^3-2t^4,2t+12t^2-20t^3+16t^4-4t^5,0)
the Blanchfield form on it
x
213
First homology
of the double branched cover of 12a_0336
Z/213
-4 4
12a_0337
2

detected by
the Lickorish test
3-22t+62t^2-85t^3+62t^4-22t^5+3t^6
Seifert matrix of 12a_0337
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 1 -1 0
-1 -1 0 -1 0 0
1 0 -1 1 -2 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-1+3-t
259
First homology
of the double branched cover of 12a_0337
Z/259
-2 2
12a_0338
2

detected by
the Lickorish test
2-16t+45t^2-61t^3+45t^4-16t^5+2t^6
Seifert matrix of 12a_0338
-1 -1 0 0 0 0
0 1 0 0 0 0
1 1 -2 0 0 0
0 0 -1 -1 0 0
-1 0 0 0 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,3-2t,1,0)
the Blanchfield form on it
4t^-2-26t^-1+47-26t+4t^2
187
First homology
of the double branched cover of 12a_0338
Z/187
-2 2
12a_0339
2

detected by
the Lickorish test
-9+39t-59t^2+39t^3-9t^4
Seifert matrix of 12a_0339
1 0 0 0
-1 -3 0 -1
1 1 -2 0
0 -1 -1 -2
1
Generator of the Alexander module
(0,1-t,0,3-2t)
the Blanchfield form on it
69t^-2-302t^-1+460-302t+69t^2
155
First homology
of the double branched cover of 12a_0339
Z/155
-2 2
12a_0340
1

detected by
an unknotting move
3-21t+59t^2-81t^3+59t^4-21t^5+3t^6
Seifert matrix of 12a_0340
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 -2 -1 -1 -1
1 -1 -1 -2 -1 -1
1 -1 -1 -2 -2 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,-2+3t+4t^2-16t^3+21t^4-2t^5-15t^6+8t^7+2t^8-2t^9,3-7t+12t^2-14t^3+13t^4-4t^5-7t^6+4t^7+2t^8-2t^9,-1+6t-4t^2-2t^3+13t^4-7t^5-11t^6+10t^7-2t^9,-2+11t-14t^2+4t^3+15t^4-16t^5-7t^6+12t^7-2t^8-2t^9,-5t+11t^2-14t^3+2t^4+11t^5-6t^6-2t^7+2t^8)
the Blanchfield form on it
x
247
First homology
of the double branched cover of 12a_0340
Z/247
-2 2
12a_0341
1

detected by
an unknotting move
-1+8t-26t^2+49t^3-61t^4+49t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0341
1 0 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 -1 -1
-1 0 -1 -1 0 0 -1 0
0 0 0 1 0 0 1 1
0 0 0 -1 -1 0 -1 -1
-1 0 -1 -1 0 -1 -1 -1
0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,3t^2-3t^3+3t^4-t^5,0,4t+t^2-3t^3+3t^4-t^5,3+3t^2-t^3+2t^4-t^5,-7t-t^2+3t^3-5t^4+2t^5,2+2t-3t^2+3t^3-t^4,0)
the Blanchfield form on it
x
229
First homology
of the double branched cover of 12a_0341
Z/229
0 0
12a_0342
1

detected by
an unknotting move
-1+8t-26t^2+51t^3-65t^4+51t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0342
1 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 -1 -1
-1 0 -1 0 0 0 -1 0
0 0 0 -1 0 0 1 0
0 0 0 0 1 0 0 0
-1 0 -1 0 0 -1 -1 -1
0 0 0 0 1 0 1 1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,t+3t^2+t^3+t^4+2t^6-3t^7+2t^8,1+t+t^2+2t^4-3t^5+2t^6,-4t-7t^2-9t^4+2t^5+2t^6+t^7-5t^8+2t^9,2+4t+2t^2+t^3+2t^4-t^5-t^6+2t^7,-1-3t-t^2-t^3-2t^5+3t^6-2t^7,1+3t+t^2+t^3+2t^5-3t^6+2t^7,0)
the Blanchfield form on it
x
237
First homology
of the double branched cover of 12a_0342
Z/237
0 0
12a_0343
1

detected by
an unknotting move
3-19t+47t^2-61t^3+47t^4-19t^5+3t^6
Seifert matrix of 12a_0343
1 0 0 0 0 0
0 -1 0 -1 0 -1
1 -1 -2 -1 -1 -1
0 0 0 -1 0 -1
1 -1 -1 -1 -2 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-3+12t^-2-29t^-1+38-29t+12t^2-2t^3
199
First homology
of the double branched cover of 12a_0343
Z/199
-2 2
12a_0344
3

detected by
the signature
5-17t+30t^2-35t^3+30t^4-17t^5+5t^6
Seifert matrix of 12a_0344
-1 1 0 0 0 0
0 -3 -1 0 -1 0
0 -1 -2 0 -2 0
0 0 -1 -1 -1 0
0 -1 -1 0 -2 0
0 0 -1 -1 -1 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
139
First homology
of the double branched cover of 12a_0344
Z/139
-6 6
12a_0345
2

detected by
the signature
8-26t+37t^2-26t^3+8t^4
Seifert matrix of 12a_0345
-1 1 0 0
0 -3 1 0
0 1 -3 0
0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
3t^-1-5+3t
105
First homology
of the double branched cover of 12a_0345
Z/105
-4 4
12a_0346
1

detected by
an unknotting move
2-11t+27t^2-42t^3+49t^4-42t^5+27t^6-11t^7+2t^8
Seifert matrix of 12a_0346
-1 0 -1 0 0 0 -1 0
0 1 0 0 0 0 0 0
0 -1 -2 -1 -1 0 -2 -1
0 1 0 1 0 0 0 0
0 1 0 1 1 0 0 1
0 -1 -1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 0 -2 -1
0 1 0 1 0 0 0 1
1 or 2
213
First homology
of the double branched cover of 12a_0346
Z/213
0 2
12a_0347
2

detected by
the Lickorish test
4-23t+54t^2-69t^3+54t^4-23t^5+4t^6
Seifert matrix of 12a_0347
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 -1 -2 0 -2 1
0 -1 -1 -1 -1 1
0 0 -1 0 -2 1
0 -1 0 0 0 2
2
231
First homology
of the double branched cover of 12a_0347
Z/231
-2 2
12a_0348
2

detected by
the Nakanishi index
-2+17t-54t^2+79t^3-54t^4+17t^5-2t^6
Seifert matrix of 12a_0348
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 1 0 0
-1 -1 0 -1 0 0
0 0 0 0 1 -1
0 -1 -1 0 0 -1
2
225
First homology
of the double branched cover of 12a_0348
Z/45+Z/5
0 0
12a_0349
2

detected by
the signature
1-8t+26t^2-43t^3+49t^4-43t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0349
-1 0 -1 0 0 0 -1 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 0 0 1 0 1 0 0
-1 0 0 1 1 1 -1 1
0 0 0 0 0 1 0 0
0 1 -1 0 0 0 -1 0
-1 0 0 1 0 1 -1 1
1 or 2
205
First homology
of the double branched cover of 12a_0349
Z/205
4 4
12a_0350
2

detected by
the signature
-5+25t-52t^2+65t^3-52t^4+25t^5-5t^6
Seifert matrix of 12a_0350
1 0 0 0 0 0
0 -1 0 0 -1 0
1 0 -2 -1 -1 -2
1 0 -1 -2 -1 -1
1 0 -1 0 -2 -1
1 0 -1 -1 -1 -2
1 or 2
229
First homology
of the double branched cover of 12a_0350
Z/229
-4 4
12a_0351
1

detected by
an unknotting move
1-7t+24t^2-48t^3+61t^4-48t^5+24t^6-7t^7+t^8
Seifert matrix of 12a_0351
-1 0 -1 -1 0 0 -1 -1
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 -1 -1
-1 0 0 -1 1 1 0 -1
0 0 0 0 0 1 0 0
0 1 -1 0 0 0 -1 0
0 1 -1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,-t)
the Blanchfield form on it
3t^-2-6t^-1+8-6t+3t^2
221
First homology
of the double branched cover of 12a_0351
Z/221
0 0
12a_0352
1

detected by
an unknotting move
-1+8t-28t^2+57t^3-71t^4+57t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0352
-1 0 -1 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 -1 0
-1 0 0 -1 1 1 -1 1
0 0 0 0 0 1 0 0
0 1 -1 0 0 0 -1 0
-1 0 0 -1 0 1 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-1+1-t
259
First homology
of the double branched cover of 12a_0352
Z/259
2 2
12a_0353
1

detected by
an unknotting move
4-19t+43t^2-55t^3+43t^4-19t^5+4t^6
Seifert matrix of 12a_0353
-1 -1 0 0 0 0
0 -2 -1 0 -1 0
0 0 -2 0 -1 0
0 1 0 1 0 1
0 0 -2 0 -2 0
0 0 -1 0 -1 1
1
Generator of the Alexander module
(1-t,0,0,2-t,0,0)
the Blanchfield form on it
4t^-2-15t^-1+22-15t+4t^2
187
First homology
of the double branched cover of 12a_0353
Z/187
-2 2
12a_0354
1

detected by
an unknotting move
5-26t+60t^2-77t^3+60t^4-26t^5+5t^6
Seifert matrix of 12a_0354
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 0 -2 0 -1 -1
0 1 0 1 0 0
0 0 -1 -1 -2 0
0 1 0 1 1 -2
1 or 2
259
First homology
of the double branched cover of 12a_0354
Z/259
-2 2
12a_0355
3

detected by
the signature
5-16t+27t^2-31t^3+27t^4-16t^5+5t^6
Seifert matrix of 12a_0355
-1 1 -1 0 -1 0
0 -3 1 0 1 0
0 1 -2 0 -2 0
0 0 -1 -1 -1 0
0 1 -1 0 -2 0
0 0 -1 -1 -1 -1
1
Generator of the Alexander module
(-t,0,0,1+t+t^2,0,0)
the Blanchfield form on it
15t^-2-28t^-1+32-28t+15t^2
127
First homology
of the double branched cover of 12a_0355
Z/127
-6 6
12a_0356
2

detected by
the signature
8-25t+35t^2-25t^3+8t^4
Seifert matrix of 12a_0356
-1 1 1 0
0 -3 -1 0
0 -1 -3 0
0 0 -1 -1
1
Generator of the Alexander module
(-1+t,0,0,3-2t)
the Blanchfield form on it
24t^-1-43+24t
101
First homology
of the double branched cover of 12a_0356
Z/101
-4 4
12a_0357
1

detected by
an unknotting move
-3+17t-40t^2+53t^3-40t^4+17t^5-3t^6
Seifert matrix of 12a_0357
-1 -1 0 0 0 -1
0 -2 0 0 0 -1
0 1 1 1 0 0
0 0 0 1 0 0
0 0 0 0 1 -1
0 -1 0 0 0 -2
1
Generator of the Alexander module
(-1+t,0,-2+t,0,0,0)
the Blanchfield form on it
-3t^-2+14t^-1-22+14t-3t^2
173
First homology
of the double branched cover of 12a_0357
Z/173
0 0
12a_0358
1

detected by
an unknotting move
-1+8t-28t^2+56t^3-69t^4+56t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0358
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 -1
0 -1 0 0 -1 -1 0 -1
0 1 0 0 0 1 0 0
0 -1 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,2+7t+3t^2+13t^3-15t^4+9t^5-t^7,1-6t^2+t^3-19t^4+19t^5-10t^6+t^8,2+7t-17t^2+17t^3-62t^4+54t^5-22t^6-3t^7+3t^8,4-2t+6t^2-12t^3-t^4+5t^5-2t^6-2t^7+t^8,2+7t+3t^2+13t^3-15t^4+9t^5-t^7,2+t-4t^2+t^3-21t^4+22t^5-11t^6+t^8,2-t+5t^2-6t^3+4t^4-t^5)
the Blanchfield form on it
x
255
First homology
of the double branched cover of 12a_0358
Z/255
-2 2
12a_0359
1

detected by
an unknotting move
1-9t+33t^2-67t^3+85t^4-67t^5+33t^6-9t^7+t^8
Seifert matrix of 12a_0359
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 -1 1
0 -1 0 0 -1 -1 -1 0
0 1 0 0 0 1 0 0
0 0 0 0 0 -1 -1 0
0 0 0 0 -1 0 0 1
1
Generator of the Alexander module
(0,1,-t,-3t,-t,1,0,-t)
the Blanchfield form on it
-1
305
First homology
of the double branched cover of 12a_0359
Z/305
0 0
12a_0360
1

detected by
an unknotting move
-3+20t-53t^2+73t^3-53t^4+20t^5-3t^6
Seifert matrix of 12a_0360
1 0 0 0 0 0
0 1 0 -1 0 -1
1 0 -2 -1 0 -1
1 0 -2 -2 0 -1
0 1 -1 -1 1 -1
1 0 -1 -1 0 -2
1
Generator of the Alexander module
(0,-6+13t-8t^2+197t^3-377t^4+221t^5-39t^6,-1-131t+471t^2-821t^3+741t^4-299t^5+39t^6,-66t+367t^2-782t^3+741t^4-299t^5+39t^6,2t+63t^2+94t^3-600t^4+702t^5-299t^6+39t^7,-10-50t+360t^2-847t^3+845t^4-338t^5+39t^6)
the Blanchfield form on it
x
225
First homology
of the double branched cover of 12a_0360
Z/225
0 0
12a_0361
1

detected by
an unknotting move
1-9t+34t^2-73t^3+95t^4-73t^5+34t^6-9t^7+t^8
Seifert matrix of 12a_0361
-1 0 0 -1 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 -1 0 0
0 0 0 -1 -1 0 -1 -1
0 -1 -1 0 0 -1 0 0
0 -1 0 1 0 -1 1 1
0 0 0 1 0 -1 0 1
1 or 2
329
First homology
of the double branched cover of 12a_0361
Z/329
0 0
12a_0362
2

detected by
the signature
1-9t+31t^2-56t^3+67t^4-56t^5+31t^6-9t^7+t^8
Seifert matrix of 12a_0362
-1 1 -1 0 0 0 1 0
0 1 0 1 0 0 1 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
-1 0 0 0 1 -1 0 1
-1 1 -1 1 0 -1 1 0
0 0 0 1 0 0 1 0
0 0 0 0 0 -1 0 1
1
Generator of the Alexander module
(0,-1+t-t^2,0,0,1+t-t^2+t^3,0,0,0)
the Blanchfield form on it
-2t^-3+17t^-2-52t^-1+72-52t+17t^2-2t^3
261
First homology
of the double branched cover of 12a_0362
Z/261
4 4
12a_0363
2

detected by
the signature
1-8t+27t^2-49t^3+59t^4-49t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0363
-1 1 -1 0 0 0 -1 1
0 1 0 1 0 0 0 1
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
-1 0 0 0 1 1 0 0
0 0 0 0 0 1 0 0
0 1 -1 0 0 0 -1 0
0 0 0 1 0 0 0 1
1 or 2
229
First homology
of the double branched cover of 12a_0363
Z/229
4 4
12a_0364 1 or 2
1-8t+29t^2-63t^3+81t^4-63t^5+29t^6-8t^7+t^8
Seifert matrix of 12a_0364
-1 1 -1 0 0 0 1 0
0 1 0 0 0 0 1 0
0 0 1 0 0 0 0 0
-1 1 -1 -1 0 0 1 0
-1 0 0 -1 1 -1 0 1
-1 0 -1 -1 0 -1 0 0
0 0 0 0 0 0 1 0
0 0 0 -1 0 -1 0 1
1
Generator of the Alexander module
(20-143t-963t^2-547t^3-2043t^4-2059t^5+1302t^6+264t^7-128t^8,-23+13t-79t^2-68t^3-86t^4-140t^5+64t^6,-23+26t-26t^2-29t^3+58t^4-16t^5,2+49t+169t^2+180t^3+459t^4+354t^5-192t^6,-148+240t-38t^2+72t^3+766t^4+84t^5-128t^6,-10+124t+322t^2+358t^3+971t^4+690t^5-384t^6,105-190t+57t^2-53t^3-527t^4+10t^5+64t^6,1
the Blanchfield form on it
x
283
First homology
of the double branched cover of 12a_0364
Z/283
2 2
12a_0365
1

detected by
an unknotting move
-2+9t-18t^2+24t^3-25t^4+24t^5-18t^6+9t^7-2t^8
Seifert matrix of 12a_0365
-1 0 -1 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 -2 -1 -1 0 -1 -1
0 1 0 1 0 0 1 0
0 1 0 1 1 0 1 1
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 1 0
0 1 0 1 0 0 1 1
1
Generator of the Alexander module
(-1+t,0,0,0,0,-2+t,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-8t^-1+8-8t+7t^2-2t^3
131
First homology
of the double branched cover of 12a_0365
Z/131
2 2
12a_0366
1

detected by
an unknotting move
-4+20t-44t^2+57t^3-44t^4+20t^5-4t^6
Seifert matrix of 12a_0366
-1 0 -1 0 0 0
0 1 0 0 0 0
0 0 -2 1 -1 0
0 -1 0 2 0 0
0 1 0 -1 1 0
0 -1 -1 1 -1 -1
1 or 2
193
First homology
of the double branched cover of 12a_0366
Z/193
0 0
12a_0367
4

detected by
the signature
3-9t+17t^2-24t^3+27t^4-24t^5+17t^6-9t^7+3t^8
Seifert matrix of 12a_0367
-1 0 -1 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 0
0 0 -2 -2 -1 0 -2 -2
0 0 -1 -2 -1 0 -1 -2
0 0 -1 -1 -2 0 -1 -1
0 -1 0 0 -1 -1 0 0
0 0 -1 -2 -1 0 -2 -2
0 0 -1 -1 -1 0 -1 -2
1
Generator of the Alexander module
(1,0,0,0,0,1,0,0)
the Blanchfield form on it
6t^-3-15t^-2+22t^-1-24+22t-15t^2+6t^3
133
First homology
of the double branched cover of 12a_0367
Z/133
-8 8
12a_0368
3

detected by
the signature
6-20t+36t^2-43t^3+36t^4-20t^5+6t^6
Seifert matrix of 12a_0368
-1 0 -1 1 -1 0
0 -1 0 0 -1 0
0 0 -2 2 -1 0
0 0 1 -3 1 0
0 0 -1 1 -2 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(t+t^2,0,-1+t,2,-1,0)
the Blanchfield form on it
9t^-2-19t^-1+22-19t+9t^2
167
First homology
of the double branched cover of 12a_0368
Z/167
-6 6
12a_0369
3

detected by
the signature
1-3t+6t^2-8t^3+10t^4-11t^5+10t^6-8t^7+6t^8-3t^9+t^10
Seifert matrix of 12a_0369
-1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0 0 0
-1 0 -1 0 0 0 0 0 0 0
-1 1 -1 1 0 0 1 1 0 0
-1 1 -1 1 1 0 1 1 1 0
-1 1 -1 1 1 1 1 1 1 1
0 0 0 0 0 0 1 0 0 0
0 1 0 0 0 0 1 1 0 0
-1 1 -1 1 0 0 1 1 1 0
-1 1 -1 1 1 0 1 1 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0,0,0)
the Blanchfield form on it
-t^-4+3t^-3-6t^-2+8t^-1-9+8t-6t^2+3t^3-t^4
67
First homology
of the double branched cover of 12a_0369
Z/67
6 6
12a_0370
2

detected by
the signature
2-7t+15t^2-21t^3+23t^4-21t^5+15t^6-7t^7+2t^8
Seifert matrix of 12a_0370
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 0 0 1 1
1 -1 1 -1 2 0 -1 -1
-1 1 -1 1 -1 1 1 1
0 0 0 0 0 0 1 0
0 1 0 0 0 0 1 1
1
Generator of the Alexander module
(t,0,-t,0,1+t-2t^2,0,0,2+2t-4t^2)
the Blanchfield form on it
-61t^-3+202t^-2-448t^-1+583-448t+202t^2-61t^3
113
First homology
of the double branched cover of 12a_0370
Z/113
4 4
12a_0371
2

detected by
the signature
-2+7t-14t^2+17t^3-17t^4+17t^5-14t^6+7t^7-2t^8
Seifert matrix of 12a_0371
-1 0 0 0 0 0 0 0
0 2 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 -1 -1 1 0 0 0 0
-1 -1 -1 1 1 0 1 0
-1 -1 -1 1 1 1 1 1
-1 -1 -1 1 0 0 1 0
-1 -1 -1 1 1 0 1 1
1
Generator of the Alexander module
(-24+131t+1790t^2-826t^3-7840t^4-501t^5-1771t^6+1403t^7+422t^8+2772t^9,-12+363t+2402t^2-1257t^3-9479t^4-9730t^5-2631t^6-953t^7+2221t^8+3194t^9+2772t^10,21+112t-492t^2+108t^3-74t^4+182t^5+14t^6+198t^7,-33+123t+2221t^2-291t^3-11072t^4+230t^5-2137t^6+2649t^7+633t^8+4158t^9,8-35t-878t^2-2886t^3-6674t^4+
the Blanchfield form on it
x
97
First homology
of the double branched cover of 12a_0371
Z/97
4 4
12a_0372
2

detected by
the Lickorish test
4-16t+35t^2-45t^3+35t^4-16t^5+4t^6
Seifert matrix of 12a_0372
-1 0 0 0 0 0
0 2 0 0 0 0
-1 0 -1 0 0 0
-1 -1 -1 1 0 0
1 1 1 -1 2 0
-1 -1 -1 1 -1 1
1 or 2
155
First homology
of the double branched cover of 12a_0372
Z/155
2 2
12a_0373
3

detected by
the signature
-1+7t-18t^2+30t^3-35t^4+30t^5-18t^6+7t^7-t^8
Seifert matrix of 12a_0373
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 1 0
0 0 0 0 -1 0 0 0
0 -1 0 0 -1 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,t,1+t,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-9t^-1+11-9t+5t^2-t^3
147
First homology
of the double branched cover of 12a_0373
Z/147
-6 6
12a_0374
1

detected by
an unknotting move
1-7t+22t^2-40t^3+49t^4-40t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0374
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 -1 0 0
-1 0 -1 1 1 -1 0 1
0 0 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 0
-1 0 -1 1 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+7t^-2-19t^-1+25-19t+7t^2-t^3
189
First homology
of the double branched cover of 12a_0374
Z/189
0 0
12a_0375
2

detected by
the signature
2-7t+15t^2-22t^3+25t^4-22t^5+15t^6-7t^7+2t^8
Seifert matrix of 12a_0375
-1 0 0 0 0 0 0 0
0 1 0 0 1 0 0 0
-1 0 -1 0 0 0 0 0
0 0 0 1 0 0 0 1
0 0 0 0 1 0 0 0
0 1 0 0 1 1 0 0
1 -1 1 1 -1 -1 2 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,1,0)
the Blanchfield form on it
-3t^-3+9t^-2-15t^-1+17-15t+9t^2-3t^3
117
First homology
of the double branched cover of 12a_0375
Z/117
4 4
12a_0376
2

detected by
the Lickorish test
4-15t+30t^2-37t^3+30t^4-15t^5+4t^6
Seifert matrix of 12a_0376
-1 0 0 0 0 0
0 2 0 0 0 0
-1 0 -1 0 0 0
0 0 0 1 0 1
1 1 1 1 2 1
0 0 0 0 0 1
2
135
First homology
of the double branched cover of 12a_0376
Z/135
2 2
12a_0377
1

detected by
an unknotting move
1-8t+26t^2-48t^3+59t^4-48t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0377
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 -1 0 -1
0 1 0 0 0 1 0 1
0 -1 0 0 -1 -1 -1 -1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,-1-t+t^2,0,0,2+t-3t^2+t^3,0)
the Blanchfield form on it
t^-3-7t^-2+18t^-1-22+18t-7t^2+t^3
225
First homology
of the double branched cover of 12a_0377
Z/225
0 0
12a_0378
1

detected by
an unknotting move
2-12t+30t^2-39t^3+30t^4-12t^5+2t^6
Seifert matrix of 12a_0378
-1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 0 0 0
0 0 0 -1 0 0
0 -1 0 -1 -1 0
1 0 1 1 0 2
1
Generator of the Alexander module
(0,0,0,0,2-t,1)
the Blanchfield form on it
t^-1-1+t
127
First homology
of the double branched cover of 12a_0378
Z/127
-2 2
12a_0379
1

detected by
an unknotting move
3-9t+15t^2-17t^3+15t^4-9t^5+3t^6
Seifert matrix of 12a_0379
-1 0 0 0 0 0
0 1 0 0 1 0
-1 0 -1 0 0 0
-1 1 -1 3 1 1
0 0 0 0 1 0
0 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-6+5t-3t^2+t^3
71
First homology
of the double branched cover of 12a_0379
Z/71
2 2
12a_0380
1

detected by
an unknotting move
6-19t+27t^2-19t^3+6t^4
Seifert matrix of 12a_0380
-1 0 0 0
0 2 0 0
-1 0 -1 0
-1 -1 -1 3
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
4t^-1-7+4t
77
First homology
of the double branched cover of 12a_0380
Z/77
0 2
12a_0381
2

detected by
the Lickorish test
3-17t+36t^2-43t^3+36t^4-17t^5+3t^6
Seifert matrix of 12a_0381
1 0 0 0 0 0
0 -1 0 -1 0 0
1 -1 -2 -1 0 -1
0 0 0 -1 0 0
0 0 0 0 1 -1
1 0 -1 0 0 -2
2
155
First homology
of the double branched cover of 12a_0381
Z/155
-2 2
12a_0382
2

detected by
the signature
1-7t+18t^2-26t^3+29t^4-26t^5+18t^6-7t^7+t^8
Seifert matrix of 12a_0382
-1 0 0 0 0 -1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 0 1 1 0
0 -1 0 1 1 1 1 1
0 0 0 0 0 1 0 0
0 0 0 0 0 1 1 0
0 -1 0 1 0 1 1 1
1
Generator of the Alexander module
(2+4t-6t^2+2t^3,-2t-14t^2+5t^3+4t^4-21t^5+16t^6+5t^7+t^8-8t^9+3t^10,1+3t-t^2-2t^3+t^4,-t-5t^2+6t^3-5t^4-6t^5+9t^6-3t^7,-t-7t^2+2t^3+t^4-8t^5+9t^6-3t^7,1+2t-5t^2-2t^3+11t^4+t^5-8t^6+3t^7,3+5t-18t^2+10t^3-6t^4-13t^5+18t^6-6t^7,-1-3t+3t^2+6t^3-8t^4+3t^6-t^7)
the Blanchfield form on it
x
133
First homology
of the double branched cover of 12a_0382
Z/133
4 4
12a_0383
1

detected by
an unknotting move
-1+7t-20t^2+34t^3-39t^4+34t^5-20t^6+7t^7-t^8
Seifert matrix of 12a_0383
-1 0 0 0 0 -1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 0 0 1 0
0 -1 0 1 1 0 1 1
0 0 0 0 0 -1 0 0
1 0 0 0 0 1 1 0
0 -1 0 1 0 0 1 1
1
Generator of the Alexander module
(168+369t+201t^2-362t^3,-t-34t^2-31t^3+2t^4-38t^5,-t-155t^2-366t^3-212t^4+400t^5,150+300t+188t^2-186t^3-40t^5-62t^6+4t^7-76t^8,58+116t+77t^2-67t^3-20t^5-31t^6+2t^7-38t^8,-47-77t-30t^2+36t^3,68+161t+93t^2-176t^3,-38-101t-82t^2+104t^3+20t^5+31t^6-2t^7+38t^8)
the Blanchfield form on it
x
163
First homology
of the double branched cover of 12a_0383
Z/163
2 2
12a_0384
1

detected by
an unknotting move
2-14t+36t^2-47t^3+36t^4-14t^5+2t^6
Seifert matrix of 12a_0384
-1 0 0 -1 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 1 1 0
0 1 0 -1 -1 2
1
Generator of the Alexander module
(3-t,0,0,0,-1,1)
the Blanchfield form on it
-2t^-2+10t^-1-15+10t-2t^2
151
First homology
of the double branched cover of 12a_0384
Z/151
2 2
12a_0385
1

detected by
an unknotting move
-2+14t-38t^2+53t^3-38t^4+14t^5-2t^6
Seifert matrix of 12a_0385
-1 0 0 -1 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 -1 0 0
1 0 0 1 1 0
0 1 0 0 -1 2
1
Generator of the Alexander module
(0,2-24t-2t^2+42t^3-192t^4+296t^5+71t^6-990t^7+2328t^8-2909t^9+1910t^10-604t^11+72t^12,17+39t-45t^2-32t^3+63t^4-434t^5+558t^6+139t^7-513t^8+248t^9-36t^10,-35-91t+70t^2-70t^4+1008t^5-1337t^6+588t^7-84t^8,-14+44t+232t^2-76t^3-86t^4+432t^5-2368t^6+2060t^7-102t^8-328t^9+72t^10,-13+18t+498t^2+63t^3-702t^
the Blanchfield form on it
x
161
First homology
of the double branched cover of 12a_0385
Z/161
0 0
12a_0386
3

detected by
the new u==2 criterion
1-8t+25t^2-39t^3+43t^4-39t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_0386
1 0 0 0 0 1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
1 -1 0 0 1 1 -1 1
0 0 0 0 0 1 0 0
0 -1 -1 1 0 0 -1 0
1 0 0 0 0 1 -1 1
2
189
First homology
of the double branched cover of 12a_0386
Z/63+Z/3
4 4
12a_0387
1

detected by
an unknotting move
1-8t+27t^2-53t^3+67t^4-53t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0387
-1 -1 -1 1 0 0 -1 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
-1 -1 0 0 1 -1 -1 1
-1 -1 -1 1 0 -1 -1 0
0 -1 -1 1 0 0 -1 0
0 0 0 0 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,2,1,0,t)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+19-14t+6t^2-t^3
245
First homology
of the double branched cover of 12a_0387
Z/245
0 0
12a_0388
1

detected by
an unknotting move
1-8t+27t^2-53t^3+67t^4-53t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0388
-1 0 0 0 0 -1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 1 1 -1 1
0 0 0 0 0 1 0 0
0 -1 -1 -1 0 0 -1 0
0 0 0 -1 0 1 -1 1
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+19-14t+6t^2-t^3
245
First homology
of the double branched cover of 12a_0388
Z/245
0 0
12a_0389
2

detected by
the Lickorish test
1-9t+33t^2-70t^3+89t^4-70t^5+33t^6-9t^7+t^8
Seifert matrix of 12a_0389
-1 1 -1 1 0 0 -1 0
0 1 0 1 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
-1 0 0 0 1 -1 -1 1
-1 1 -1 1 0 -1 -1 0
0 1 -1 0 0 0 -1 0
0 0 0 0 0 -1 0 1
1 or 2
315
First homology
of the double branched cover of 12a_0389
Z/315
2 2
12a_0390
1

detected by
an unknotting move
-2+11t-29t^2+50t^3-59t^4+50t^5-29t^6+11t^7-2t^8
Seifert matrix of 12a_0390
-1 0 -1 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 -1 -2 -2 -1 0 -2 -1
0 0 -1 -2 -1 0 -1 -1
0 1 0 0 1 0 0 1
0 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -2 -1 0 -2 -1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(-11-13t+61t^2+28t^3+1258t^4+1559t^5+691t^6+402t^7-2671t^8+378t^9+182t^10-4t^11,0,87+633t-546t^2-52t^3-27894t^4-42803t^5-19153t^6-16048t^7+63299t^8-2713t^9-6472t^10+220t^11,-34-319t+244t^2+13t^3+13285t^4+20062t^5+8249t^6+7806t^7-30820t^8+2979t^9+2522t^10-88t^11,615-25t+63t^2-20520t^3-37268t^4-18754t
the Blanchfield form on it
x
243
First homology
of the double branched cover of 12a_0390
Z/243
-2 2
12a_0391
3

detected by
the signature
7-23t+40t^2-47t^3+40t^4-23t^5+7t^6
Seifert matrix of 12a_0391
-1 1 -1 0 0 0
0 -3 1 -1 -1 -1
0 1 -2 -1 -1 -1
0 -1 0 -2 -1 -2
0 -1 0 -2 -2 -2
0 -1 0 -1 -1 -2
1 or 2
187
First homology
of the double branched cover of 12a_0391
Z/187
-6 6
12a_0392
2

detected by
the signature
12-38t+53t^2-38t^3+12t^4
Seifert matrix of 12a_0392
-1 1 -1 0
0 -3 1 1
0 1 -2 1
0 1 0 -3
1
Generator of the Alexander module
(t^2,0,t,1)
the Blanchfield form on it
16t^-1-30+16t
153
First homology
of the double branched cover of 12a_0392
Z/153
-4 4
12a_0393
2

detected by
the signature
-5+27t-60t^2+77t^3-60t^4+27t^5-5t^6
Seifert matrix of 12a_0393
-1 0 -1 -1 -1 0
0 1 0 0 0 0
0 0 -2 -1 -1 -1
0 0 -1 -2 -1 0
0 -1 -1 -2 -2 0
0 1 0 1 1 -2
1 or 2
261
First homology
of the double branched cover of 12a_0393
Z/261
-4 4
12a_0394
2

detected by
the signature
2-9t+23t^2-36t^3+41t^4-36t^5+23t^6-9t^7+2t^8
Seifert matrix of 12a_0394
-1 0 0 0 0 0 0 0
0 2 0 1 0 0 1 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 0 0 0
-1 -1 -1 0 1 0 0 0
-1 -1 -1 0 1 1 0 1
-1 0 -1 1 0 0 1 0
-1 -1 -1 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+9t^-2-21t^-1+27-21t+9t^2-2t^3
181
First homology
of the double branched cover of 12a_0394
Z/181
4 4
12a_0395
2

detected by
the Lickorish test
4-18t+42t^2-55t^3+42t^4-18t^5+4t^6
Seifert matrix of 12a_0395
-1 0 0 0 0 0
0 2 0 1 1 0
-1 0 -1 0 0 0
-1 0 -1 1 0 0
-1 0 -1 1 1 0
1 1 1 0 0 2
1
Generator of the Alexander module
(0,0,0,-1,0,1)
the Blanchfield form on it
6t^-3-28t^-2+65t^-1-86+65t-28t^2+6t^3
183
First homology
of the double branched cover of 12a_0395
Z/183
2 2
12a_0396
2

detected by
the Nakanishi index
-1+7t-22t^2+40t^3-49t^4+40t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0396
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 1 0
-1 -1 1 1 -1 0 1 1
0 0 0 0 -1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 -1 1 1 0
-1 -1 1 0 -1 0 1 1
2
189
First homology
of the double branched cover of 12a_0396
Z/63+Z/3
0 0
12a_0397
2

detected by
the signature
-3+20t-48t^2+63t^3-48t^4+20t^5-3t^6
Seifert matrix of 12a_0397
-1 0 0 0 0 0
0 -2 0 0 0 -1
-1 0 -1 0 0 0
-1 1 -1 1 -1 0
0 0 0 0 -1 -1
0 -1 0 0 0 -2
1
Generator of the Alexander module
(0,-1,1+2t,2t,1-t,1)
the Blanchfield form on it
-10t^-2+55t^-1-86+55t-10t^2
205
First homology
of the double branched cover of 12a_0397
Z/205
-4 4
12a_0398
2

detected by
the signature
1-7t+22t^2-39t^3+47t^4-39t^5+22t^6-7t^7+t^8
Seifert matrix of 12a_0398
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 -1 0 -1
0 -1 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
0 -1 0 0 -1 -1 -1 -1
0 -1 0 0 0 -1 0 -1
1 or 2
185
First homology
of the double branched cover of 12a_0398
Z/185
-4 4
12a_0399
1

detected by
an unknotting move
5-22t+48t^2-61t^3+48t^4-22t^5+5t^6
Seifert matrix of 12a_0399
-1 0 0 0 0 0
0 2 0 1 1 0
-1 0 -1 0 0 0
0 1 0 2 1 1
0 1 0 2 2 1
1 1 1 1 1 2
1 or 2
211
First homology
of the double branched cover of 12a_0399
Z/211
2 2
12a_0400
1

detected by
an unknotting move
3-18t+48t^2-65t^3+48t^4-18t^5+3t^6
Seifert matrix of 12a_0400
-1 0 0 0 0 0
0 -2 0 0 -1 0
-1 0 -1 0 0 0
-1 1 -1 1 1 1
0 -1 0 0 -2 0
0 0 0 0 1 1
1
Generator of the Alexander module
(29-21t+6t^2,9-3t,-16+5t,-38+16t+14t^2-5t^3,-4t^2+18t^3-5t^4,35-15t-2t^2+18t^3-5t^4)
the Blanchfield form on it
-27959t^-2+84607t^-1-118638+84607t-27959t^2
203
First homology
of the double branched cover of 12a_0400
Z/203
-2 2
12a_0401
2

detected by
the Lickorish test
2-14t+38t^2-51t^3+38t^4-14t^5+2t^6
Seifert matrix of 12a_0401
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 0
0 0 0 -1 0 0
0 0 -1 1 1 0
1 1 1 0 -1 2
1
Generator of the Alexander module
(0,0,2,0,0,1-2t)
the Blanchfield form on it
t^-3-5t^-2+8t^-1-6+8t-5t^2+t^3
159
First homology
of the double branched cover of 12a_0401
Z/159
-2 2
12a_0402
1

detected by
an unknotting move
-1+8t-29t^2+60t^3-75t^4+60t^5-29t^6+8t^7-t^8
Seifert matrix of 12a_0402
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 -1 -1 1
0 -1 0 0 -1 -1 -1 0
0 0 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 0
0 0 0 0 -1 0 0 1
1
Generator of the Alexander module
(0,23-47t+52t^2-17t^3+31t^4-51t^5+27t^6+6t^7-6t^8,t-t^2-5t^3+10t^4-4t^5,25t-49t^2+35t^3+2t^4-6t^5,9-17t+11t^2+8t^3-6t^4+t^5-4t^6+2t^7,3-9t+18t^2-9t^3+t^4+5t^5-10t^6+4t^7,-3t+7t^2-10t^3+4t^4,15t-35t^2+49t^3-16t^4-2t^5)
the Blanchfield form on it
x
271
First homology
of the double branched cover of 12a_0402
Z/271
-2 2
12a_0403
1

detected by
an unknotting move
-3+19t-49t^2+67t^3-49t^4+19t^5-3t^6
Seifert matrix of 12a_0403
1 0 0 0 0 0
0 1 0 -1 0 -1
1 0 -2 -1 0 -2
1 0 -1 -2 0 -1
0 1 0 -1 1 -1
1 0 -1 -1 0 -2
1
Generator of the Alexander module
(0,-1,0,0,0,1)
the Blanchfield form on it
-3t^-2+16t^-1-27+16t-3t^2
209
First homology
of the double branched cover of 12a_0403
Z/209
0 0
12a_0404
2

detected by
the Lickorish test
3-17t+37t^2-45t^3+37t^4-17t^5+3t^6
Seifert matrix of 12a_0404
1 0 0 0 0 0
0 1 -1 1 0 -1
1 0 -2 0 0 -1
0 0 0 1 0 -1
0 1 -1 1 1 -1
1 0 -1 0 0 -2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-3t^-2+16t^-1-27+16t-3t^2
159
First homology
of the double branched cover of 12a_0404
Z/159
2 2
12a_0405
1

detected by
an unknotting move
3-19t+45t^2-57t^3+45t^4-19t^5+3t^6
Seifert matrix of 12a_0405
1 0 0 0 0 0
1 -2 -2 -1 0 -1
1 -1 -2 -1 0 -1
1 -2 -2 -2 0 -1
0 -1 0 -1 1 -1
1 -1 -1 -1 0 -2
1
Generator of the Alexander module
(0,-6t-6t^2+107t^3-12t^4-65t^5+49t^6-12t^7,1-19t+19t^2+10t^3-20t^4+6t^5,-1+19t+5t^2+6t^3+8t^4-6t^5,-2-10t+25t^2+39t^3-47t^4+10t^5+14t^6-6t^7,-2+14t+12t^2+18t^3-5t^4-3t^5)
the Blanchfield form on it
x
191
First homology
of the double branched cover of 12a_0405
Z/191
-2 2
12a_0406
1

detected by
an unknotting move
2-16t+43t^2-57t^3+43t^4-16t^5+2t^6
Seifert matrix of 12a_0406
-1 0 0 0 0 -1
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 0 1 -1 0
0 0 0 0 -1 0
0 0 0 0 1 -2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
t^-2-7t^-1+13-7t+t^2
179
First homology
of the double branched cover of 12a_0406
Z/179
-2 2
12a_0407
1

detected by
an unknotting move
3-21t+60t^2-83t^3+60t^4-21t^5+3t^6
Seifert matrix of 12a_0407
2 0 0 1 1 1
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 -1 -1 0 0
0 -1 0 0 1 0
1 0 0 1 0 2
1
Generator of the Alexander module
(1+t^2,t+2t^2,0,0,1,0)
the Blanchfield form on it
-2t^-5+5t^-4+16t^-3-53t^-2+51t^-1-34+51t-53t^2+16t^3+5t^4-2t^5
251
First homology
of the double branched cover of 12a_0407
Z/251
2 2
12a_0408
2

detected by
the signature
-5+29t-66t^2+85t^3-66t^4+29t^5-5t^6
Seifert matrix of 12a_0408
-1 0 -1 0 -1 0
0 -1 0 -1 0 -1
0 0 -2 0 -1 -1
0 0 0 1 0 0
0 0 -1 -1 -2 0
0 0 0 0 1 -2
2
285
First homology
of the double branched cover of 12a_0408
Z/285
-4 4
12a_0409
3

detected by
the signature
-2+10t-20t^2+27t^3-29t^4+27t^5-20t^6+10t^7-2t^8
Seifert matrix of 12a_0409
-1 0 -1 -1 -1 0 -1 -1
0 1 0 0 0 0 0 0
0 -1 -2 -2 -2 0 -2 -2
0 -1 -1 -2 -2 0 -1 -2
0 0 -1 -1 -2 0 -1 -1
0 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -2 -2 0 -2 -2
0 -1 -1 -1 -2 0 -1 -2
1 or 2
147
First homology
of the double branched cover of 12a_0409
Z/147
-6 6
12a_0410
2

detected by
the signature
-4+22t-48t^2+61t^3-48t^4+22t^5-4t^6
Seifert matrix of 12a_0410
-1 0 -1 1 -1 0
0 1 0 0 0 0
0 -1 -2 2 -2 0
0 1 1 -3 2 0
0 0 -1 1 -2 0
0 -1 -1 1 -1 -1
1 or 2
209
First homology
of the double branched cover of 12a_0410
Z/209
-4 4
12a_0411
2

detected by
the signature
2-9t+21t^2-29t^3+31t^4-29t^5+21t^6-9t^7+2t^8
Seifert matrix of 12a_0411
-1 0 0 0 0 0 0 0
0 2 0 1 1 0 1 1
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 0 0 0
-1 0 -1 1 1 0 1 0
-1 -1 -1 0 0 1 0 0
-1 0 -1 1 0 0 1 0
-1 0 -1 1 1 0 1 1
1
Generator of the Alexander module
(0,-6+16t-14t^2+4t^3,3-5t+2t^2,0,0,7-13t+9t^2-2t^3,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
153
First homology
of the double branched cover of 12a_0411
Z/153
4 4
12a_0412
1

detected by
an unknotting move
4-20t+49t^2-65t^3+49t^4-20t^5+4t^6
Seifert matrix of 12a_0412
-1 0 0 0 0 0
0 2 0 1 -1 0
-1 0 -1 0 0 0
-1 0 -1 1 0 0
1 0 1 -1 2 0
-1 -1 -1 0 0 1
1
Generator of the Alexander module
(0,0,3-5t+2t^2,3-5t+2t^2,-3+5t-2t^2,7-10t+4t^2)
the Blanchfield form on it
-2t^-1+3-2t
211
First homology
of the double branched cover of 12a_0412
Z/211
2 2
12a_0413
2

detected by
the Nakanishi index
-1+8t-29t^2+62t^3-79t^4+62t^5-29t^6+8t^7-t^8
Seifert matrix of 12a_0413
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 -1 0
-1 0 -1 0 0 0 0 0
-1 -1 -1 1 -1 0 -1 1
0 -1 0 0 -1 0 -1 0
0 0 0 0 0 1 0 0
0 0 0 0 0 -1 -1 0
0 -1 0 0 -1 0 0 1
2
279
First homology
of the double branched cover of 12a_0413
Z/93+Z/3
-2 2
12a_0414
1

detected by
an unknotting move
-9+37t-55t^2+37t^3-9t^4
Seifert matrix of 12a_0414
1 0 0 0
-1 -3 -1 -1
0 -1 -2 1
-1 -2 0 -3
1
Generator of the Alexander module
(0,7-4t,-23+16t,-35+24t)
the Blanchfield form on it
-1526t^-1+3663-1526t
147
First homology
of the double branched cover of 12a_0414
Z/147
-2 2
12a_0415
1

detected by
an unknotting move
1-8t+27t^2-54t^3+69t^4-54t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0415
-1 0 0 0 -1 0 0 -1
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 0 1 0 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 0 1 0 0
0 -1 0 1 0 1 1 0
0 0 0 -1 -1 -1 0 -1
1 or 2
249
First homology
of the double branched cover of 12a_0415
Z/249
0 0
12a_0416
2

detected by
the Lickorish test
-1+8t-25t^2+44t^3-51t^4+44t^5-25t^6+8t^7-t^8
Seifert matrix of 12a_0416
-1 0 0 0 -1 0 -1 -1
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 0 1 0 0
0 0 0 -1 -1 -1 0 0
0 0 0 0 0 1 0 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 -1 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,1+t+t^3,0,0,1+t-t^2+t^3-t^4,0)
the Blanchfield form on it
-t^-3+8t^-2-24t^-1+35-24t+8t^2-t^3
207
First homology
of the double branched cover of 12a_0416
Z/207
-2 2
12a_0417
1

detected by
an unknotting move
-1+8t-28t^2+55t^3-67t^4+55t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0417
-1 -1 -1 1 0 0 -1 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
-1 -1 0 0 1 1 -1 1
0 0 0 0 0 1 0 0
0 -1 -1 1 0 0 -1 0
-1 0 0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,1+2t+2t^2+2t^3-4t^4,-1-2t-4t^2-6t^3+4t^4,-2t-t^2+2t^3-2t^4+10t^5-4t^6,2-9t-2t^2-2t^3+2t^4+12t^5,4t+2t^2-4t^3+4t^4-20t^5+8t^6,-4t+2t^4+4t^5)
the Blanchfield form on it
x
251
First homology
of the double branched cover of 12a_0417
Z/251
2 2
12a_0418
1

detected by
an unknotting move
-1+8t-27t^2+54t^3-67t^4+54t^5-27t^6+8t^7-t^8
Seifert matrix of 12a_0418
1 0 0 1 0 -1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 -1 0 0
-1 0 0 0 -1 0 -1 -1
0 -1 -1 0 0 -1 0 0
1 -1 0 1 0 -1 1 1
1 0 0 1 0 -1 0 1
1
Generator of the Alexander module
(-t-2t^2-t^3-t^4,1+t^2+t^3,-4t-2t^2-3t^3-4t^4,-1+6t+6t^2+4t^3+6t^4,-17t+2t^2-5t^3-9t^4+8t^5,4t^2+2t^3+7t^4+5t^5+4t^7,9t+4t^2+4t^3+7t^4,t+21t^2+6t^3+16t^4+18t^5+t^6)
the Blanchfield form on it
x
247
First homology
of the double branched cover of 12a_0418
Z/247
2 2
12a_0419
2

detected by
the Lickorish test
-1+9t-32t^2+61t^3-73t^4+61t^5-32t^6+9t^7-t^8
Seifert matrix of 12a_0419
-1 0 0 0 -1 0 0 -1
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 -1 0 0
0 0 0 -1 -1 0 -1 0
0 -1 -1 0 0 -1 0 0
0 -1 0 1 0 -1 1 0
0 0 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(3t-2t^2,-6t+2t^2+6t^3-4t^4-4t^7,-t-6t^3+4t^4,-9t+4t^2+12t^3-4t^4-4t^5,3t-t^2,-1-18t^3+12t^4,-2t^2-3t^4+2t^5,-t^2+6t^3-2t^4-2t^5)
the Blanchfield form on it
x
279
First homology
of the double branched cover of 12a_0419
Z/279
-2 2
12a_0420
3

detected by
the signature
5-15t+23t^2-25t^3+23t^4-15t^5+5t^6
Seifert matrix of 12a_0420
-1 1 0 0 0 0
0 -3 -1 -1 -1 -1
0 -1 -2 -2 -2 -2
0 -1 -1 -2 -1 -2
0 -1 -1 -2 -2 -2
0 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-2-3t^-1+3-3t+2t^2
111
First homology
of the double branched cover of 12a_0420
Z/111
-6 6
12a_0421
2

detected by
the signature
10-33t+47t^2-33t^3+10t^4
Seifert matrix of 12a_0421
-1 1 0 0
0 -3 -1 1
0 -1 -2 2
0 1 1 -3
1 or 2
133
First homology
of the double branched cover of 12a_0421
Z/133
-4 4
12a_0422
2

detected by
the signature
-2+6t-10t^2+11t^3-11t^4+11t^5-10t^6+6t^7-2t^8
Seifert matrix of 12a_0422
-1 -1 0 0 0 0 0 0
0 -2 0 0 0 0 0 0
0 1 1 0 0 1 0 0
0 1 1 1 0 1 1 0
0 1 1 1 1 1 1 1
0 0 0 0 0 1 0 0
0 1 1 0 0 1 1 0
0 1 1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
2t^-3-6t^-2+10t^-1-11+10t-6t^2+2t^3
69
First homology
of the double branched cover of 12a_0422
Z/69
4 4
12a_0423
1

detected by
an unknotting move
4-14t+26t^2-31t^3+26t^4-14t^5+4t^6
Seifert matrix of 12a_0423
-1 -1 0 0 0 0
0 -2 0 0 0 0
0 1 1 0 0 1
0 -1 -1 2 0 -1
0 1 1 -1 1 1
0 0 0 0 0 1
1 or 2
119
First homology
of the double branched cover of 12a_0423
Z/119
2 2
12a_0424
1

detected by
an unknotting move
4-15t+29t^2-35t^3+29t^4-15t^5+4t^6
Seifert matrix of 12a_0424
-1 -1 0 0 0 0
0 -2 0 0 0 0
0 0 1 0 0 1
0 0 0 1 0 0
0 -1 1 -1 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(-1+2t-t^2,t^2,t^2,1-t,t-t^2-t^3,0)
the Blanchfield form on it
-7t^-5+44t^-4-128t^-3+246t^-2-353t^-1+396-353t+246t^2-128t^3+44t^4-7t^5
131
First homology
of the double branched cover of 12a_0424
Z/131
2 2
12a_0425
1

detected by
an unknotting move
6-20t+29t^2-20t^3+6t^4
Seifert matrix of 12a_0425
-1 -1 0 0
0 -2 0 0
0 1 3 1
0 0 0 1
1
Generator of the Alexander module
(0,0,1-6t+3t^2,2-t)
the Blanchfield form on it
-47t^-3+254t^-2-601t^-1+786-601t+254t^2-47t^3
81
First homology
of the double branched cover of 12a_0425
Z/81
0 0
12a_0426
1

detected by
an unknotting move
-1+8t-29t^2+60t^3-77t^4+60t^5-29t^6+8t^7-t^8
Seifert matrix of 12a_0426
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 1 0 -1 0
0 0 0 -1 0 0 -1 0
0 0 0 -1 1 0 -1 0
-1 -1 0 0 0 1 0 1
0 0 0 0 0 0 -1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(0,1+t-4t^2,2+2t-4t^2,t,1+t,6t-8t^2,-1,-3+3t)
the Blanchfield form on it
1
273
First homology
of the double branched cover of 12a_0426
Z/273
0 0
12a_0427
2

detected by
the Nakanishi index
1-8t+26t^2-48t^3+59t^4-48t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0427
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
-1 -1 0 -1 1 1 0 1
0 0 0 0 0 1 0 0
0 0 0 0 0 0 -1 0
-1 0 0 0 0 1 1 1
2
225
First homology
of the double branched cover of 12a_0427
Z/15+Z/15
0 0
12a_0428
2

detected by
the Lickorish test
2-9t+21t^2-32t^3+37t^4-32t^5+21t^6-9t^7+2t^8
Seifert matrix of 12a_0428
-1 0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 0 1 0 1 0 1 0
0 0 1 0 1 1 1 1
0 1 1 0 0 0 1 0
0 0 1 0 1 0 1 1
1
Generator of the Alexander module
(-t,0,0,0,1+t^2-t^3,0,0,0)
the Blanchfield form on it
2t^-2-7t^-1+10-7t+2t^2
165
First homology
of the double branched cover of 12a_0428
Z/165
0 2
12a_0429
2

detected by
the Lickorish test
4-19t+42t^2-53t^3+42t^4-19t^5+4t^6
Seifert matrix of 12a_0429
-1 0 -1 0 0 0
0 -1 -1 0 0 0
0 0 -2 0 0 0
0 -1 -1 -1 0 0
0 1 1 0 1 0
0 0 -1 0 -1 2
2
183
First homology
of the double branched cover of 12a_0429
Z/183
-2 2
12a_0430
2

detected by
the signature
-2+10t-27t^2+45t^3-53t^4+45t^5-27t^6+10t^7-2t^8
Seifert matrix of 12a_0430
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 1 0 0 0
0 0 1 2 1 0 -1 2
0 0 0 0 1 0 0 0
-1 -1 0 -1 0 1 1 -1
0 0 0 0 0 0 1 0
0 0 1 1 1 0 -1 2
1
Generator of the Alexander module
(0,2-8t+7t^2+t^3-7t^4+6t^5-2t^6,-2+5t+t^2+31t^3-39t^4-17t^5+102t^6-105t^7+9t^8+82t^9-92t^10+48t^11-12t^12,-4-3t+3t^2+15t^3-8t^4-7t^5-2t^6+36t^7-43t^8+3t^9+40t^10-45t^11+24t^12-6t^13,-2t+8t^2+9t^3-20t^4-3t^5+47t^6-54t^7+9t^8+38t^9-45t^10+24t^11-6t^12,3-t-3t^2+9t^3-10t^4+4t^5+5t^6-9t^7+6t^8-2t^9,-6+2t
the Blanchfield form on it
x
221
First homology
of the double branched cover of 12a_0430
Z/221
4 4
12a_0431
3

detected by
the signature
8-31t+61t^2-75t^3+61t^4-31t^5+8t^6
Seifert matrix of 12a_0431
-1 0 -1 1 -1 0
0 -1 0 -1 0 -1
0 0 -2 1 -1 -1
0 0 1 -3 2 -1
0 0 -1 1 -2 0
0 0 0 -1 1 -2
1 or 2
275
First homology
of the double branched cover of 12a_0431
Z/275
-6 6
12a_0432
3

detected by
the signature
7-25t+46t^2-55t^3+46t^4-25t^5+7t^6
Seifert matrix of 12a_0432
-1 1 -1 0 -1 0
0 -3 1 -1 1 -1
0 1 -2 -1 -2 -1
0 -1 0 -2 0 -2
0 1 -1 -1 -2 -1
0 -1 0 -1 0 -2
1 or 2
211
First homology
of the double branched cover of 12a_0432
Z/211
-6 6
12a_0433
3

detected by
the new u==2 criterion
-3+19t-44t^2+57t^3-44t^4+19t^5-3t^6
Seifert matrix of 12a_0433
-1 -1 -1 0 0 -1
0 -2 -1 0 0 -2
0 -1 -2 0 0 -1
0 0 1 1 -1 0
0 0 0 0 -1 0
0 -1 -1 0 0 -2
2
189
First homology
of the double branched cover of 12a_0433
Z/63+Z/3
-4 4
12a_0434
2

detected by
the Lickorish test
1-8t+23t^2-41t^3+49t^4-41t^5+23t^6-8t^7+t^8
Seifert matrix of 12a_0434
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 1 1 0 1 0
-1 -1 0 0 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 0 1 0 1 1
1 or 2
195
First homology
of the double branched cover of 12a_0434
Z/195
2 2
12a_0435
2

detected by
the Nakanishi index
-1+8t-26t^2+48t^3-59t^4+48t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0435
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 1 0 0 1 0
0 0 0 1 0 0 0 0
-1 -1 0 0 1 1 1 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
225
First homology
of the double branched cover of 12a_0435
Z/75+Z/3
0 0
12a_0436
2

detected by
the Lickorish test
1-7t+18t^2-29t^3+33t^4-29t^5+18t^6-7t^7+t^8
Seifert matrix of 12a_0436
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 1 1 0 1 0
0 0 0 1 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+7t^-2-17t^-1+23-17t+7t^2-t^3
143
First homology
of the double branched cover of 12a_0436
Z/143
2 2
12a_0437
1

detected by
an unknotting move
-2+14t-35t^2+47t^3-35t^4+14t^5-2t^6
Seifert matrix of 12a_0437
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 1 0
0 0 0 -1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+7t^-2-18t^-1+24-18t+7t^2-t^3
149
First homology
of the double branched cover of 12a_0437
Z/149
0 0
12a_0438
1

detected by
an unknotting move
1-8t+25t^2-44t^3+53t^4-44t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_0438
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 -1 0 -1 0 0 0
-1 -1 0 0 -1 1 -1 1
-1 -1 -1 1 -1 0 -1 0
0 0 0 0 0 0 -1 1
1
Generator of the Alexander module
(0,1-3t+t^2,0,0,0,-3+4t-t^2,-6t+8t^2-2t^3,0)
the Blanchfield form on it
-5t^-3-26t^-2+160t^-1-233+160t-26t^2-5t^3
209
First homology
of the double branched cover of 12a_0438
Z/209
0 2
12a_0439
1

detected by
an unknotting move
-1+9t-34t^2+71t^3-91t^4+71t^5-34t^6+9t^7-t^8
Seifert matrix of 12a_0439
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
0 0 -1 0 0 0 -1 0
0 0 0 1 1 0 0 1
0 0 0 0 1 0 -1 1
-1 0 0 -1 -1 -1 0 0
0 0 0 0 0 0 -1 0
0 0 -1 0 0 0 -1 1
1
Generator of the Alexander module
(0,1+3t+27t^2+48t^3-86t^4+28t^5,0,-1-3t-8t^2-2t^3+29t^4-14t^5,-2-6t-16t^2-4t^3+58t^4-28t^5,2+6t+73t^2+142t^3-229t^4+70t^5,0,0)
the Blanchfield form on it
x
321
First homology
of the double branched cover of 12a_0439
Z/321
0 0
12a_0440
2

detected by
the signature
2-9t+20t^2-28t^3+31t^4-28t^5+20t^6-9t^7+2t^8
Seifert matrix of 12a_0440
-1 0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 -1 -1 -1 -1 0 -1 0
0 -1 -1 0 -1 0 0 0
0 0 1 0 0 1 0 1
0 -1 -1 0 -1 0 -1 0
0 1 1 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+2t^-2-3t^-1+3-3t+2t^2-t^3
149
First homology
of the double branched cover of 12a_0440
Z/149
-4 4
12a_0441
1

detected by
an unknotting move
4-20t+46t^2-59t^3+46t^4-20t^5+4t^6
Seifert matrix of 12a_0441
-1 0 -1 0 0 0
0 -1 -1 0 -1 0
0 0 -2 0 -1 0
0 0 1 1 0 1
0 0 0 0 -2 0
0 1 1 0 0 1
1
Generator of the Alexander module
(1-t,0,0,2-t,0,0)
the Blanchfield form on it
4t^-2-16t^-1+24-16t+4t^2
199
First homology
of the double branched cover of 12a_0441
Z/199
-2 2
12a_0442
3

detected by
the signature
5-14t+21t^2-23t^3+21t^4-14t^5+5t^6
Seifert matrix of 12a_0442
-1 1 -1 -1 -1 -1
0 -3 1 1 1 1
0 1 -2 -2 -2 -2
0 1 -1 -2 -1 -2
0 1 -1 -2 -2 -2
0 1 -1 -1 -1 -2
1
Generator of the Alexander module
(-1,0,0,0,1,0)
the Blanchfield form on it
10t^-2-23t^-1+28-23t+10t^2
103
First homology
of the double branched cover of 12a_0442
Z/103
-6 6
12a_0443
2

detected by
the signature
10-31t+43t^2-31t^3+10t^4
Seifert matrix of 12a_0443
-1 1 -1 1
0 -3 1 -1
0 1 -2 2
0 -1 1 -3
1
Generator of the Alexander module
(t,0,1,0)
the Blanchfield form on it
15t^-1-28+15t
125
First homology
of the double branched cover of 12a_0443
Z/125
-4 4
12a_0444
2

detected by
the signature
-2+13t-30t^2+39t^3-30t^4+13t^5-2t^6
Seifert matrix of 12a_0444
-1 0 0 0 0 0
0 -2 0 0 0 0
-1 0 -1 0 0 0
-1 1 -1 1 1 0
0 0 0 0 -1 0
0 0 0 0 -1 -1
2
129
First homology
of the double branched cover of 12a_0444
Z/129
-4 4
12a_0445
1

detected by
an unknotting move
1-7t+20t^2-36t^3+43t^4-36t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0445
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 0 0
-1 -1 1 1 -1 0 0 1
0 0 0 0 -1 0 0 0
0 0 0 0 1 1 1 0
0 0 0 0 0 0 1 0
-1 -1 1 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+7t^-2-17t^-1+23-17t+7t^2-t^3
171
First homology
of the double branched cover of 12a_0445
Z/171
2 2
12a_0446
2

detected by
the Lickorish test
-1+8t-26t^2+50t^3-61t^4+50t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0446
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 -1 0 0 -1 -1 0 0
0 0 0 0 1 0 1 1
0 1 0 0 1 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,-t,t,-1)
the Blanchfield form on it
-t^-3+7t^-2-18t^-1+24-18t+7t^2-t^3
231
First homology
of the double branched cover of 12a_0446
Z/231
-2 2
12a_0447
1

detected by
an unknotting move
-2+12t-28t^2+37t^3-28t^4+12t^5-2t^6
Seifert matrix of 12a_0447
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 0
0 0 1 1 1 0
0 0 0 0 1 0
1 1 1 0 0 2
1
Generator of the Alexander module
(0,0,0,2-t,0,1)
the Blanchfield form on it
-t^-1+1-t
121
First homology
of the double branched cover of 12a_0447
Z/121
0 0
12a_0448
2

detected by
the Lickorish test
5-26t+43t^2-26t^3+5t^4
Seifert matrix of 12a_0448
1 0 0 0
-1 -3 0 1
0 0 1 -1
1 1 0 -2
2
105
First homology
of the double branched cover of 12a_0448
Z/105
0 0
12a_0449
2

detected by
the Lickorish test
2-16t+45t^2-61t^3+45t^4-16t^5+2t^6
Seifert matrix of 12a_0449
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 0 0 0
0 0 1 1 -1 1
-1 1 1 0 -1 0
0 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,-2+3t-2t^2,3-2t,0)
the Blanchfield form on it
29t^-3-232t^-2+653t^-1-886+653t-232t^2+29t^3
187
First homology
of the double branched cover of 12a_0449
Z/187
2 2
12a_0450
2

detected by
the Lickorish test
2-16t+50t^2-71t^3+50t^4-16t^5+2t^6
Seifert matrix of 12a_0450
2 0 0 0 1 1
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 -1 0 0 1 0
0 -1 -1 1 0 -1
1 or 2
207
First homology
of the double branched cover of 12a_0450
Z/207
2 2
12a_0451
1

detected by
an unknotting move
-1+8t-27t^2+53t^3-65t^4+53t^5-27t^6+8t^7-t^8
Seifert matrix of 12a_0451
-1 -1 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 0
-1 0 -1 1 -1 0 -1 1
0 0 0 0 -1 0 0 0
0 0 0 0 -1 -1 0 0
-1 -1 -1 0 0 0 -1 0
0 0 -1 0 -1 0 -1 1
1
Generator of the Alexander module
(0,0,1,1+t,1,-1+t,1,t)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+19-14t+6t^2-t^3
243
First homology
of the double branched cover of 12a_0451
Z/243
-2 2
12a_0452
1

detected by
an unknotting move
1-8t+28t^2-55t^3+69t^4-55t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0452
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 1 0 0 1 1 0 0
-1 0 -1 0 0 1 1 1
-1 0 -1 0 0 1 0 1
1
Generator of the Alexander module
(2t^2-2t^3+2t^4,3t-8t^2+4t^3,2t+2t^2-4t^3-4t^4+6t^5-4t^6-4t^7+8t^8-4t^9,-1+2t^2+2t^3-4t^4+2t^5+2t^6-4t^7+2t^8,5-4t^2+8t^3-4t^4,-2-10t+12t^3-24t^4+20t^5-4t^6,2t^2,-2t+6t^2-2t^3)
the Blanchfield form on it
x
253
First homology
of the double branched cover of 12a_0452
Z/253
0 0
12a_0453
1

detected by
an unknotting move
1-7t+18t^2-30t^3+37t^4-30t^5+18t^6-7t^7+t^8
Seifert matrix of 12a_0453
-1 0 0 0 0 -1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 0 -1 0 0
0 -1 0 1 1 -1 0 1
0 0 0 0 0 -1 0 0
-1 0 0 0 0 -1 -1 0
0 -1 0 1 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,-1)
the Blanchfield form on it
-t^-2+6t^-1-10+6t-t^2
149
First homology
of the double branched cover of 12a_0453
Z/149
0 0
12a_0454
1

detected by
an unknotting move
2-12t+24t^2-27t^3+24t^4-12t^5+2t^6
Seifert matrix of 12a_0454
-1 0 0 -1 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 -1 0 0
-1 0 0 -1 -1 0
0 1 0 1 0 2
1
Generator of the Alexander module
(0,0,0,0,t^2,-1-t)
the Blanchfield form on it
2t^-2-12t^-1+21-12t+2t^2
103
First homology
of the double branched cover of 12a_0454
Z/103
-2 2
12a_0455
1

detected by
an unknotting move
1-8t+27t^2-52t^3+63t^4-52t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0455
1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 -1
0 0 1 0 0 0 -1 1
0 0 1 1 1 0 0 1
0 0 1 0 1 0 0 1
-1 0 -1 -1 -1 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 1
1
Generator of the Alexander module
(0,3+15t-72t^2+32t^3-23t^4-52t^5+332t^6-176t^7+24t^8,-3-8t+42t^2-22t^3+3t^4,3t-10t^2+4t^3+3t^4-t^5,4t-5t^2-t^3+4t^4-t^5,-2-2t-9t^2-26t^3+166t^4-88t^5+12t^6,2-4t+t^2,-8-12t+83t^2-44t^3+6t^4)
the Blanchfield form on it
x
239
First homology
of the double branched cover of 12a_0455
Z/239
2 2
12a_0456
2

detected by
the Lickorish test
1-8t+25t^2-48t^3+61t^4-48t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_0456
-1 0 0 0 0 -1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 -1 0 1 1 -1 -1 1
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
-1 0 0 0 0 -1 -1 0
-1 0 0 0 1 0 -1 1
1
Generator of the Alexander module
(0,-t^2+t^5,0,-t^2-3t^3-t^4+2t^6,-1+t^2+t^3-t^5,0,1-t^2-2t^3-t^4+t^5+t^6,2t-t^3-2t^4+t^6)
the Blanchfield form on it
x
225
First homology
of the double branched cover of 12a_0456
Z/225
0 0
12a_0457
1

detected by
an unknotting move
1-8t+29t^2-60t^3+75t^4-60t^5+29t^6-8t^7+t^8
Seifert matrix of 12a_0457
1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 -1
0 0 1 1 1 0 0 1
0 0 0 1 0 0 0 0
0 0 0 1 1 0 -1 1
-1 0 -1 0 -1 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 1 0 0 -1 1
1
Generator of the Alexander module
(0,-2t+t^2+t^3,-1+3t-t^2-t^3,0,-2+t+t^2,1-t+t^2,2-t-t^2,1-t+t^2)
the Blanchfield form on it
-79t^-3+436t^-2-988t^-1+1288-988t+436t^2-79t^3
271
First homology
of the double branched cover of 12a_0457
Z/271
2 2
12a_0458
2

detected by
the Lickorish test
-1+9t-32t^2+63t^3-79t^4+63t^5-32t^6+9t^7-t^8
Seifert matrix of 12a_0458
1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 -1
0 0 1 1 0 0 0 1
0 0 0 1 0 0 0 0
-1 0 -1 0 -1 0 0 0
-1 0 -1 0 -1 -1 0 -1
0 0 0 0 0 0 -1 0
0 0 0 1 0 0 -1 1
1
Generator of the Alexander module
(0,1-5t-17t^2+13t^3-2t^4,3+3t-2t^2,0,1-2t-8t^2+4t^3,-3t-9t^2+9t^3-2t^4,3+3t-2t^2,0)
the Blanchfield form on it
-138t^-3+740t^-2-1623t^-1+2058-1623t+740t^2-138t^3
289
First homology
of the double branched cover of 12a_0458
Z/289
0 0
12a_0459
1

detected by
an unknotting move
3-21t+58t^2-79t^3+58t^4-21t^5+3t^6
Seifert matrix of 12a_0459
1 0 0 0 0 0
-1 -1 1 -1 -1 1
0 0 2 0 0 1
0 0 -1 1 0 -1
-1 0 0 -1 -1 1
0 0 1 0 0 2
1
Generator of the Alexander module
(0,-2+14t+12t^2-37t^3-72t^4+26t^5+160t^6-126t^7+18t^8,5+10t+4t^2-14t^3-18t^4+18t^5,-3-3t+9t^2+38t^3+2t^4-50t^5+18t^7,5+11t+22t^2-40t^3-132t^4-14t^5+138t^6+176t^7-216t^8+36t^9,5+13t+7t^2-18t^3-46t^4+20t^5+36t^6-18t^7)
the Blanchfield form on it
x
243
First homology
of the double branched cover of 12a_0459
Z/243
2 2
12a_0460
2

detected by
the Lickorish test
-2+17t-53t^2+77t^3-53t^4+17t^5-2t^6
Seifert matrix of 12a_0460
-1 0 0 -1 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 1 0 -2 0 0
1 0 0 1 1 -1
0 -1 1 1 0 -1
1
Generator of the Alexander module
(0,0,0,1,1-t,-1)
the Blanchfield form on it
-t^-1+3-t
221
First homology
of the double branched cover of 12a_0460
Z/221
0 0
12a_0461
2

detected by
the signature
-5+25t-53t^2+67t^3-53t^4+25t^5-5t^6
Seifert matrix of 12a_0461
1 0 0 0 0 0
0 -1 0 0 0 0
0 0 -1 0 -1 -1
1 0 0 -2 0 -1
1 -1 0 -1 -2 -1
1 0 0 -1 -1 -2
1 or 2
233
First homology
of the double branched cover of 12a_0461
Z/233
-4 4
12a_0462
1

detected by
an unknotting move
1-7t+19t^2-32t^3+39t^4-32t^5+19t^6-7t^7+t^8
Seifert matrix of 12a_0462
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
-1 -1 0 -1 1 0 -1 0
-1 -1 0 -1 1 1 -1 1
0 0 0 0 0 0 -1 0
-1 -1 0 -1 1 0 -1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+7t^-2-16t^-1+19-16t+7t^2-t^3
157
First homology
of the double branched cover of 12a_0462
Z/157
0 0
12a_0463
1

detected by
an unknotting move
2-12t+26t^2-31t^3+26t^4-12t^5+2t^6
Seifert matrix of 12a_0463
-1 -1 -1 -1 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 -1 -1 0 0
0 0 0 0 -1 0
1 1 0 1 1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-5t^-2+10t^-1-12+10t-5t^2+t^3
111
First homology
of the double branched cover of 12a_0463
Z/111
-2 2
12a_0464
2

detected by
the Lickorish test
1-7t+24t^2-49t^3+63t^4-49t^5+24t^6-7t^7+t^8
Seifert matrix of 12a_0464
-1 0 -1 -1 -1 0 0 -1
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 -1 0 0 -1
0 1 -1 0 -1 0 0 0
-1 0 0 -1 0 1 1 0
0 0 0 0 0 0 1 0
0 1 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,-3t+3t^2-t^3,-3+3t-t^2,0,6t^2-9t^3+5t^4-t^5,-1+11t-16t^2+9t^3-2t^4,-4+8t-5t^2+t^3,-3+3t-t^2)
the Blanchfield form on it
x
225
First homology
of the double branched cover of 12a_0464
Z/225
0 0
12a_0465
2

detected by
A(F_2)
1-8t+26t^2-52t^3+67t^4-52t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0465
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 0 0 1 0 0 -1 0
0 -1 -1 0 -1 0 0 0
-1 -1 0 1 -1 1 -1 1
0 0 0 0 0 0 -1 0
-1 0 0 1 0 0 -1 1
2
241
First homology
of the double branched cover of 12a_0465
Z/241
0 0
12a_0466
2

detected by
the signature
1-8t+26t^2-44t^3+51t^4-44t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0466
-1 0 -1 0 -1 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 0 0 1 0 0 1 0
0 1 -1 0 -1 0 0 0
-1 0 0 1 -1 1 1 1
0 0 0 0 0 0 1 0
-1 0 0 1 0 0 1 1
2
209
First homology
of the double branched cover of 12a_0466
Z/209
4 4
12a_0467
1

detected by
an unknotting move
-1+8t-29t^2+60t^3-75t^4+60t^5-29t^6+8t^7-t^8
Seifert matrix of 12a_0467
-1 0 -1 0 -1 0 0 -1
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 0 0 1 0 0 1 0
0 1 -1 0 -1 0 0 0
-1 0 0 1 0 1 1 -1
0 0 0 0 0 0 1 0
0 1 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,-3+t,1+6t-5t^2+t^3,3t-t^2,1-3t^2+t^3,3t-t^2,0)
the Blanchfield form on it
2t^-3-11t^-2+29t^-1-38+29t-11t^2+2t^3
271
First homology
of the double branched cover of 12a_0467
Z/271
2 2
12a_0468
1

detected by
an unknotting move
1-8t+23t^2-40t^3+47t^4-40t^5+23t^6-8t^7+t^8
Seifert matrix of 12a_0468
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 1 1 0 1 0
-1 -1 0 0 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 1 1 0 1 1
1
Generator of the Alexander module
(0,3t-14t^2+40t^3-63t^4+59t^5-32t^6+9t^7-t^8,-t-t^2+15t^3-35t^4+40t^5-25t^6+8t^7-t^8,-1-2t+13t^2-22t^3+18t^4-7t^5+t^6,-5+13t-9t^2-21t^3+59t^4-68t^5+44t^6-15t^7+2t^8,1+18t-65t^2+120t^3-136t^4+103t^5-53t^6+16t^7-2t^8,-1-2t+13t^2-22t^3+18t^4-7t^5+t^6,1+4t-8t^2-t^3+16t^4-17t^5+7t^6-t^7)
the Blanchfield form on it
x
191
First homology
of the double branched cover of 12a_0468
Z/191
2 2
12a_0469
1

detected by
an unknotting move
1-7t+24t^2-47t^3+59t^4-47t^5+24t^6-7t^7+t^8
Seifert matrix of 12a_0469
-1 0 0 0 0 0 0 0
0 1 0 0 1 0 -1 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 1 1 -1 0
0 0 0 0 1 0 0 0
0 1 0 0 1 1 -1 0
0 0 0 0 0 0 -1 0
0 -1 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,1,0,0,1,1,0,-t)
the Blanchfield form on it
-t^-3+7t^-2-17t^-1+23-17t+7t^2-t^3
217
First homology
of the double branched cover of 12a_0469
Z/217
0 0
12a_0470
1

detected by
an unknotting move
-1+8t-27t^2+54t^3-67t^4+54t^5-27t^6+8t^7-t^8
Seifert matrix of 12a_0470
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 -1 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 1 0 -1 0
0 1 0 0 1 0 -1 0
0 -1 0 -1 -1 -1 0 0
0 0 0 0 0 0 -1 0
0 -1 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,2-t,0,3-3t+t^2,0,0)
the Blanchfield form on it
-t^-3+6t^-2-14t^-1+19-14t+6t^2-t^3
247
First homology
of the double branched cover of 12a_0470
Z/247
-2 2
12a_0471
1

detected by
an unknotting move
4-21t+35t^2-21t^3+4t^4
Seifert matrix of 12a_0471
1 0 0 0
1 -2 0 0
0 0 -1 0
0 -1 1 2
1
Generator of the Alexander module
(0,0,1,-1)
the Blanchfield form on it
-2t^-1+5-2t
85
First homology
of the double branched cover of 12a_0471
Z/85
0 0
12a_0472
2

detected by
the signature
-3+22t-56t^2+75t^3-56t^4+22t^5-3t^6
Seifert matrix of 12a_0472
2 0 0 1 1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 -1 0 1 0 0
1 0 0 0 2 0
-1 -1 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-3t^-1+5-3t
237
First homology
of the double branched cover of 12a_0472
Z/237
4 4
12a_0473
1

detected by
an unknotting move
-1+8t-30t^2+64t^3-83t^4+64t^5-30t^6+8t^7-t^8
Seifert matrix of 12a_0473
-1 1 -1 0 -1 0 0 1
0 1 0 0 0 0 0 1
0 0 1 0 0 0 0 0
-1 1 -1 -1 -1 0 0 1
0 1 -1 0 -1 0 0 0
0 0 0 -1 0 1 -1 0
-1 0 -1 -1 -1 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,t,1,0)
the Blanchfield form on it
-t^-3+8t^-2-24t^-1+35-24t+8t^2-t^3
289
First homology
of the double branched cover of 12a_0473
Z/289
0 0
12a_0474
1

detected by
an unknotting move
-1+9t-32t^2+63t^3-77t^4+63t^5-32t^6+9t^7-t^8
Seifert matrix of 12a_0474
-1 1 -1 0 -1 0 0 1
0 1 0 1 0 0 0 1
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 1 -1 0 -1 0 0 0
0 0 0 0 0 1 -1 0
-1 1 -1 1 -1 0 -1 1
0 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,-t^2,1+2t,0,0,-t^2-4t^3+2t^4,-t-4t^2+2t^3,0)
the Blanchfield form on it
-t^-3+4t^-2-7t^-1+7-7t+4t^2-t^3
287
First homology
of the double branched cover of 12a_0474
Z/287
2 2
12a_0475
2

detected by
the Lickorish test
-1+8t-28t^2+56t^3-69t^4+56t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0475
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 -1 0 0 -1 -1 0 0
-1 0 -1 0 0 0 1 1
0 1 0 0 1 0 0 1
2
255
First homology
of the double branched cover of 12a_0475
Z/255
-2 2
12a_0476
2

detected by
the signature
1-7t+20t^2-33t^3+39t^4-33t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0476
1 0 0 0 0 0 1 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
1 -1 0 1 1 0 1 0
1 0 0 0 1 0 1 0
1 -1 0 1 1 1 1 0
0 0 0 0 0 0 1 0
-1 0 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,4t^2-4t^3+t^4,4t^2-4t^3+t^4,0,0,-1+2t-3t^2-3t^3+4t^4-t^5)
the Blanchfield form on it
161
First homology
of the double branched cover of 12a_0476
Z/161
4 4
12a_0477
1

detected by
an unknotting move
-1+11t-41t^2+63t^3-41t^4+11t^5-t^6
Seifert matrix of 12a_0477
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 -1 0 0
0 0 0 -1 0 0
0 0 0 1 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-2+13t^-1-23+13t-2t^2
169
First homology
of the double branched cover of 12a_0477
Z/169
0 0
12a_0478
2

detected by
the Lickorish test
-1+8t-25t^2+46t^3-55t^4+46t^5-25t^6+8t^7-t^8
Seifert matrix of 12a_0478
1 0 0 0 0 0 1 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
1 -1 0 1 1 0 1 0
1 0 0 0 1 0 1 0
-1 0 0 -1 -1 -1 0 0
0 0 0 0 0 0 1 0
-1 0 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(15t+49t^2+62t^3-42t^4-224t^5-152t^6+64t^7+96t^8+64t^9+32t^10,1+6t+10t^2-9t^3-46t^4-38t^5+36t^6+56t^7+16t^8,1+3t+4t^2-2t^3-12t^4-8t^5,-6t-21t^2-23t^3+26t^4+98t^5+48t^6-64t^7-48t^8,2t-t^2+2t^3+2t^4+8t^5-24t^7-16t^8,-6t-7t^2+t^3+38t^4+18t^5-52t^6-64t^7+8t^8+64t^9+32t^10,t+t^2+8t^3+10t^4+4t^5-16t^6-32t
the Blanchfield form on it
x
215
First homology
of the double branched cover of 12a_0478
Z/215
2 2
12a_0479
1

detected by
an unknotting move
1-8t+28t^2-56t^3+71t^4-56t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0479
-1 -1 -1 1 0 -1 -1 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 0 0 1 -1 0 1
0 -1 -1 1 0 -1 0 0
0 -1 -1 1 0 -1 -1 0
0 0 0 0 0 -1 0 1
1
Generator of the Alexander module
(-t-6t^2+18t^3-24t^4+27t^5-12t^6-5t^7+5t^8-t^9,-4t-24t^2+78t^3-62t^4-26t^5+42t^6-2t^7-8t^8+2t^9,-2-14t+24t^2-14t^3-13t^4+17t^5-4t^7+t^8,1+7t-14t^2-7t^3+31t^4-17t^5-4t^6+5t^7-t^8,4t-7t^2-20t^3+37t^4-11t^5-9t^6+6t^7-t^8,-t-8t^2+5t^3+6t^4-5t^5+t^6,-2t-15t^2+17t^3-4t^5+t^6,-3t^2-18t^3+54t^4-78t^5+36t^6+
the Blanchfield form on it
x
257
First homology
of the double branched cover of 12a_0479
Z/257
0 0
12a_0480
2

detected by
the Lickorish test
-1+8t-30t^2+64t^3-81t^4+64t^5-30t^6+8t^7-t^8
Seifert matrix of 12a_0480
-1 0 0 0 0 0 0 0
0 1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 -1 1 -1 0
0 0 0 0 -1 0 -1 0
0 1 0 0 -1 1 -1 0
0 0 0 0 0 0 -1 0
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1+2t-t^2,3+6t-3t^2,1+2t-t^2,0,0,-3+3t^2-t^3)
the Blanchfield form on it
-t^-3+5t^-2-13t^-1+17-13t+5t^2-t^3
287
First homology
of the double branched cover of 12a_0480
Z/287
-2 2
12a_0481
2

detected by
2-13t+28t^2-33t^3+28t^4-13t^5+2t^6
Seifert matrix of 12a_0481
-2 0 0 0 0 0
0 -1 -1 0 0 0
0 0 1 0 0 0
1 -1 0 1 0 0
1 -1 0 1 1 1
1 -1 0 1 0 1
2
119
First homology
of the double branched cover of 12a_0481
Z/119
2 2
12a_0482
1

detected by
an unknotting move
4-23t+39t^2-23t^3+4t^4
Seifert matrix of 12a_0482
-2 0 0 0
0 -1 -1 0
0 0 1 0
-1 1 0 2
1 or 2
93
First homology
of the double branched cover of 12a_0482
Z/93
0 0
12a_0483
1

detected by
an unknotting move
1-9t+35t^2-75t^3+95t^4-75t^5+35t^6-9t^7+t^8
Seifert matrix of 12a_0483
-1 1 -1 0 -1 0 0 1
0 1 0 0 0 0 0 1
0 0 1 0 0 0 0 0
0 0 0 1 0 0 -1 0
0 1 -1 0 -1 0 0 0
-1 0 0 1 0 1 -1 0
-1 0 -1 0 -1 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,5+6t-7t^2+2t^3+5t^4-34t^5+35t^6-14t^7+2t^8,-5-t+23t^2-57t^3+76t^4-50t^5+16t^6-2t^7,10t+2t^2-46t^3+114t^4-152t^5+100t^6-32t^7+4t^8,5t+t^2-23t^3+57t^4-76t^5+50t^6-16t^7+2t^8,6+11t-21t^2-29t^3+135t^4-247t^5+245t^6-131t^7+36t^8-4t^9,-5-t+13t^2-29t^3+18t^4+26t^5-34t^6+14t^7-2t^8,0)
the Blanchfield form on it
x
335
First homology
of the double branched cover of 12a_0483
Z/335
2 2
12a_0484
1

detected by
an unknotting move
1-9t+32t^2-63t^3+79t^4-63t^5+32t^6-9t^7+t^8
Seifert matrix of 12a_0484
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 1 0 0 1 1 0 0
-1 0 -1 0 0 1 1 1
0 0 0 0 1 1 0 1
1
Generator of the Alexander module
(0,0,t-t^2-3t^3+2t^4,1-t^2-3t^3+2t^4,1+t-2t^2,2+t+t^2-2t^3,-1+2t-6t^3+4t^4,0)
the Blanchfield form on it
t^-2-5t^-1+7-5t+t^2
289
First homology
of the double branched cover of 12a_0484
Z/289
0 0
12a_0485
1

detected by
an unknotting move
-1+8t-28t^2+56t^3-69t^4+56t^5-28t^6+8t^7-t^8
Seifert matrix of 12a_0485
-1 0 0 0 0 0 -1 -1
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 1 0 1 0
0 0 0 0 1 0 1 0
0 -1 0 1 1 1 1 0
0 0 0 0 0 0 1 0
0 0 0 -1 -1 0 -1 -1
1 or 2
255
First homology
of the double branched cover of 12a_0485
Z/255
2 2
12a_0486
2

detected by
the Lickorish test
1-9t+31t^2-59t^3+73t^4-59t^5+31t^6-9t^7+t^8
Seifert matrix of 12a_0486
-1 0 0 0 0 -1 -1 -1
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 1 1 0 1 0
0 0 0 0 1 0 1 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 0 0 1 0
0 0 0 0 -1 -1 -1 -1
1
Generator of the Alexander module
(2-t,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
273
First homology
of the double branched cover of 12a_0486
Z/273
0 2
12a_0487
1

detected by
an unknotting move
-1+8t-29t^2+58t^3-71t^4+58t^5-29t^6+8t^7-t^8
Seifert matrix of 12a_0487
-1 0 -1 -1 1 0 -1 0
0 1 0 0 0 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 1 -1 0 0 1 -1 1
0 0 -1 -1 1 0 -1 0
0 1 0 0 0 0 -1 1
1
Generator of the Alexander module
(-6t^3+7t^4+22t^5-72t^6+100t^7-79t^8+36t^9-9t^10+t^11,0,1+12t-8t^2-51t^3+122t^4-128t^5+58t^6+7t^7-18t^8+7t^9-t^10,6t-t^2-29t^3+50t^4-28t^5-21t^6+43t^7-27t^8+8t^9-t^10,-12t+8t^2+51t^3-122t^4+128t^5-58t^6-7t^7+18t^8-7t^9+t^10,0,6t^2-7t^3-22t^4+72t^5-100t^6+79t^7-36t^8+9t^9-t^10,-3t+2t^2+12t^3-30t^4+35
the Blanchfield form on it
x
263
First homology
of the double branched cover of 12a_0487
Z/263
2 2
12a_0488
2

detected by
the Lickorish test
-1+7t-22t^2+37t^3-41t^4+37t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0488
-1 -1 -1 -1 1 0 -1 -1
0 -1 -1 -1 1 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 -1 0 0 1 -1 0
0 0 -1 -1 1 0 -1 0
0 -1 -1 -1 1 0 -1 -1
1 or 2
175
First homology
of the double branched cover of 12a_0488
Z/175
-2 2
12a_0489
1

detected by
an unknotting move
3-20t+50t^2-65t^3+50t^4-20t^5+3t^6
Seifert matrix of 12a_0489
1 0 0 0 0 0
-1 -1 -1 1 -1 1
0 0 1 0 0 0
1 0 0 -2 0 -1
-1 0 -1 1 -1 1
1 0 1 -1 0 -2
1
Generator of the Alexander module
(0,2+4t-2t^2,0,-1-4t-3t^2+2t^3,3+6t-t^2-t^3,-4t-8t^2+4t^3)
the Blanchfield form on it
6t^-2-22t^-1+31-22t+6t^2
211
First homology
of the double branched cover of 12a_0489
Z/211
-2 2
12a_0490
3

detected by
the signature
7-25t+45t^2-53t^3+45t^4-25t^5+7t^6
Seifert matrix of 12a_0490
-1 1 -1 0 0 -1
0 -3 1 -1 0 1
0 1 -2 -1 0 -2
0 -1 0 -2 0 0
0 0 -1 -1 -1 -1
0 1 -1 -1 0 -2
1 or 2
207
First homology
of the double branched cover of 12a_0490
Z/207
-6 6
12a_0491
1

detected by
an unknotting move
-2+14t-42t^2+61t^3-42t^4+14t^5-2t^6
Seifert matrix of 12a_0491
-1 0 -1 0 0 -1
0 1 0 0 0 0
0 1 -2 0 0 -1
-1 0 0 1 -1 0
-1 0 -1 0 -1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1+4t-36t^2+84t^3-75t^4+30t^5-5t^6,3t^2+77t^3-263t^4+304t^5-165t^6+45t^7-5t^8,t+26t^2-79t^3+75t^4-30t^5+5t^6,-t-26t^2+79t^3-75t^4+30t^5-5t^6)
the Blanchfield form on it
x
177
First homology
of the double branched cover of 12a_0491
Z/177
0 0
12a_0492
1

detected by
an unknotting move
-2+15t-47t^2+69t^3-47t^4+15t^5-2t^6
Seifert matrix of 12a_0492
-1 -1 1 1 0 -1
0 1 0 0 0 0
0 0 1 0 0 0
0 1 0 -2 0 0
0 0 0 1 1 -1
0 -1 1 1 0 -1
1 or 2
197
First homology
of the double branched cover of 12a_0492
Z/197
0 0
12a_0493
2

detected by
the Nakanishi index
-1+7t-22t^2+36t^3-39t^4+36t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0493
-1 -1 -1 -1 1 0 -1 -1
0 -1 -1 -1 1 0 0 -1
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 -1 -1 0 0 1 -1 -1
0 -1 -1 -1 1 0 -1 -1
0 0 -1 -1 1 0 0 -1
2
171
First homology
of the double branched cover of 12a_0493
Z/57+Z/3
-2 2
12a_0494
2

detected by
-2+15t-48t^2+71t^3-48t^4+15t^5-2t^6
Seifert matrix of 12a_0494
-1 1 -1 -1 1 0
0 -2 1 1 -1 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 1 -1 0 0 1
2
201
First homology
of the double branched cover of 12a_0494
Z/201
0 0
12a_0495
2

detected by
the signature
2-11t+30t^2-50t^3+59t^4-50t^5+30t^6-11t^7+2t^8
Seifert matrix of 12a_0495
-1 0 -1 -1 0 -1 0 0
0 1 0 0 0 0 0 0
0 -1 -2 -2 0 -2 -1 0
0 0 -1 -2 0 -1 -1 0
0 -1 -1 -1 -1 -1 -1 0
0 -1 -1 -2 0 -2 -1 0
0 1 0 0 0 0 1 0
0 -1 -1 -1 -1 -1 -1 -1
1
Generator of the Alexander module
(t^2,0,-1-t,-1-t,0,-t,0,0)
the Blanchfield form on it
2t^-3-7t^-2+14t^-1-16+14t-7t^2+2t^3
245
First homology
of the double branched cover of 12a_0495
Z/245
-4 4
12a_0496
1

detected by
an unknotting move
-2+12t-32t^2+55t^3-65t^4+55t^5-32t^6+12t^7-2t^8
Seifert matrix of 12a_0496
-1 0 0 -1 0 0 0 0
0 1 0 0 0 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 1 -1 0 -1 1 -1 1
0 0 -1 -1 -1 0 -1 0
0 1 0 0 -1 0 -1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,-2)
the Blanchfield form on it
-2t^-2+4t^-1-5+4t-2t^2
267
First homology
of the double branched cover of 12a_0496
Z/267
-2 2
12a_0497
1

detected by
an unknotting move
1-7t+23t^2-45t^3+57t^4-45t^5+23t^6-7t^7+t^8
Seifert matrix of 12a_0497
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 -1 0
0 0 1 0 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 1 0 1
0 0 0 0 0 1 0 0
0 0 1 0 0 -1 -1 0
0 0 0 0 0 1 0 1
1
Generator of the Alexander module
(0,-t,-1,0,0,1,-t,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
209
First homology
of the double branched cover of 12a_0497
Z/209
0 0
12a_0498
1

detected by
an unknotting move
-1+7t-23t^2+45t^3-55t^4+45t^5-23t^6+7t^7-t^8
Seifert matrix of 12a_0498
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 -1 0
0 0 1 0 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 0 1
0 0 -1 0 0 -1 -1 0
0 0 0 0 0 0 -1 0
0 1 0 0 0 1 1 1
1
Generator of the Alexander module
(0,0,0,t,1+t,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-11t^-1+15-11t+5t^2-t^3
207
First homology
of the double branched cover of 12a_0498
Z/207
-2 2
12a_0499
1

detected by
an unknotting move
1-7t+25t^2-51t^3+65t^4-51t^5+25t^6-7t^7+t^8
Seifert matrix of 12a_0499
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 -1 0
0 0 1 0 0 0 -1 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 0 1
0 0 1 0 0 1 -1 0
0 0 0 0 0 0 -1 0
0 1 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,t,1+t,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+13t^-1-17+13t-5t^2+t^3
233
First homology
of the double branched cover of 12a_0499
Z/233
0 0
12a_0500
1

detected by
an unknotting move
-1+7t-21t^2+35t^3-39t^4+35t^5-21t^6+7t^7-t^8
Seifert matrix of 12a_0500
1 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 -1 0
-1 0 -1 0 0 0 -1 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 1
-1 0 -1 0 0 -1 -1 0
-1 0 0 -1 0 0 -1 -1
0 0 0 1 0 0 0 1
1
Generator of the Alexander module
(-2-t^3,-4-7t-t^2+6t^3+22t^4+4t^6,-2t,0,1+4t^2+11t^3+2t^5,-4-9t-2t^3,2+4t+t^3,1+4t^2+11t^3+2t^5)
the Blanchfield form on it
x
167
First homology
of the double branched cover of 12a_0500
Z/167
-2 2
12a_0501
1

detected by
an unknotting move
-1+7t-23t^2+43t^3-51t^4+43t^5-23t^6+7t^7-t^8
Seifert matrix of 12a_0501
1 0 0 0 0 0 0 0
-1 -1 0 0 0 -1 0 0
0 0 1 0 0 0 0 0
0 0 0 -1 -1 0 1 -1
0 0 0 0 -1 0 1 0
-1 0 -1 0 0 -1 -1 0
0 0 1 0 0 0 1 0
0 0 0 0 -1 0 1 -1
1
Generator of the Alexander module
(0,1-t-2t^2-3t^3+2t^4+4t^5-8t^6,-2-3t+2t^2+t^3-6t^4-4t^5+8t^6,t-3t^3-2t^4-8t^7,2+4t+3t^2+2t^3+4t^4+8t^5,-4t+t^2-4t^3-5t^4-2t^5+4t^6-8t^7,-2-5t-3t^2-2t^3-8t^4-8t^5,0)
the Blanchfield form on it
x
199
First homology
of the double branched cover of 12a_0501
Z/199
-2 2
12a_0502
3

detected by
the signature
-2+8t-13t^2+15t^3-15t^4+15t^5-13t^6+8t^7-2t^8
Seifert matrix of 12a_0502
1 0 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 -1 1
-1 0 -1 -1 0 0 -1 1
-1 0 0 -1 0 0 0 1
0 0 0 0 -1 0 0 -1
-1 0 -1 -1 0 -1 -1 1
-1 0 0 -1 0 0 -1 1
1 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-3t^-1+3-3t+3t^2-t^3
91
First homology
of the double branched cover of 12a_0502
Z/91
-6 6
12a_0503
2

detected by
the Nakanishi index
-1+7t-19t^2+27t^3-27t^4+27t^5-19t^6+7t^7-t^8
Seifert matrix of 12a_0503
1 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 -1 -1
-1 0 -1 0 0 0 -1 -1
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
-1 0 -1 0 0 -1 -1 -1
-1 0 0 -1 0 0 -1 -1
-1 0 0 0 -1 0 0 -1
2
135
First homology
of the double branched cover of 12a_0503
Z/45+Z/3
-2 2
12a_0504
2

detected by
the signature
-4+18t-34t^2+41t^3-34t^4+18t^5-4t^6
Seifert matrix of 12a_0504
1 0 0 0 0 0
-1 -1 1 -1 0 1
1 0 -2 1 0 -1
-1 0 0 -1 0 1
0 0 0 0 -1 -1
1 0 0 0 0 -2
1 or 2
153
First homology
of the double branched cover of 12a_0504
Z/153
-4 4
12a_0505
1

detected by
an unknotting move
-1+7t-21t^2+39t^3-47t^4+39t^5-21t^6+7t^7-t^8
Seifert matrix of 12a_0505
1 0 0 0 0 0 0 0
-1 -1 0 0 0 -1 0 -1
0 0 1 0 0 0 0 0
0 0 1 1 0 0 1 0
0 0 0 0 1 0 0 0
-1 0 -1 -1 0 -1 -1 -1
0 0 1 0 0 0 1 0
-1 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,3-3t+t^2,0,-2-2t-3t^2+8t^3-5t^4+t^5,0,3t+9t^2-17t^3+10t^4-2t^5,0,-6t+6t^2-2t^3)
the Blanchfield form on it
x
183
First homology
of the double branched cover of 12a_0505
Z/183
2 2
12a_0506
1

detected by
an unknotting move
1-7t+21t^2-39t^3+49t^4-39t^5+21t^6-7t^7+t^8
Seifert matrix of 12a_0506
-1 0 0 -1 -1 0 0 -1
0 1 0 0 0 0 0 -1
0 0 -1 0 0 -1 0 0
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 1 0 0 0 1 0 -1
0 1 0 0 0 1 1 -1
0 0 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-11t^-1+15-11t+5t^2-t^3
185
First homology
of the double branched cover of 12a_0506
Z/185
0 0
12a_0507
3

detected by
the signature
-2+8t-15t^2+21t^3-23t^4+21t^5-15t^6+8t^7-2t^8
Seifert matrix of 12a_0507
-1 0 0 -1 0 0 0 0
0 -1 0 -1 0 -1 -1 -1
0 0 1 0 0 0 0 0
0 0 0 -2 0 0 0 0
0 -1 0 -1 -1 -1 -1 -1
0 0 -1 -1 0 -1 -1 -1
0 0 -1 -1 0 0 -1 0
0 0 -1 -1 0 0 -1 -1
1
Generator of the Alexander module
(t+t^4,0,2+t^2+t^3+t^5,-4+t-2t^3+t^4,-t^2+t^3-t^5,2t^2-2t^3+2t^5,1-2t+t^3-t^4,4t^2-4t^3+4t^5)
the Blanchfield form on it
x
115
First homology
of the double branched cover of 12a_0507
Z/115
-6 6
12a_0508
2

detected by
the signature
-4+16t-28t^2+33t^3-28t^4+16t^5-4t^6
Seifert matrix of 12a_0508
-1 0 0 -1 0 0
0 -1 0 -1 0 1
0 0 1 0 0 0
0 0 0 -2 0 0
0 -1 0 -1 -1 1
0 0 1 1 0 -2
1
Generator of the Alexander module
(2t^2-t^3,0,2-t,0,-2+t-2t^2+t^3,1+2t-t^2)
the Blanchfield form on it
4t^-2-6t^-1+8-6t+4t^2
129
First homology
of the double branched cover of 12a_0508
Z/129
-4 4
12a_0509
1

detected by
an unknotting move
-2+10t-26t^2+45t^3-53t^4+45t^5-26t^6+10t^7-2t^8
Seifert matrix of 12a_0509
-1 0 0 -1 0 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 1 0 0
0 0 0 -2 0 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 1 0 0
0 0 -1 -1 0 0 -1 0
0 0 -1 -1 0 0 -1 -1
1
Generator of the Alexander module
(-t,0,-t^3,1,2+t^3,0,0,-t^2)
the Blanchfield form on it
-2t^-3+16t^-2-40t^-1+53-40t+16t^2-2t^3
219
First homology
of the double branched cover of 12a_0509
Z/219
-2 2
12a_0510
1

detected by
an unknotting move
-4+20t-44t^2+57t^3-44t^4+20t^5-4t^6
Seifert matrix of 12a_0510
-1 0 0 -1 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 -2 0 0
0 -1 0 -1 -1 1
0 -1 1 0 0 2
1 or 2
193
First homology
of the double branched cover of 12a_0510
Z/193
0 0
12a_0511
2

detected by
the signature
2-8t+17t^2-23t^3+25t^4-23t^5+17t^6-8t^7+2t^8
Seifert matrix of 12a_0511
-1 0 0 0 0 0 0 0
0 1 0 0 1 0 0 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 1 1 -1 0
0 0 0 0 1 0 0 0
0 1 0 0 1 1 0 0
0 -1 0 0 -1 -1 2 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-2t^-1+3-2t
125
First homology
of the double branched cover of 12a_0511
Z/125
4 4
12a_0512
1

detected by
an unknotting move
-1+7t-19t^2+31t^3-35t^4+31t^5-19t^6+7t^7-t^8
Seifert matrix of 12a_0512
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
0 0 1 0 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 1 1 0
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
0 0 -1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,t,1+t,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-7t^-1+7-7t+5t^2-t^3
151
First homology
of the double branched cover of 12a_0512
Z/151
2 2
12a_0513
1

detected by
an unknotting move
4-18t+40t^2-51t^3+40t^4-18t^5+4t^6
Seifert matrix of 12a_0513
-1 0 0 0 0 0
0 2 0 0 0 0
-1 0 -1 0 0 0
-1 -1 -1 1 -1 0
0 1 0 0 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-3-11t^-2+27t^-1-36+27t-11t^2+2t^3
175
First homology
of the double branched cover of 12a_0513
Z/175
2 2
12a_0514
2

detected by
the Lickorish test
4-19t+43t^2-55t^3+43t^4-19t^5+4t^6
Seifert matrix of 12a_0514
-1 0 0 0 0 0
0 2 0 0 0 -1
0 0 1 0 0 0
-1 0 0 -1 0 0
-1 -1 0 -1 1 1
0 -2 1 0 0 3
1
Generator of the Alexander module
(0,0,0,t,1+t,0)
the Blanchfield form on it
4t^-2-11t^-1+15-11t+4t^2
187
First homology
of the double branched cover of 12a_0514
Z/187
2 2
12a_0515
1

detected by
an unknotting move
1-7t+21t^2-37t^3+45t^4-37t^5+21t^6-7t^7+t^8
Seifert matrix of 12a_0515
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
0 0 -1 0 0 0 -1 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 1 1 1
0 0 0 0 0 1 0 0
0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 1
1
Generator of the Alexander module
(0,-t+5t^2-13t^3+16t^4-7t^5-t^6+t^7,-2t+3t^2-13t^3+16t^4-7t^5-t^6+t^7,1-t+5t^2-5t^3+t^4+t^5,2+10t^2+t^3-7t^4-2t^5+7t^6-t^7-t^8,-1-4t^2-2t^3+10t^4-7t^5+t^7,-1-4t^2-2t^3+10t^4-7t^5+t^7,-2+4t-13t^2+20t^3-5t^4-11t^5+8t^6-t^8)
the Blanchfield form on it
x
177
First homology
of the double branched cover of 12a_0515
Z/177
0 2
12a_0516
1

detected by
an unknotting move
-1+7t-23t^2+47t^3-59t^4+47t^5-23t^6+7t^7-t^8
Seifert matrix of 12a_0516
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
0 0 -1 0 0 0 -1 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 1 0 1
0 0 0 0 0 1 0 0
0 0 0 0 0 0 -1 0
0 0 1 0 0 1 1 1
1
Generator of the Alexander module
(1+t-28t^2+60t^3+61t^4-448t^5+606t^6+92t^7-1242t^8+1782t^9-1394t^10+698t^11-226t^12+44t^13-4t^14,2+6t-39t^2+51t^3+122t^4-392t^5+290t^6+302t^7-834t^8+836t^9-492t^10+182t^11-40t^12+4t^13,-2-7t+37t^2-31t^3-170t^4+410t^5-194t^6-492t^7+1008t^8-926t^9+520t^10-186t^11+40t^12-4t^13,1+t-19t^2+73t^3-128t^4+86
the Blanchfield form on it
x
215
First homology
of the double branched cover of 12a_0516
Z/215
-2 2
12a_0517
2

detected by
the signature
1-7t+19t^2-29t^3+33t^4-29t^5+19t^6-7t^7+t^8
Seifert matrix of 12a_0517
1 0 0 0 0 0 0 0
-1 -1 -1 0 -1 -1 0 0
-1 0 -1 0 0 -1 0 0
0 0 0 1 0 0 -1 0
-1 0 -1 0 -1 -1 0 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,5t+2t^2,0,0,-1-3t+4t^2+2t^3,0,2t+3t^2+t^3)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-9+9t-5t^2+t^3
145
First homology
of the double branched cover of 12a_0517
Z/145
-4 4
12a_0518
1

detected by
an unknotting move
-2+13t-37t^2+53t^3-37t^4+13t^5-2t^6
Seifert matrix of 12a_0518
1 0 0 0 0 0
-1 -1 0 -1 0 0
0 0 1 0 0 0
-1 0 -1 -1 -1 0
0 0 1 0 1 0
0 0 0 0 -1 -2
1 or 2
157
First homology
of the double branched cover of 12a_0518
Z/157
0 0
12a_0519
3

detected by
the signature
-2+8t-14t^2+20t^3-23t^4+20t^5-14t^6+8t^7-2t^8
Seifert matrix of 12a_0519
1 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 1
-1 0 -1 0 0 0 0 1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
-1 0 -1 0 0 -1 0 1
0 0 0 0 -1 0 -1 -1
1 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+8t^-2-13t^-1+15-13t+8t^2-2t^3
111
First homology
of the double branched cover of 12a_0519
Z/111
-6 6
12a_0520
2

detected by
the signature
-4+17t-29t^2+33t^3-29t^4+17t^5-4t^6
Seifert matrix of 12a_0520
1 0 0 0 0 0
-1 -1 -1 -1 0 1
-1 0 -1 0 0 1
-1 0 -1 -1 0 1
0 0 0 0 -2 0
1 0 0 0 -1 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-4t^-2+17t^-1-25+17t-4t^2
133
First homology
of the double branched cover of 12a_0520
Z/133
-4 4
12a_0521
2

detected by
the signature
1-7t+17t^2-21t^3+21t^4-21t^5+17t^6-7t^7+t^8
Seifert matrix of 12a_0521
1 0 0 0 0 0 0 0
-1 -1 -1 0 -1 -1 -1 0
-1 0 -1 0 -1 0 -1 0
0 0 0 -1 0 0 0 -1
-1 0 0 0 -1 0 0 0
-1 0 -1 0 -1 -1 -1 0
-1 0 0 0 -1 0 -1 -1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,3-t,0,0,1,0)
the Blanchfield form on it
-t^-3+3t^-2-3t^-1+3-3t+3t^2-t^3
113
First homology
of the double branched cover of 12a_0521
Z/113
-4 4
12a_0522
2

detected by
the signature
-4+19t-39t^2+49t^3-39t^4+19t^5-4t^6
Seifert matrix of 12a_0522
1 0 0 0 0 0
-1 -1 1 0 -1 -1
1 0 -2 0 1 2
0 0 0 -1 0 -1
-1 0 0 0 -1 0
-1 0 1 0 -1 -3
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+7t^-1-9+7t-2t^2
173
First homology
of the double branched cover of 12a_0522
Z/173
-4 4
12a_0523
1

detected by
an unknotting move
2-10t+26t^2-43t^3+51t^4-43t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_0523
-1 0 0 -1 0 0 0 0
0 1 0 0 0 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 1 0 0 1 0 -1 0
0 1 -1 0 1 1 -1 1
0 0 -1 -1 0 0 -1 0
0 1 -1 0 1 0 -1 1
1
Generator of the Alexander module
(-1+2t,0,0,0,1,0,1,0)
the Blanchfield form on it
2t^-3-7t^-2+14t^-1-16+14t-7t^2+2t^3
213
First homology
of the double branched cover of 12a_0523
Z/213
0 2
12a_0524
1

detected by
an unknotting move
2-15t+41t^2-55t^3+41t^4-15t^5+2t^6
Seifert matrix of 12a_0524
-1 1 -1 -1 0 0
0 -2 1 1 0 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 0 -1 0 1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(13-20t+20t^2-20t^3+8t^4,0,6-4t,12t^2-8t^3,12-8t-12t^2+8t^3,0)
the Blanchfield form on it
-2t^-2+11t^-1-15+11t-2t^2
171
First homology
of the double branched cover of 12a_0524
Z/171
-2 2
12a_0525
1

detected by
an unknotting move
-2+13t-33t^2+45t^3-33t^4+13t^5-2t^6
Seifert matrix of 12a_0525
1 0 0 0 0 0
-1 -1 0 -1 -1 0
0 0 1 0 0 0
-1 0 -1 -1 -1 0
-1 0 0 0 -1 1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,1,1,t,t,1)
the Blanchfield form on it
-2t^-2+9t^-1-15+9t-2t^2
141
First homology
of the double branched cover of 12a_0525
Z/141
0 0
12a_0526
1

detected by
an unknotting move
-2+10t-25t^2+43t^3-51t^4+43t^5-25t^6+10t^7-2t^8
Seifert matrix of 12a_0526
-1 0 0 -1 0 0 0 0
0 1 0 0 0 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 1 0 0
0 0 -1 -1 0 -1 -1 -1
0 1 0 0 0 1 0 1
1
Generator of the Alexander module
(t^2-2t^3+t^5,0,-2+5t-4t^2-2t^3+7t^4+t^5,-1+5t-t^2-3t^3+3t^4+7t^5+5t^6,1-2t-3t^2+5t^3-2t^4-4t^5-7t^6-5t^7,-3+6t-2t^2-3t^3+2t^4+2t^5+5t^6,2t-6t^2+4t^3-t^4-2t^5-2t^6-5t^7,-2+6t-4t^2+t^3+2t^4+2t^5+5t^6)
the Blanchfield form on it
x
211
First homology
of the double branched cover of 12a_0526
Z/211
-2 2
12a_0527
2

detected by
the signature
2-10t+25t^2-39t^3+45t^4-39t^5+25t^6-10t^7+2t^8
Seifert matrix of 12a_0527
-1 0 0 -1 0 0 0 0
0 1 0 0 0 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 0 -1 -1 -1 0 0 -1
0 1 0 0 -1 1 -1 -1
0 0 -1 -1 -1 0 -1 -1
0 0 -1 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,-1,0,0,1,0,0)
the Blanchfield form on it
2t^-3-8t^-2+17t^-1-21+17t-8t^2+2t^3
197
First homology
of the double branched cover of 12a_0527
Z/197
-4 4
12a_0528
1

detected by
an unknotting move
-1+7t-21t^2+39t^3-47t^4+39t^5-21t^6+7t^7-t^8
Seifert matrix of 12a_0528
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 1 0 0 1
0 0 0 0 1 0 0 0
0 -1 0 0 0 1 1 0
0 0 0 0 0 0 1 0
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+3t^-1-5+3t-t^2
183
First homology
of the double branched cover of 12a_0528
Z/183
2 2
12a_0529
1

detected by
an unknotting move
-2+15t-45t^2+65t^3-45t^4+15t^5-2t^6
Seifert matrix of 12a_0529
1 0 0 0 0 0
-1 -1 0 -1 0 0
0 0 -1 0 0 1
-1 0 0 -1 1 -1
0 0 0 0 2 0
0 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,-5t+4t^2-t^3,-1,0,-5+4t-t^2)
the Blanchfield form on it
4t^-2-20t^-1+37-20t+4t^2
189
First homology
of the double branched cover of 12a_0529
Z/189
0 0
12a_0530
1

detected by
an unknotting move
-3+19t-51t^2+71t^3-51t^4+19t^5-3t^6
Seifert matrix of 12a_0530
1 0 0 0 0 0
-1 -1 1 0 1 0
1 0 -2 0 -1 -1
0 0 0 1 0 0
1 0 -1 -1 -2 -1
0 0 0 1 0 1
1
Generator of the Alexander module
(0,t,1+3t^3,0,t^2+2t^5,0)
the Blanchfield form on it
-2t^-8+12t^-7-26t^-6-2t^-5+112t^-4-182t^-3+3t^-2+393t^-1-616+393t+3t^2-182t^3+112t^4-2t^5-26t^6+12t^7-2t^8
217
First homology
of the double branched cover of 12a_0530
Z/217
0 0
12a_0531
1

detected by
an unknotting move
-2+8t-18t^2+30t^3-35t^4+30t^5-18t^6+8t^7-2t^8
Seifert matrix of 12a_0531
-1 0 0 -1 0 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 1 0
0 0 0 -2 0 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -1 0 -1 -1 0
0 1 0 0 0 0 1 0
0 -1 -1 -1 0 -1 -1 -1
1
Generator of the Alexander module
(3-2t,0,0,0,0,0,0,-1+t)
the Blanchfield form on it
-6t^-3+16t^-2-27t^-1+39-27t+16t^2-6t^3
151
First homology
of the double branched cover of 12a_0531
Z/151
-2 2
12a_0532
1

detected by
an unknotting move
-4+15t-27t^2+33t^3-27t^4+15t^5-4t^6
Seifert matrix of 12a_0532
-1 0 0 -1 0 0
0 1 0 0 0 0
0 1 1 0 1 0
0 0 0 -2 0 0
0 1 0 0 1 0
0 1 1 1 1 -2
1
Generator of the Alexander module
(1,0,1,0,0,3)
the Blanchfield form on it
4t^-2-9t^-1+13-9t+4t^2
125
First homology
of the double branched cover of 12a_0532
Z/125
0 2
12a_0533
2

detected by
the signature
2-8t+18t^2-26t^3+29t^4-26t^5+18t^6-8t^7+2t^8
Seifert matrix of 12a_0533
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 1 -1 0 0
0 0 0 0 1 0 0 0
0 1 0 0 -1 2 1 1
0 0 0 0 0 0 1 0
0 1 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
137
First homology
of the double branched cover of 12a_0533
Z/137
4 4
12a_0534
1

detected by
an unknotting move
4-17t+37t^2-47t^3+37t^4-17t^5+4t^6
Seifert matrix of 12a_0534
-1 0 0 0 0 0
0 2 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 1 1 -1
0 0 0 0 1 0
0 -1 0 0 -1 2
1
Generator of the Alexander module
(0,0,t,1+t,0,0)
the Blanchfield form on it
4t^-2-9t^-1+11-9t+4t^2
163
First homology
of the double branched cover of 12a_0534
Z/163
2 2
12a_0535
1

detected by
an unknotting move
-1+7t-21t^2+37t^3-43t^4+37t^5-21t^6+7t^7-t^8
Seifert matrix of 12a_0535
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 1 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 1 0 0
0 0 0 0 0 1 0 0
0 1 0 0 0 0 1 0
0 -1 -1 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,2-t^2,2-2t^2,0,0,1+t)
the Blanchfield form on it
-t^-3+5t^-2-9t^-1+11-9t+5t^2-t^3
175
First homology
of the double branched cover of 12a_0535
Z/175
2 2
12a_0536
2

detected by
the signature
1-7t+19t^2-27t^3+29t^4-27t^5+19t^6-7t^7+t^8
Seifert matrix of 12a_0536
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 0 0 0
0 0 -1 0 0 -1 0 -1
0 0 0 1 0 -1 0 0
-1 0 0 -1 -1 0 0 0
0 0 0 0 0 -1 0 0
0 0 -1 0 0 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,2t^2+t^3,-2-2t,1+t,0,0,0)
the Blanchfield form on it
t^-3-7t^-2+19t^-1-25+19t-7t^2+t^3
137
First homology
of the double branched cover of 12a_0536
Z/137
-4 4
12a_0537
1

detected by
an unknotting move
2-15t+43t^2-59t^3+43t^4-15t^5+2t^6
Seifert matrix of 12a_0537
1 0 0 0 0 0
-1 -1 0 0 -1 0
0 0 -2 0 0 1
0 0 0 1 0 -1
-1 0 0 -1 -1 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,4-4t+t^2,0)
the Blanchfield form on it
1
179
First homology
of the double branched cover of 12a_0537
Z/179
-2 2
12a_0538
3

detected by
the signature
2-8t+12t^2-13t^3+13t^4-13t^5+12t^6-8t^7+2t^8
Seifert matrix of 12a_0538
1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 1
0 0 -1 -1 -1 -1 -1 -1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 0 0 -1 -1 -1 -1 -1
0 0 0 0 -1 0 -1 -1
1 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
2t^-3-8t^-2+12t^-1-13+12t-8t^2+2t^3
83
First homology
of the double branched cover of 12a_0538
Z/83
-6 6
12a_0539
2

detected by
the signature
-4+18t-32t^2+37t^3-32t^4+18t^5-4t^6
Seifert matrix of 12a_0539
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 -1 1 -1 -1
0 0 0 -2 1 1
0 0 0 0 -1 -1
1 0 0 0 0 -2
1 or 2
145
First homology
of the double branched cover of 12a_0539
Z/145
-4 4
12a_0540
2

detected by
the signature
-4+19t-37t^2+45t^3-37t^4+19t^5-4t^6
Seifert matrix of 12a_0540
1 0 0 0 0 0
-1 -1 0 0 0 1
0 0 -1 -1 0 0
0 0 0 -2 0 0
0 0 -1 -1 -1 0
1 0 0 -1 0 -2
1 or 2
165
First homology
of the double branched cover of 12a_0540
Z/165
-4 4
12a_0541
2

detected by
the signature
1-7t+19t^2-31t^3+37t^4-31t^5+19t^6-7t^7+t^8
Seifert matrix of 12a_0541
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 -1 0 0
0 0 -1 -1 0 0 -1 -1
0 0 0 -1 0 0 0 -1
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 0 -1
0 0 0 -1 0 0 -1 -1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1+3t,0,-1+6t,9,0,0)
the Blanchfield form on it
2t^-3-8t^-2+14t^-1-17+14t-8t^2+2t^3
153
First homology
of the double branched cover of 12a_0541
Z/153
-4 4
12a_0542
2

detected by
the Lickorish test
-7+31t-47t^2+31t^3-7t^4
Seifert matrix of 12a_0542
1 0 0 0
-1 -1 -1 -1
-1 0 -3 -1
-1 0 -2 -3
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
3t^-2-14t^-1+22-14t+3t^2
123
First homology
of the double branched cover of 12a_0542
Z/123
-2 2
12a_0543
1

detected by
an unknotting move
3-21t+57t^2-77t^3+57t^4-21t^5+3t^6
Seifert matrix of 12a_0543
1 0 0 0 0 0
-1 -1 1 1 1 0
1 0 -2 -1 -1 -1
1 0 -1 -2 -1 -1
1 0 -1 -2 -2 0
0 0 0 0 0 1
1
Generator of the Alexander module
(5+16t-116t^2+309t^3+40t^4-278t^5+2684t^6+1646t^7+204t^8,-3+t+23t^2-96t^3-43t^4+251t^5+42t^6,-5-10t+100t^2-327t^3+53t^4+366t^5-2672t^6-1646t^7-204t^8,-5-23t+129t^2-264t^3-450t^4+715t^5-2671t^6-6328t^7-2769t^8-306t^9,4+27t-131t^2+217t^3+490t^4-563t^5+2695t^6+6328t^7+2769t^8+306t^9,-3-6t+57t^2-178t^3+
the Blanchfield form on it
x
239
First homology
of the double branched cover of 12a_0543
Z/239
-2 2
12a_0544
1

detected by
an unknotting move
2-8t+19t^2-31t^3+37t^4-31t^5+19t^6-8t^7+2t^8
Seifert matrix of 12a_0544
-1 0 0 -1 0 0 0 0
0 1 0 0 1 0 1 -1
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 0 0 0 1 0 1 0
0 1 0 0 1 1 1 -1
0 0 0 0 0 0 1 0
0 0 -1 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,-1-2t-2t^2-2t^3-t^4-3t^5+t^6-t^7,1+t+t^2+t^4,0,1+t+t^2+t^3+t^4+2t^5-t^6+t^7,0,1+2t^2+t^3+4t^4-t^5+4t^6-t^7+t^8)
the Blanchfield form on it
x
157
First homology
of the double branched cover of 12a_0544
Z/157
0 0
12a_0545
1

detected by
an unknotting move
4-16t+32t^2-39t^3+32t^4-16t^5+4t^6
Seifert matrix of 12a_0545
-1 0 -1 0 0 0
0 -1 -1 0 0 0
0 0 -2 0 0 0
0 0 0 2 1 1
0 0 0 0 1 0
0 -1 -1 0 0 -1
1 or 2
143
First homology
of the double branched cover of 12a_0545
Z/143
-2 2
12a_0546
2

detected by
the Lickorish test
3-21t+55t^2-73t^3+55t^4-21t^5+3t^6
Seifert matrix of 12a_0546
1 0 0 0 0 0
-1 -1 1 0 1 0
1 0 -2 -1 -1 -1
0 0 0 -1 0 -1
1 0 -1 -1 -2 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,-3t+t^2,-1+9t+6t^2,0,4t-2t^2,-3-2t)
the Blanchfield form on it
14t^-5-175t^-4+516t^-3-107t^-2-1662t^-1+2828-1662t-107t^2+516t^3-175t^4+14t^5
231
First homology
of the double branched cover of 12a_0546
Z/231
-2 2
12a_0547
2

detected by
the signature
-5+25t-53t^2+67t^3-53t^4+25t^5-5t^6
Seifert matrix of 12a_0547
1 0 0 0 0 0
-1 -1 1 0 1 1
1 0 -2 -1 -1 -1
0 0 0 -1 0 0
1 0 -1 -1 -2 -1
1 0 0 0 -1 -2
1 or 2
233
First homology
of the double branched cover of 12a_0547
Z/233
-4 4
12a_0548
2

detected by
the signature
-4+14t-23t^2+27t^3-23t^4+14t^5-4t^6
Seifert matrix of 12a_0548
-1 -1 0 0 0 0
0 -2 0 0 0 0
0 -1 -1 -1 1 -1
0 -1 0 -1 1 0
0 0 0 0 2 0
0 -1 0 -1 1 -1
1 or 2
109
First homology
of the double branched cover of 12a_0548
Z/109
-4 4
12a_0549
2

detected by
the Lickorish test
-8+28t-39t^2+28t^3-8t^4
Seifert matrix of 12a_0549
-1 -1 0 0
0 -2 0 0
0 0 2 0
0 1 -1 -2
1 or 2
111
First homology
of the double branched cover of 12a_0549
Z/111
-2 2
12a_0550
1

detected by
an unknotting move
-2+13t-35t^2+49t^3-35t^4+13t^5-2t^6
Seifert matrix of 12a_0550
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 1 0 0
0 0 0 1 0 0
0 0 0 0 2 0
0 0 0 -1 1 -1
1
Generator of the Alexander module
(0,2-t^2,2-2t^2,0,0,1+t)
the Blanchfield form on it
-2t^-2+9t^-1-13+9t-2t^2
149
First homology
of the double branched cover of 12a_0550
Z/149
0 0
12a_0551
1

detected by
an unknotting move
-6+26t-39t^2+26t^3-6t^4
Seifert matrix of 12a_0551
1 0 0 0
-1 -1 0 1
0 0 -3 0
1 0 1 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
1
103
First homology
of the double branched cover of 12a_0551
Z/103
-2 2
12a_0552
1

detected by
an unknotting move
2-13t+31t^2-39t^3+31t^4-13t^5+2t^6
Seifert matrix of 12a_0552
1 0 0 0 0 0
-1 -1 -1 -1 0 0
-1 0 -1 0 0 0
-1 0 -1 -1 0 -1
0 0 0 0 -2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,-12+51t+234t^2-217t^3+556t^4-192t^5-32t^6+12t^7,27+72t-48t^2+177t^3-66t^4-10t^5+4t^6,-24-75t+54t^2-179t^3+66t^4+10t^5-4t^6,13-9t+113t^2-86t^3+202t^4-102t^5+86t^6-74t^7+28t^8-4t^9,-12t-42t^2+51t^3+191t^4-243t^5+601t^6-208t^7-30t^8+12t^9)
the Blanchfield form on it
x
131
First homology
of the double branched cover of 12a_0552
Z/131
-2 2
12a_0553
2

detected by
the signature
2-10t+26t^2-41t^3+47t^4-41t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_0553
-1 0 0 -1 0 0 0 0
0 -1 -1 -1 -1 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 -1 -1 0 -1 1 -1 1
0 -1 -1 -1 -1 0 -1 0
0 -1 0 0 0 0 -1 1
1
Generator of the Alexander module
(t+t^2-2t^3,-t^2+t^3+10t^4+14t^5-24t^6-4t^7+8t^8,1+4t+7t^2-12t^3-2t^4+4t^5,16t-16t^2-23t^3+29t^4+4t^5-4t^6,4t-11t^2-t^3+10t^4,5t-14t^2+14t^3-8t^4+8t^5-t^6-9t^7+4t^8+4t^9,t+t^2+5t^3-4t^4-4t^5,-1-7t^2+11t^3-4t^5)
the Blanchfield form on it
x
205
First homology
of the double branched cover of 12a_0553
Z/205
-4 4
12a_0554
3

detected by
the Nakanishi index
-2+15t-45t^2+65t^3-45t^4+15t^5-2t^6
Seifert matrix of 12a_0554
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
1 0 0 -2 1 1
-1 -1 0 0 -1 -1
-1 0 -1 0 0 -1
3
189
First homology
of the double branched cover of 12a_0554
Z/21+Z/3+Z/3
0 0
12a_0555
1

detected by
an unknotting move
-3+18t-45t^2+61t^3-45t^4+18t^5-3t^6
Seifert matrix of 12a_0555
-1 -1 0 0 -1 0
0 -2 0 0 -1 0
0 1 1 0 1 1
0 0 0 1 -1 0
0 -1 0 0 -2 0
0 0 0 0 1 1
1
Generator of the Alexander module
(t,0,-t,0,0,1)
the Blanchfield form on it
3t^-2-14t^-1+22-14t+3t^2
193
First homology
of the double branched cover of 12a_0555
Z/193
0 0
12a_0556
2

detected by
the signature
-4+17t-32t^2+39t^3-32t^4+17t^5-4t^6
Seifert matrix of 12a_0556
-1 0 -1 0 0 0
0 -2 0 0 -1 0
0 -1 -2 0 -1 0
0 -1 -1 -1 0 0
0 0 0 0 1 0
0 -1 -1 -1 0 -1
1 or 2
145
First homology
of the double branched cover of 12a_0556
Z/145
-4 4
12a_0557
1

detected by
an unknotting move
-7+27t-39t^2+27t^3-7t^4
Seifert matrix of 12a_0557
-1 1 0 1
0 -3 0 -2
0 0 1 0
0 -1 -1 -3
1
Generator of the Alexander module
(-3t+50t^2-32t^3,-3t-16t^2+12t^3,3-2t,5+8t-68t^2+40t^3)
the Blanchfield form on it
540t^-5-1428t^-4-15863t^-3+98132t^-2-240418t^-1+318074-240418t+98132t^2-15863t^3-1428t^4+540t^5
107
First homology
of the double branched cover of 12a_0557
Z/107
-2 2
12a_0558
2

detected by
the signature
2-11t+29t^2-47t^3+55t^4-47t^5+29t^6-11t^7+2t^8
Seifert matrix of 12a_0558
-1 0 -1 -1 0 0 -1 -1
0 1 0 0 0 0 0 0
0 0 -2 -1 -1 0 -1 -2
0 -1 -2 -2 -1 0 -2 -2
0 1 0 0 1 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 0 -2 -1 -1 0 -2 -2
0 0 -1 -1 -1 0 -1 -2
1 or 2
233
First homology
of the double branched cover of 12a_0558
Z/233
-4 4
12a_0559
1

detected by
an unknotting move
4-21t+49t^2-63t^3+49t^4-21t^5+4t^6
Seifert matrix of 12a_0559
-1 0 1 -1 0 0
0 1 0 0 0 0
0 0 -3 1 1 0
0 -1 2 -2 -1 0
0 1 0 0 1 0
0 -1 1 -1 -1 -1
1 or 2
211
First homology
of the double branched cover of 12a_0559
Z/211
-2 2
12a_0560
1

detected by
an unknotting move
-2+15t-41t^2+57t^3-41t^4+15t^5-2t^6
Seifert matrix of 12a_0560
-1 0 0 0 0 0
0 2 0 0 1 0
0 0 1 0 0 0
-1 0 0 -1 0 0
-1 0 0 -1 1 0
0 -1 1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,1)
the Blanchfield form on it
-2t^-2+7t^-1-11+7t-2t^2
173
First homology
of the double branched cover of 12a_0560
Z/173
0 0
12a_0561
3

detected by
the new u==2 criterion
1-7t+25t^2-49t^3+61t^4-49t^5+25t^6-7t^7+t^8
Seifert matrix of 12a_0561
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 -1 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 1
0 0 0 0 -1 0 0 0
0 0 0 0 -1 -1 0 0
0 0 0 0 0 0 -1 0
0 1 0 0 -1 0 1 1
2
225
First homology
of the double branched cover of 12a_0561
Z/45+Z/5
-4 4
12a_0562
2

detected by
the Lickorish test
2-15t+41t^2-55t^3+41t^4-15t^5+2t^6
Seifert matrix of 12a_0562
1 0 0 0 0 0
0 1 0 0 -1 0
1 0 -2 1 0 0
-1 -1 0 -1 0 0
0 0 0 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1-16t^2+8t^3,8t^2,0,0)
the Blanchfield form on it
2t^-2-9t^-1+13-9t+2t^2
171
First homology
of the double branched cover of 12a_0562
Z/171
-2 2
12a_0563
3

detected by
the new u==2 criterion
-4+16t-25t^2+27t^3-25t^4+16t^5-4t^6
Seifert matrix of 12a_0563
1 0 0 0 0 0
0 -1 -1 0 -1 -1
0 0 -1 0 0 -1
1 0 0 -2 0 -1
0 0 -1 0 -1 -1
1 0 0 0 0 -2
2
117
First homology
of the double branched cover of 12a_0563
Z/39+Z/3
-4 4
12a_0564
2

detected by
the Lickorish test
-8+34t-51t^2+34t^3-8t^4
Seifert matrix of 12a_0564
1 0 0 0
1 -2 0 -1
0 0 -2 0
1 0 -1 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
4t^-2-17t^-1+26-17t+4t^2
135
First homology
of the double branched cover of 12a_0564
Z/135
-2 2
12a_0565
2

detected by
the signature
1-7t+23t^2-41t^3+49t^4-41t^5+23t^6-7t^7+t^8
Seifert matrix of 12a_0565
-1 0 0 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1
0 0 0 1 0 0 0 0
-1 0 0 0 1 1 0 0
0 0 0 0 0 1 0 0
0 1 1 -1 0 0 -1 1
0 1 0 0 0 0 0 1
1 or 2
193
First homology
of the double branched cover of 12a_0565
Z/193
4 4
12a_0566
2

detected by
the Lickorish test
2-13t+37t^2-51t^3+37t^4-13t^5+2t^6
Seifert matrix of 12a_0566
-1 -1 0 0 -1 0
0 1 0 0 0 0
-1 0 1 1 0 0
0 0 0 1 0 0
0 -1 0 0 -1 -1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,0,1,1,0,0)
the Blanchfield form on it
-2t^-2+9t^-1-15+9t-2t^2
155
First homology
of the double branched cover of 12a_0566
Z/155
2 2
12a_0567
1

detected by
an unknotting move
2-12t+31t^2-50t^3+59t^4-50t^5+31t^6-12t^7+2t^8
Seifert matrix of 12a_0567
-1 0 0 -1 0 0 0 -1
0 1 0 0 0 0 0 0
0 1 1 0 0 0 1 0
0 0 -1 -2 -1 0 0 -2
0 1 1 0 1 0 1 0
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 1 0
0 0 0 -1 -1 0 0 -2
1
Generator of the Alexander module
(-4t+11t^2-17t^3-27t^4-22t^5,7-10t-6t^2-26t^3+34t^4+4t^5,-3+7t+20t^2-73t^3+34t^4-98t^5+128t^6+8t^7,-4+8t-15t^2+10t^3+20t^4,-19t+27t^2+7t^3+31t^4-100t^5-12t^6,14t^2+83t^3+27t^4+22t^5,-3+6t+25t^2-59t^3+34t^4-98t^5+128t^6+8t^7,-7+12t-7t^2-8t^3-34t^4-4t^5)
the Blanchfield form on it
x
249
First homology
of the double branched cover of 12a_0567
Z/249
0 2
12a_0568
2

detected by
the signature
-4+18t-35t^2+43t^3-35t^4+18t^5-4t^6
Seifert matrix of 12a_0568
1 0 0 0 0 0
0 -1 0 0 -1 0
0 0 -1 0 0 -1
1 -1 0 -2 -1 -1
0 0 0 0 -1 0
1 0 0 0 0 -2
1
Generator of the Alexander module
(0,t^2,0,1+t+t^2,-t,0)
the Blanchfield form on it
-4t^-2+16t^-1-23+16t-4t^2
157
First homology
of the double branched cover of 12a_0568
Z/157
-4 4
12a_0569
3

detected by
the new u==2 criterion
1-7t+21t^2-31t^3+33t^4-31t^5+21t^6-7t^7+t^8
Seifert matrix of 12a_0569
1 0 0 0 0 1 0 0
0 -1 0 -1 0 0 0 -1
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
1 -1 0 0 1 1 1 0
0 0 0 0 0 1 0 0
1 0 0 0 0 1 1 0
0 0 1 -1 0 0 0 -1
2
153
First homology
of the double branched cover of 12a_0569
Z/51+Z/3
4 4
12a_0570
2

detected by
the Lickorish test
2-15t+47t^2-67t^3+47t^4-15t^5+2t^6
Seifert matrix of 12a_0570
2 0 0 0 0 0
0 -1 0 -1 0 -1
0 0 1 0 0 0
0 0 0 1 0 0
-1 -1 0 0 1 0
0 0 1 -1 0 -1
1 or 2
195
First homology
of the double branched cover of 12a_0570
Z/195
2 2
12a_0571
1

detected by
an unknotting move
-2+12t-33t^2+58t^3-69t^4+58t^5-33t^6+12t^7-2t^8
Seifert matrix of 12a_0571
-1 0 -1 -1 0 0 0 -1
0 1 0 0 0 0 0 0
0 0 -2 -1 -1 0 0 -2
0 0 -2 -2 -1 0 -1 -2
0 1 0 0 1 0 1 0
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 1 0
0 0 -1 -1 -1 0 0 -2
1
Generator of the Alexander module
(-15t+36t^2-34t^3+14t^4-2t^5,0,3-14t+22t^2-12t^3+2t^4,7-20t+24t^2-12t^3+2t^4,-4+6t-2t^2,8-12t+4t^2,0,7-24t+30t^2-14t^3+2t^4)
the Blanchfield form on it
x
279
First homology
of the double branched cover of 12a_0571
Z/279
-2 2
12a_0572
1

detected by
an unknotting move
-2+9t-21t^2+35t^3-41t^4+35t^5-21t^6+9t^7-2t^8
Seifert matrix of 12a_0572
-1 0 0 -1 0 0 0 0
0 -1 0 -1 0 0 -1 0
0 0 1 0 0 0 0 0
0 0 0 -2 -1 0 0 -1
0 0 1 0 1 0 0 1
0 -1 0 -1 0 -1 -1 0
0 0 -1 -1 -1 0 -1 -1
0 0 1 0 0 0 0 1
1
Generator of the Alexander module
(6t^3-13t^4+16t^5-11t^6+5t^7-t^8,0,0,1-2t+7t^2-8t^3-t^4+9t^5-9t^6+5t^7-t^8,t+4t^2-5t^4+4t^5+3t^6-5t^7+4t^8-t^9,-2t-5t^3+5t^5-4t^6-3t^7+5t^8-4t^9+t^10,-t+8t^2-20t^3+24t^4-10t^5-4t^6+8t^7-5t^8+t^9,0)
the Blanchfield form on it
x
175
First homology
of the double branched cover of 12a_0572
Z/175
-2 2
12a_0573
1

detected by
an unknotting move
-2+9t-19t^2+27t^3-29t^4+27t^5-19t^6+9t^7-2t^8
Seifert matrix of 12a_0573
-1 0 0 -1 0 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 1 0
0 0 0 -2 -1 0 0 -1
0 1 1 0 1 0 1 1
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 1 0
0 1 1 0 0 0 1 1
1
Generator of the Alexander module
(-2t^2+2t^4-2t^5,0,0,2t-2t^3+2t^4,0,1-t,1-t^2+t^3,0)
the Blanchfield form on it
143
First homology
of the double branched cover of 12a_0573
Z/143
2 2
12a_0574
4

detected by
the signature
3-9t+16t^2-20t^3+21t^4-20t^5+16t^6-9t^7+3t^8
Seifert matrix of 12a_0574
-1 0 0 -1 -1 0 0 -1
0 -1 -1 0 -1 0 -1 0
0 0 -1 0 -1 0 0 0
0 0 0 -2 -1 0 0 -2
0 0 0 -1 -2 0 0 -1
0 -1 -1 0 -1 -1 -1 0
0 0 -1 0 -1 0 -1 0
0 0 0 -1 -1 0 0 -2
2
117
First homology
of the double branched cover of 12a_0574
Z/39+Z/3
-8 8
12a_0575
3

detected by
the signature
6-21t+40t^2-49t^3+40t^4-21t^5+6t^6
Seifert matrix of 12a_0575
-1 0 0 -1 -1 -1
0 -2 1 0 1 0
0 0 -1 0 -1 0
0 0 0 -2 -1 -2
0 0 0 -1 -2 -1
0 0 0 -1 -1 -2
1
Generator of the Alexander module
(0,-1+3t-2t^2+2t^3,0,0,0,-2+3t-4t^2+2t^3)
the Blanchfield form on it
-123t^-5+669t^-4-1951t^-3+3874t^-2-5711t^-1+6474-5711t+3874t^2-1951t^3+669t^4-123t^5
183
First homology
of the double branched cover of 12a_0575
Z/183
-6 6
12a_0576
3

detected by
the signature
1-3t+6t^2-8t^3+9t^4-9t^5+9t^6-8t^7+6t^8-3t^9+t^10
Seifert matrix of 12a_0576
-1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0 0 0
0 1 1 0 0 0 1 1 0 0
-1 0 0 -1 0 0 0 0 0 0
-1 1 1 -1 1 0 1 1 1 0
-1 1 1 -1 1 1 1 1 1 1
0 0 0 0 0 0 1 0 0 0
0 1 0 0 0 0 1 1 0 0
0 1 1 0 0 0 1 1 1 0
-1 1 1 -1 1 0 1 1 1 1
2
63
First homology
of the double branched cover of 12a_0576
Z/21+Z/3
6 6
12a_0577
2

detected by
the signature
2-7t+15t^2-22t^3+25t^4-22t^5+15t^6-7t^7+2t^8
Seifert matrix of 12a_0577
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
0 -1 2 0 0 0 -1 0
-1 0 0 -1 0 0 0 0
-1 1 -1 -1 1 0 1 0
-1 1 -1 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 1 -1 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-13t^-1+15-13t+7t^2-2t^3
117
First homology
of the double branched cover of 12a_0577
Z/117
4 4
12a_0578
2

detected by
the signature
-2+8t-19t^2+30t^3-35t^4+30t^5-19t^6+8t^7-2t^8
Seifert matrix of 12a_0578
-1 0 0 0 0 0 0 0
0 2 1 0 0 0 1 0
0 2 2 0 0 0 2 0
-1 0 0 -1 0 0 0 0
-1 -1 -1 -1 1 0 -1 0
-1 -1 -1 -1 1 1 -1 1
0 2 1 0 0 0 2 0
-1 -1 -1 -1 1 0 -1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
2t^-3-8t^-2+16t^-1-19+16t-8t^2+2t^3
153
First homology
of the double branched cover of 12a_0578
Z/153
4 4
12a_0579
1

detected by
an unknotting move
1-7t+21t^2-37t^3+45t^4-37t^5+21t^6-7t^7+t^8
Seifert matrix of 12a_0579
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 -1 0 0
0 0 0 0 0 -1 0 0
0 -1 -1 0 0 -1 -1 -1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,-t,0,0,0,1+t,0)
the Blanchfield form on it
-t^-3+7t^-2-19t^-1+25-19t+7t^2-t^3
177
First homology
of the double branched cover of 12a_0579
Z/177
0 2
12a_0580
2

detected by
the signature
2-6t+10t^2-11t^3+11t^4-11t^5+10t^6-6t^7+2t^8
Seifert matrix of 12a_0580
-1 0 0 0 0 0 0 0
0 1 0 0 1 0 0 0
0 1 1 0 1 1 0 0
-1 0 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
0 1 0 0 1 1 0 0
0 1 1 0 1 1 1 0
1 -1 -1 1 -1 -1 -1 2
1
Generator of the Alexander module
(0,0,0,-t,0,0,0,1+t)
the Blanchfield form on it
2t^-3-3t^-2+3t^-1-3+3t-3t^2+2t^3
69
First homology
of the double branched cover of 12a_0580
Z/69
4 4
12a_0581
1

detected by
an unknotting move
4-14t+26t^2-31t^3+26t^4-14t^5+4t^6
Seifert matrix of 12a_0581
-1 0 0 0 0 0
0 1 0 0 1 0
0 -1 2 0 -1 0
-1 0 0 -1 0 0
0 0 0 0 1 0
1 -1 1 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-3-7t^-2+13t^-1-16+13t-7t^2+2t^3
119
First homology
of the double branched cover of 12a_0581
Z/119
2 2
12a_0582
1

detected by
an unknotting move
4-15t+29t^2-35t^3+29t^4-15t^5+4t^6
Seifert matrix of 12a_0582
-1 0 0 0 0 0
0 2 1 0 1 0
0 2 2 0 2 0
-1 0 0 -1 0 0
0 2 1 0 2 0
1 1 1 1 1 2
1
Generator of the Alexander module
(0,0,0,-t,0,1+t)
the Blanchfield form on it
4t^-2-9t^-1+11-9t+4t^2
131
First homology
of the double branched cover of 12a_0582
Z/131
2 2
12a_0583
1

detected by
an unknotting move
1-7t+19t^2-33t^3+41t^4-33t^5+19t^6-7t^7+t^8
Seifert matrix of 12a_0583
-1 -1 0 0 0 -1 -1 0
0 -1 0 0 0 -1 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 0 1 1 0 1
0 0 0 0 0 1 0 0
0 -1 0 0 0 -1 -1 0
0 0 0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-13t^-1+17-13t+7t^2-2t^3
161
First homology
of the double branched cover of 12a_0583
Z/161
0 0
12a_0584
1

detected by
an unknotting move
-1+7t-19t^2+29t^3-31t^4+29t^5-19t^6+7t^7-t^8
Seifert matrix of 12a_0584
-1 -1 0 0 0 -1 -1 0
0 -1 0 0 0 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 0 1 0 0 1
0 -1 0 0 0 -1 -1 0
0 0 0 0 0 0 -1 0
1 1 0 0 0 1 1 1
1 or 2
143
First homology
of the double branched cover of 12a_0584
Z/143
-2 2
12a_0585
1

detected by
an unknotting move
-2+15t-43t^2+61t^3-43t^4+15t^5-2t^6
Seifert matrix of 12a_0585
-1 1 0 0 0 0
0 -2 0 0 0 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 0 -1 0 1 1
1 -1 0 0 0 1
1
Generator of the Alexander module
(0,7-24t^3+7t^4+12t^5-13t^6+12t^7-4t^8,3-20t+7t^2-11t^3+70t^4-40t^5-33t^6+55t^7-49t^8+24t^9-4t^10,0,-17t+6t^2-t^3+55t^4-42t^5-28t^6+51t^7-45t^8+24t^9-4t^10,14t-48t^4+14t^5+24t^6-26t^7+24t^8-8t^9)
the Blanchfield form on it
x
181
First homology
of the double branched cover of 12a_0585
Z/181
0 0
12a_0586
3

detected by
the signature
7-24t+44t^2-53t^3+44t^4-24t^5+7t^6
Seifert matrix of 12a_0586
-1 0 1 -1 0 0
0 -1 1 0 0 1
0 0 -3 1 0 -1
0 0 1 -2 0 -1
0 -1 1 0 -1 1
0 0 -1 0 0 -2
1 or 2
203
First homology
of the double branched cover of 12a_0586
Z/203
-6 6
12a_0587
3

detected by
the signature
-2+10t-22t^2+34t^3-39t^4+34t^5-22t^6+10t^7-2t^8
Seifert matrix of 12a_0587
-1 0 0 -1 -1 0 0 -1
0 -1 0 -1 -1 0 -1 -1
0 0 1 0 0 0 0 0
0 0 -1 -2 -2 0 0 -2
0 0 0 -1 -2 0 0 -1
0 -1 0 -1 -1 -1 -1 -1
0 0 -1 -1 -1 0 -1 -1
0 0 -1 -1 -2 0 0 -2
1
Generator of the Alexander module
(56+238t+192t^2-190t^3-292t^4-62t^5+136t^6+60t^7,15+56t-112t^2-393t^3-558t^4+162t^5+752t^6+296t^7-328t^8-160t^9,53+202t+27t^2-500t^3-756t^4+112t^5+840t^6+336t^7-328t^8-160t^9,10-17t-88t^2-159t^3+32t^4+193t^5+76t^6-82t^7-40t^8,5+3t-2t^2-2t^3,6t-43t^2-171t^3-282t^4+72t^5+374t^6+148t^7-164t^8-80t^9,-10
the Blanchfield form on it
x
175
First homology
of the double branched cover of 12a_0587
Z/175
-6 6
12a_0588
1

detected by
an unknotting move
-2+11t-30t^2+53t^3-63t^4+53t^5-30t^6+11t^7-2t^8
Seifert matrix of 12a_0588
-1 0 0 -1 -1 0 0 -1
0 1 0 0 0 0 0 0
0 1 1 0 0 0 1 0
0 0 -1 -2 -2 0 0 -2
0 0 0 -1 -2 0 0 -1
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 1 0
0 0 -1 -1 -2 0 0 -2
1
Generator of the Alexander module
(4t-2t^2-t^3,0,t^2+t^3-5t^4+2t^5+2t^6,-2t+t^2-3t^3+5t^4-2t^6,1-t+2t^2-3t^3+2t^5,-4t+5t^4-4t^6,-t-t^2+2t^3,-3t+2t^2-3t^3+5t^4-2t^6)
the Blanchfield form on it
x
255
First homology
of the double branched cover of 12a_0588
Z/255
-2 2
12a_0589
2

detected by
the signature
2-9t+23t^2-37t^3+43t^4-37t^5+23t^6-9t^7+2t^8
Seifert matrix of 12a_0589
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
0 -1 2 0 1 0 -1 1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 0 0
-1 1 -1 -1 0 1 1 0
0 0 0 0 0 0 1 0
-1 0 0 -1 1 0 0 1
1
Generator of the Alexander module
(0,t+t^2-2t^3,t+t^2-2t^3,2-t-2t^2,0,1+t-2t^2,0,0)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-6+5t-3t^2+t^3
185
First homology
of the double branched cover of 12a_0589
Z/185
4 4
12a_0590
3

detected by
the signature
-2+9t-19t^2+29t^3-33t^4+29t^5-19t^6+9t^7-2t^8
Seifert matrix of 12a_0590
-1 0 -1 -1 -1 0 0 0
0 1 0 0 0 0 0 0
0 0 -2 -1 -2 0 0 0
0 0 -2 -2 -2 0 0 0
0 0 -1 -1 -2 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -1 -1 0 -1 0
0 -1 -1 -1 -1 0 -1 -1
1
Generator of the Alexander module
(-4+8t+15t^2-34t^3+2t^4+6t^5-6t^6,-4t^2-2t^3+28t^4-58t^5+34t^6-12t^7,0,0,-6-9t+26t^2-17t^3+6t^4,-12t+4t^2+67t^3-106t^4+110t^5-162t^6+72t^7-4t^8-18t^9+6t^10,5-13t-5t^2+35t^3-30t^4+30t^5-32t^6+18t^7-6t^8,2+t-14t^2+29t^3-17t^4+6t^5)
the Blanchfield form on it
x
151
First homology
of the double branched cover of 12a_0590
Z/151
-6 6
12a_0591
2

detected by
the signature
-3+13t-24t^2+29t^3-24t^4+13t^5-3t^6
Seifert matrix of 12a_0591
-1 0 1 0 0 0
0 1 0 0 0 0
0 0 -3 0 0 0
0 -1 1 -1 -1 -1
0 -1 1 0 -1 0
0 -1 1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-3t^-2+13t^-1-19+13t-3t^2
109
First homology
of the double branched cover of 12a_0591
Z/109
-4 4
12a_0592
2

detected by
the signature
-5+24t-49t^2+61t^3-49t^4+24t^5-5t^6
Seifert matrix of 12a_0592
1 0 0 0 0 0
1 -2 0 -1 -1 -1
0 -1 -1 0 -1 -1
1 -1 0 -2 -1 -1
1 -2 0 -1 -2 -1
1 -1 0 0 -1 -2
1 or 2
217
First homology
of the double branched cover of 12a_0592
Z/217
-4 4
12a_0593
1

detected by
an unknotting move
-4+19t-41t^2+53t^3-41t^4+19t^5-4t^6
Seifert matrix of 12a_0593
-1 -1 0 0 0 0
0 -2 -1 0 0 -1
0 0 1 0 -1 1
0 -1 -1 -1 1 -1
0 0 0 0 2 0
0 0 0 0 -1 1
1
Generator of the Alexander module
(-2-7t-23t^2-7t^3+22t^4+16t^5-2t^6+24t^7-8t^8,4t+16t^2+20t^3-8t^4,-1-4t-5t^2+2t^3,2+10t+7t^2+3t^3-2t^4,1-29t^2+25t^3+30t^4-86t^5+34t^6+34t^7-120t^8+136t^9-32t^10,-2-15t-3t^2-10t^3-26t^4+38t^5+8t^6-34t^7+60t^8-16t^9)
the Blanchfield form on it
x
181
First homology
of the double branched cover of 12a_0593
Z/181
0 0
12a_0594
2

detected by
the Nakanishi index
3-11t+22t^2-27t^3+22t^4-11t^5+3t^6
Seifert matrix of 12a_0594
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 1 0
-1 -1 1 1 1 1
0 0 0 0 3 0
-1 -1 1 0 1 1
2
99
First homology
of the double branched cover of 12a_0594
Z/33+Z/3
2 2
12a_0595
1

detected by
an unknotting move
2-13t+33t^2-43t^3+33t^4-13t^5+2t^6
Seifert matrix of 12a_0595
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
0 0 0 -1 -1 1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,1,3,0,t,1)
the Blanchfield form on it
4t^-2-14t^-1+19-14t+4t^2
139
First homology
of the double branched cover of 12a_0595
Z/139
-2 2
12a_0596
1

detected by
an unknotting move
6-20t+29t^2-20t^3+6t^4
Seifert matrix of 12a_0596
-1 0 0 0
-1 -1 0 0
0 0 3 0
1 1 -1 2
1
Generator of the Alexander module
(0,-1,0,1)
the Blanchfield form on it
3t^-1-5+3t
81
First homology
of the double branched cover of 12a_0596
Z/81
0 0
12a_0597
2

detected by
the Lickorish test
2-13t+29t^2-35t^3+29t^4-13t^5+2t^6
Seifert matrix of 12a_0597
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 1 1 0 1
0 0 0 1 0 0
0 0 0 1 -2 0
0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-3+6t^-2-12t^-1+14-12t+6t^2-t^3
123
First homology
of the double branched cover of 12a_0597
Z/123
2 2
12a_0598
1

detected by
an unknotting move
-2+10t-25t^2+43t^3-51t^4+43t^5-25t^6+10t^7-2t^8
Seifert matrix of 12a_0598
-1 0 0 -1 -1 0 -1 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1
0 -1 -1 -2 -2 0 -2 -1
0 0 0 -1 -2 0 -1 0
0 -1 -1 -1 -1 -1 -1 -1
0 -1 -1 -1 -2 0 -2 -1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(7t-3t^2+12t^3-14t^4+9t^5-4t^6-10t^7+7t^8+t^9-4t^10+2t^11,7t^3-3t^4+12t^5-14t^6+9t^7-4t^8-10t^9+7t^10+t^11-4t^12+2t^13,7+5t+8t^2+2t^3+7t^4-20t^5+33t^6-22t^7+7t^8+22t^9-16t^10-2t^11+8t^12-4t^13,7t^3-3t^4+12t^5-14t^6+9t^7-4t^8-10t^9+7t^10+t^11-4t^12+2t^13,5-3t+11t^2+7t^3-t^4+8t^5+4t^6-6t^7+t^8+2t^9-2t
the Blanchfield form on it
x
211
First homology
of the double branched cover of 12a_0598
Z/211
-2 2
12a_0599
2

detected by
the signature
2-10t+26t^2-42t^3+49t^4-42t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_0599
-1 0 0 0 0 0 0 0
0 2 1 0 1 0 1 1
0 2 2 0 1 0 1 2
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 0 0
-1 -1 -1 -1 0 1 0 -1
-1 0 0 -1 1 0 1 0
0 2 1 0 1 0 1 2
1
Generator of the Alexander module
(0,0,0,0,2-t+2t^2,1-t+t^2,0,0)
the Blanchfield form on it
-6t^-3+20t^-2-38t^-1+42-38t+20t^2-6t^3
209
First homology
of the double branched cover of 12a_0599
Z/209
4 4
12a_0600
2

detected by
the signature
-4+15t-23t^2+25t^3-23t^4+15t^5-4t^6
Seifert matrix of 12a_0600
1 0 0 0 0 0
0 -2 -2 -1 -1 -2
0 -1 -2 -1 -1 -1
1 0 0 -2 0 0
0 -2 -2 -1 -2 -2
0 -1 -2 -1 -1 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-4t^-2+15t^-1-21+15t-4t^2
109
First homology
of the double branched cover of 12a_0600
Z/109
-4 4
12a_0601
1

detected by
an unknotting move
-8+32t-47t^2+32t^3-8t^4
Seifert matrix of 12a_0601
1 0 0 0
0 -3 2 1
0 1 -2 -1
1 0 0 -2
1 or 2
127
First homology
of the double branched cover of 12a_0601
Z/127
-2 2
12a_0602
1

detected by
an unknotting move
2-11t+28t^2-46t^3+55t^4-46t^5+28t^6-11t^7+2t^8
Seifert matrix of 12a_0602
-1 0 0 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1
0 0 -1 -2 -1 0 -2 0
0 1 1 0 1 0 0 1
0 0 -1 -1 -1 -1 -1 0
0 0 0 -1 -1 0 -2 0
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(3-2t,0,-2,2t,-4t,0,0,0)
the Blanchfield form on it
-7t^-4+28t^-3-34t^-2+9t^-1+2+9t-34t^2+28t^3-7t^4
229
First homology
of the double branched cover of 12a_0602
Z/229
0 0
12a_0603
1

detected by
an unknotting move
4-22t+50t^2-63t^3+50t^4-22t^5+4t^6
Seifert matrix of 12a_0603
-1 -1 0 0 -1 0
0 -2 0 0 -2 1
0 0 1 0 0 0
0 -1 0 -1 -1 1
0 -1 -1 0 -2 0
0 0 1 0 0 2
1
Generator of the Alexander module
(-t,0,0,-1+t,0,1)
the Blanchfield form on it
2t^-2-10t^-1+17-10t+2t^2
215
First homology
of the double branched cover of 12a_0603
Z/215
-2 2
12a_0604
1

detected by
an unknotting move
3-20t+53t^2-71t^3+53t^4-20t^5+3t^6
Seifert matrix of 12a_0604
1 0 0 0 0 0
0 -1 0 0 0 -1
0 0 -1 0 -1 0
1 -1 0 -2 -1 -1
1 -1 0 -1 -2 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,-t,0,1,0)
the Blanchfield form on it
2t^-2-10t^-1+17-10t+2t^2
223
First homology
of the double branched cover of 12a_0604
Z/223
-2 2
12a_0605
1

detected by
an unknotting move
-2+9t-20t^2+30t^3-33t^4+30t^5-20t^6+9t^7-2t^8
Seifert matrix of 12a_0605
-1 0 0 -1 0 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1
0 0 0 -2 -1 0 -1 0
0 1 1 0 1 0 1 1
0 0 -1 -1 -1 -1 -1 0
0 1 1 0 0 0 1 1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(2t-2t^2+t^3,0,0,-2+2t-t^2,0,-1+2t-t^2,0,0)
the Blanchfield form on it
6t^-3-29t^-2+65t^-1-84+65t-29t^2+6t^3
155
First homology
of the double branched cover of 12a_0605
Z/155
2 2
12a_0606
1

detected by
an unknotting move
-4+18t-38t^2+49t^3-38t^4+18t^5-4t^6
Seifert matrix of 12a_0606
-1 -1 0 0 0 0
0 -2 -1 0 -1 0
0 0 1 0 1 0
0 -1 0 -1 0 1
0 0 0 0 1 0
0 0 1 0 1 2
1 or 2
169
First homology
of the double branched cover of 12a_0606
Z/169
0 0
12a_0607
2

detected by
the signature
2-9t+22t^2-34t^3+39t^4-34t^5+22t^6-9t^7+2t^8
Seifert matrix of 12a_0607
-1 0 0 0 0 0 0 0
0 2 1 0 1 0 1 1
0 0 1 0 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 1 -1 1 0 1 0
-1 -1 0 -1 0 1 0 0
0 0 1 0 0 0 1 0
-1 0 1 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,1,-t,1,0,0)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
173
First homology
of the double branched cover of 12a_0607
Z/173
4 4
12a_0608
1

detected by
an unknotting move
4-19t+44t^2-57t^3+44t^4-19t^5+4t^6
Seifert matrix of 12a_0608
-1 0 0 0 0 0
1 2 1 0 0 1
-1 0 -1 0 0 0
-1 -1 -1 1 0 0
1 1 1 0 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-3-10t^-2+23t^-1-30+23t-10t^2+2t^3
191
First homology
of the double branched cover of 12a_0608
Z/191
2 2
12a_0609
1

detected by
an unknotting move
5-23t+51t^2-65t^3+51t^4-23t^5+5t^6
Seifert matrix of 12a_0609
-1 0 0 0 0 0
1 2 1 1 1 1
0 1 2 0 0 1
-1 0 0 -1 0 0
1 1 1 1 2 1
1 2 1 1 1 2
1
Generator of the Alexander module
(0,-4-37t+182t^2-362t^3+451t^4-325t^5+94t^6+24t^7-24t^8,-18t+69t^2-132t^3+167t^4-130t^5+60t^6-12t^7,9-30t+51t^2-67t^3+66t^4-63t^5+58t^6-36t^7+12t^8,-1-139t+553t^2-1063t^3+1395t^4-1220t^5+808t^6-539t^7+392t^8-248t^9+96t^10-24t^11,-14+97t-230t^2+298t^3-217t^4+t^5+122t^6-96t^7+24t^8)
the Blanchfield form on it
x
223
First homology
of the double branched cover of 12a_0609
Z/223
2 2
12a_0610
2

detected by
the signature
11-34t+47t^2-34t^3+11t^4
Seifert matrix of 12a_0610
-1 -1 -1 0
0 -2 -1 -1
0 -1 -4 1
0 0 1 -2
1 or 2
137
First homology
of the double branched cover of 12a_0610
Z/137
-4 4
12a_0611
2

detected by
the signature
-4+24t-55t^2+71t^3-55t^4+24t^5-4t^6
Seifert matrix of 12a_0611
-1 0 1 -1 0 0
0 1 0 0 0 0
0 1 -3 1 0 0
0 -1 2 -2 0 0
0 1 -1 0 -1 0
0 -1 1 -1 0 -1
1 or 2
237
First homology
of the double branched cover of 12a_0611
Z/237
-4 4
12a_0612
2

detected by
the signature
-4+17t-32t^2+39t^3-32t^4+17t^5-4t^6
Seifert matrix of 12a_0612
-1 -1 -1 0 -1 0
0 -2 -2 0 -2 1
0 -1 -2 0 -1 0
0 -1 -1 -1 -1 1
0 -1 -2 0 -2 1
0 0 0 0 0 2
1 or 2
145
First homology
of the double branched cover of 12a_0612
Z/145
-4 4
12a_0613
1

detected by
an unknotting move
3-15t+36t^2-47t^3+36t^4-15t^5+3t^6
Seifert matrix of 12a_0613
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 0 0 0
-1 -1 0 1 0 1
-1 -1 1 0 1 0
0 0 -1 0 -1 3
1
Generator of the Alexander module
(186-86t-210t^2+112t^3,67-30t-131t^2+63t^3+120t^4-64t^5,-40+19t+30t^2-16t^3,85+309t-249t^2-342t^3+208t^4,-76+35t+90t^2-48t^3,-5-2t+t^2)
the Blanchfield form on it
160672t^-7-734060t^-6+840218t^-5+1246386t^-4-4511585t^-3+3660435t^-2+3396456t^-1-8127540+3396456t+3660435t^2-4511585t^3+1246386t^4+840218t^5-734060t^6+160672t^7
155
First homology
of the double branched cover of 12a_0613
Z/155
2 2
12a_0614
1

detected by
an unknotting move
3-20t+51t^2-67t^3+51t^4-20t^5+3t^6
Seifert matrix of 12a_0614
-1 0 -1 0 0 -1
0 -1 -1 0 0 0
0 0 -2 0 0 -1
0 1 1 1 0 1
0 0 0 0 1 -1
0 0 -1 0 0 -2
1
Generator of the Alexander module
(-1,0,0,1,0,0)
the Blanchfield form on it
3t^-2-14t^-1+22-14t+3t^2
215
First homology
of the double branched cover of 12a_0614
Z/215
-2 2
12a_0615
3

detected by
the signature
7-27t+54t^2-67t^3+54t^4-27t^5+7t^6
Seifert matrix of 12a_0615
-1 -1 0 1 0 0
0 -2 0 1 0 -1
0 0 -1 1 0 1
0 1 0 -3 0 -1
0 0 0 -1 -1 0
0 0 0 -1 0 -2
2
243
First homology
of the double branched cover of 12a_0615
Z/27+Z/9
-6 6
12a_0616
2

detected by
the signature
2-11t+32t^2-55t^3+65t^4-55t^5+32t^6-11t^7+2t^8
Seifert matrix of 12a_0616
-1 0 -1 -1 0 0 0 -1
0 -1 -1 -1 -1 0 -1 -1
0 0 -2 -1 -1 0 0 -2
0 0 -2 -2 -1 0 -1 -2
0 0 0 0 1 0 1 0
0 -1 -1 -1 0 -1 0 -1
0 0 0 0 0 0 1 0
0 0 -1 -1 -1 0 0 -2
1 or 2
265
First homology
of the double branched cover of 12a_0616
Z/265
-4 4
12a_0617
1

detected by
an unknotting move
2-9t+22t^2-35t^3+41t^4-35t^5+22t^6-9t^7+2t^8
Seifert matrix of 12a_0617
-1 0 0 -1 0 0 0 0
0 -1 -1 -1 -1 0 -1 -1
0 0 1 0 0 0 1 0
0 0 0 -2 -1 0 0 -1
0 0 1 0 1 0 1 1
0 -1 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
0 0 1 0 0 0 1 1
1
Generator of the Alexander module
(-t+2t^2-t^3,0,0,1-2t+t^2,0,-2t+t^2,0,0)
the Blanchfield form on it
4t^-3-12t^-2+22t^-1-25+22t-12t^2+4t^3
177
First homology
of the double branched cover of 12a_0617
Z/177
0 2
12a_0618
2

detected by
the signature
2-11t+31t^2-53t^3+63t^4-53t^5+31t^6-11t^7+2t^8
Seifert matrix of 12a_0618
-1 0 0 -1 -1 0 0 -1
0 -1 -1 -1 -1 0 -1 -1
0 0 1 0 0 0 1 0
0 0 -1 -2 -2 0 0 -2
0 0 0 -1 -2 0 0 -1
0 -1 0 -1 -1 -1 0 -1
0 0 0 0 0 0 1 0
0 0 -1 -1 -2 0 0 -2
1
Generator of the Alexander module
(t,0,0,-1,-1,-1,0,-1)
the Blanchfield form on it
2t^-3-7t^-2+15t^-1-18+15t-7t^2+2t^3
257
First homology
of the double branched cover of 12a_0618
Z/257
-4 4
12a_0619
2

detected by
the Lickorish test
-6+24t-35t^2+24t^3-6t^4
Seifert matrix of 12a_0619
1 0 0 0
0 -1 0 0
-1 0 -3 0
1 -1 1 -2
1
Generator of the Alexander module
(0,0,2-6t+3t^2,1)
the Blanchfield form on it
15t^-4-126t^-3+454t^-2-921t^-1+1156-921t+454t^2-126t^3+15t^4
95
First homology
of the double branched cover of 12a_0619
Z/95
-2 2
12a_0620
2

detected by
the signature
2-12t+33t^2-55t^3+65t^4-55t^5+33t^6-12t^7+2t^8
Seifert matrix of 12a_0620
-1 0 -1 -1 0 -1 0 -1
0 1 0 0 0 0 0 0
0 0 -2 -1 0 -2 0 -1
0 -1 -2 -2 -1 -2 0 -2
0 1 0 0 1 0 0 0
0 0 -1 -1 0 -2 0 -1
0 -1 -1 -1 -1 -1 -1 -1
0 0 -2 -1 -1 -2 0 -2
1
Generator of the Alexander module
(-3t+4t^2-3t^3+t^4,0,3-4t+3t^2-t^3,4-6t+4t^2-t^3,0,3-4t+3t^2-t^3,0,3-4t+3t^2-t^3)
the Blanchfield form on it
-2t^-2+4t^-1-5+4t-2t^2
269
First homology
of the double branched cover of 12a_0620
Z/269
-4 4
12a_0621
2

detected by
the Lickorish test
-1+8t-22t^2+36t^3-41t^4+36t^5-22t^6+8t^7-t^8
Seifert matrix of 12a_0621
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 1 0
-1 0 0 -1 1 1 1 1
-1 1 0 -1 0 0 1 0
-1 0 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,t,1+2t,-1-4t,0,0,-2t,-2t)
the Blanchfield form on it
-144t^-3+505t^-2-814t^-1+874-814t+505t^2-144t^3
175
First homology
of the double branched cover of 12a_0621
Z/175
2 2
12a_0622
1

detected by
an unknotting move
-2+17t-47t^2+65t^3-47t^4+17t^5-2t^6
Seifert matrix of 12a_0622
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 1 1 -1 0 0
-1 0 0 -1 0 0
-1 1 0 -1 1 0
1 0 0 1 -1 2
1
Generator of the Alexander module
(27-10t+15t^2-105t^3,-16t+t^2-16t^3+47t^4+3t^5,6+30t-4t^2-114t^4,37-10t+25t^2-135t^3,-12-9t-11t^2+29t^3+31t^4-3t^5,-28+2t-22t^2+93t^3+9t^4)
the Blanchfield form on it
4801t^-6-28762t^-5+12271t^-4+183082t^-3-427017t^-2+500754t^-1-485344+500754t-427017t^2+183082t^3+12271t^4-28762t^5+4801t^6
197
First homology
of the double branched cover of 12a_0622
Z/197
0 0
12a_0623
2

detected by
the signature
-4+20t-43t^2+55t^3-43t^4+20t^5-4t^6
Seifert matrix of 12a_0623
-1 0 -1 0 0 0
0 -2 0 -2 -1 -2
0 -1 -2 -1 -1 -1
0 -1 0 -2 0 -2
0 0 0 0 1 0
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(19t-39t^2-28t^3+237t^4-424t^5+507t^6-340t^7+148t^8-16t^9,-30+12t+124t^2-390t^3+516t^4-420t^5+192t^6-48t^7,-11+12t+13t^2-156t^3+278t^4-351t^5+242t^6-112t^7+16t^8,3+6t-7t^2+21t^3-51t^4+112t^5-135t^6+107t^7-48t^8+12t^9,-6+6t+23t^2-87t^3+123t^4-103t^5+48t^6-12t^7,15-6t-62t^2+195t^3-258t^4+210t^5-96t^6+
the Blanchfield form on it
x
189
First homology
of the double branched cover of 12a_0623
Z/189
-4 4
12a_0624
1

detected by
an unknotting move
4-18t+41t^2-53t^3+41t^4-18t^5+4t^6
Seifert matrix of 12a_0624
-1 0 0 0 0 0
1 2 1 0 0 0
-1 0 -1 0 0 0
-1 -1 -1 1 0 1
1 1 1 0 2 0
-1 -1 -1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-3-9t^-2+20t^-1-26+20t-9t^2+2t^3
179
First homology
of the double branched cover of 12a_0624
Z/179
2 2
12a_0625
1

detected by
an unknotting move
-3+19t-49t^2+67t^3-49t^4+19t^5-3t^6
Seifert matrix of 12a_0625
-1 0 0 0 0 0
1 2 1 1 0 1
0 1 2 0 -1 1
-1 0 0 -1 0 0
0 0 0 0 -1 0
1 2 1 1 -1 2
1
Generator of the Alexander module
(0,1-3t+t^2,6t-2t^2,3t-t^2,0,0)
the Blanchfield form on it
-3t^-2+10t^-1-16+10t-3t^2
209
First homology
of the double branched cover of 12a_0625
Z/209
0 0
12a_0626
1

detected by
an unknotting move
-2+12t-34t^2+61t^3-73t^4+61t^5-34t^6+12t^7-2t^8
Seifert matrix of 12a_0626
-1 0 0 -1 0 -1 0 -1
0 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0
0 -1 -1 -2 -1 -2 0 -2
0 1 0 0 1 0 0 0
0 0 0 -1 0 -2 0 -1
0 -1 -1 -1 -1 -1 -1 -1
0 0 -1 -1 0 -2 0 -2
1
Generator of the Alexander module
(-t+3t^2-6t^3+6t^4-4t^5,0,-1-2t+2t^2-8t^3-t^4+5t^5-14t^6+3t^7+4t^8-10t^9+4t^10,t-2t^2+5t^3+t^4-3t^5+10t^6-3t^7-4t^8+10t^9-4t^10,t^3-t^5+3t^6-3t^7-2t^8+6t^9-4t^10,-1+2t-5t^2-t^3+3t^4-10t^5+3t^6+4t^7-10t^8+4t^9,2+t-3t^2+11t^3-5t^4-2t^5+17t^6-6t^7-6t^8+16t^9-8t^10,1-4t^2+9t^3-5t^4-6t^5+21t^6-14t^7-6t^8
the Blanchfield form on it
x
291
First homology
of the double branched cover of 12a_0626
Z/291
-2 2
12a_0627
1

detected by
an unknotting move
1-8t+26t^2-49t^3+61t^4-49t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0627
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
-1 -1 0 -1 1 1 0 1
0 0 0 0 0 1 0 0
0 0 0 0 0 0 -1 0
-1 0 0 -1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-15+11t-5t^2+t^3
229
First homology
of the double branched cover of 12a_0627
Z/229
0 0
12a_0628
2

detected by
the Lickorish test
3-18t+46t^2-61t^3+46t^4-18t^5+3t^6
Seifert matrix of 12a_0628
-1 0 1 0 0 0
0 1 0 0 0 0
0 1 -3 1 0 0
0 1 0 1 0 0
0 -1 1 -1 -1 0
0 1 -1 0 0 -1
1 or 2
195
First homology
of the double branched cover of 12a_0628
Z/195
-2 2
12a_0629
1

detected by
an unknotting move
1-8t+31t^2-66t^3+85t^4-66t^5+31t^6-8t^7+t^8
Seifert matrix of 12a_0629
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 1 -1 1 1 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 0 -1 0 0 1 1
-1 1 0 -1 0 0 0 1
1
Generator of the Alexander module
(0,-1-7t-11t^2+5t^3+2t^4-18t^5-10t^6,14t+22t^2-16t^3+37t^4-4t^5+28t^6+10t^7,1+8t+17t^2+2t^3+5t^4+6t^5+28t^6+10t^7,-5+13t+19t^2-10t^3+15t^4+6t^5+28t^6+10t^7,0,2t+42t^2+8t^3-10t^4+12t^5+56t^6+20t^7,-12t+21t^2+22t^3-18t^4-14t^5+36t^6+20t^7)
the Blanchfield form on it
x
297
First homology
of the double branched cover of 12a_0629
Z/297
0 0
12a_0630
1

detected by
an unknotting move
-1+8t-27t^2+52t^3-63t^4+52t^5-27t^6+8t^7-t^8
Seifert matrix of 12a_0630
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 1 -1 1 0 1 0
-1 0 0 -1 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 0 -1 0 1 0 1
0 -1 0 0 -1 0 -1 0
-1 1 0 -1 0 0 0 1
1
Generator of the Alexander module
(0,1,-4t+4t^2,-1,1-t+2t^3,-t^2,1,0)
the Blanchfield form on it
2t^-2-8t^-1+13-8t+2t^2
239
First homology
of the double branched cover of 12a_0630
Z/239
-2 2
12a_0631
1

detected by
an unknotting move
-4+22t-52t^2+69t^3-52t^4+22t^5-4t^6
Seifert matrix of 12a_0631
-1 -1 0 0 0 0
0 -2 0 -1 0 -1
0 0 2 0 0 1
0 0 -1 1 0 0
0 -1 1 -1 -1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
225
First homology
of the double branched cover of 12a_0631
Z/225
0 0
12a_0632
1

detected by
an unknotting move
-4+17t-33t^2+41t^3-33t^4+17t^5-4t^6
Seifert matrix of 12a_0632
-1 0 -1 0 0 0
0 -2 0 0 0 -1
0 -1 -2 -1 -1 -1
0 0 0 1 1 0
0 0 0 0 1 0
0 0 0 1 1 1
1
Generator of the Alexander module
(1-9t+8t^2-4t^3,2t-t^3+t^4,2t-t^3+t^4,4-14t+12t^2-5t^3,2-2t+t^2,2-4t+3t^2-t^3)
the Blanchfield form on it
-t^-7+52t^-6-507t^-5+2527t^-4-7971t^-3+17365t^-2-27318t^-1+31706-27318t+17365t^2-7971t^3+2527t^4-507t^5+52t^6-t^7
149
First homology
of the double branched cover of 12a_0632
Z/149
0 2
12a_0633
2

detected by
the Lickorish test
4-21t+51t^2-67t^3+51t^4-21t^5+4t^6
Seifert matrix of 12a_0633
-1 0 -1 0 0 0
0 -1 0 0 -1 0
0 0 -2 0 0 0
0 0 1 1 0 1
0 0 1 0 -2 0
0 1 1 0 0 1
1
Generator of the Alexander module
(2,0,6t^2-2t^3,-6t^3+2t^4,6t-2t^2,5-8t+22t^2-14t^3+2t^4)
the Blanchfield form on it
4t^-2-13t^-1+19-13t+4t^2
219
First homology
of the double branched cover of 12a_0633
Z/219
-2 2
12a_0634
2

detected by
the Nakanishi index
4-15t+30t^2-37t^3+30t^4-15t^5+4t^6
Seifert matrix of 12a_0634
-1 0 0 0 0 0
1 2 1 1 0 1
-1 0 -1 0 0 0
0 0 0 1 0 1
1 1 1 1 2 1
0 0 0 0 0 1
2
135
First homology
of the double branched cover of 12a_0634
Z/45+Z/3
2 2
12a_0635
1

detected by
an unknotting move
-3+19t-47t^2+63t^3-47t^4+19t^5-3t^6
Seifert matrix of 12a_0635
-1 0 0 0 0 0
0 2 0 0 1 1
-1 0 -1 0 0 0
0 0 0 -1 0 0
0 0 0 -1 1 0
1 1 1 -1 1 2
1
Generator of the Alexander module
(0,0,2-3t+3t^2-3t^3+t^4,0,1,-2+t+2t^3-t^4)
the Blanchfield form on it
t^-2-5t^-1+8-5t+t^2
201
First homology
of the double branched cover of 12a_0635
Z/201
0 0
12a_0636
1

detected by
an unknotting move
7-23t+33t^2-23t^3+7t^4
Seifert matrix of 12a_0636
-1 0 0 0
-1 -1 0 0
-1 -1 3 2
0 0 1 3
1 or 2
93
First homology
of the double branched cover of 12a_0636
Z/93
0 0
12a_0637
1

detected by
an unknotting move
-1+8t-26t^2+50t^3-61t^4+50t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0637
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 1 -1 1 0 1 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 0 0
-1 0 0 -1 0 1 0 1
-1 0 0 -1 1 0 1 0
-1 1 0 -1 0 0 0 1
1
Generator of the Alexander module
(0,0,t,0,-1,-1-t,-1,-t)
the Blanchfield form on it
2t^-3-13t^-2+30t^-1-40+30t-13t^2+2t^3
231
First homology
of the double branched cover of 12a_0637
Z/231
2 2
12a_0638
2

detected by
the signature
-4+20t-41t^2+51t^3-41t^4+20t^5-4t^6
Seifert matrix of 12a_0638
-1 0 -1 -1 -1 0
0 -2 0 0 0 -1
0 -1 -2 -2 -2 0
0 -1 -1 -2 -1 -1
0 -1 -1 -2 -2 0
0 0 0 0 0 1
1
Generator of the Alexander module
(-t+12t^2-32t^3+43t^4-37t^5+20t^6-4t^7,0,2-26t+76t^2-118t^3+117t^4-77t^5+28t^6-4t^7,1-12t+32t^2-43t^3+37t^4-20t^5+4t^6,1-12t+32t^2-43t^3+37t^4-20t^5+4t^6,0)
the Blanchfield form on it
x
181
First homology
of the double branched cover of 12a_0638
Z/181
-4 4
12a_0639
1

detected by
an unknotting move
-2+10t-24t^2+40t^3-47t^4+40t^5-24t^6+10t^7-2t^8
Seifert matrix of 12a_0639
-1 0 -1 -1 -1 0 0 0
0 1 0 0 0 0 0 0
0 0 -2 -1 -2 -1 0 -1
0 0 -2 -2 -2 -1 0 -1
0 0 -1 -1 -2 -1 0 -1
0 1 0 0 0 1 0 1
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(-5+9t-9t^2+5t^3-t^4,0,0,0,0,-3+3t-3t^2+t^3,6-6t+6t^2-2t^3,0)
the Blanchfield form on it
2t^-3-6t^-2+12t^-1-14+12t-6t^2+2t^3
199
First homology
of the double branched cover of 12a_0639
Z/199
-2 2
12a_0640
1

detected by
an unknotting move
-3+14t-28t^2+35t^3-28t^4+14t^5-3t^6
Seifert matrix of 12a_0640
-1 0 1 0 0 0
0 1 0 0 0 0
0 0 -3 1 0 1
0 1 0 1 0 1
0 -1 1 -1 -1 -1
0 1 0 0 0 1
1
Generator of the Alexander module
(-3t+2t^2,0,-3+5t-2t^2,0,-2+t,0)
the Blanchfield form on it
10t^-5-91t^-4+375t^-3-922t^-2+1519t^-1-1782+1519t-922t^2+375t^3-91t^4+10t^5
125
First homology
of the double branched cover of 12a_0640
Z/125
0 2
12a_0641
2

detected by
the signature
2-6t+10t^2-12t^3+13t^4-12t^5+10t^6-6t^7+2t^8
Seifert matrix of 12a_0641
-1 0 -1 0 0 0 0 0
0 1 0 0 0 1 0 0
0 0 -2 0 0 0 0 0
0 1 1 1 0 1 1 0
0 1 1 1 1 1 1 1
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
0 1 1 1 0 1 1 1
1
Generator of the Alexander module
(1-6t+8t^2-9t^3+10t^4-10t^5+6t^6-2t^7,0,0,0,0,0,1,0)
the Blanchfield form on it
x
73
First homology
of the double branched cover of 12a_0641
Z/73
4 4
12a_0642
2

detected by
the Lickorish test
4-14t+25t^2-29t^3+25t^4-14t^5+4t^6
Seifert matrix of 12a_0642
-1 0 -1 0 0 0
0 2 0 0 0 0
0 0 -2 0 0 0
0 -1 1 1 0 0
0 -1 1 1 1 1
0 -1 1 1 0 1
1 or 2
115
First homology
of the double branched cover of 12a_0642
Z/115
2 2
12a_0643
2

detected by
the Lickorish test
4-13t+21t^2-23t^3+21t^4-13t^5+4t^6
Seifert matrix of 12a_0643
-1 0 -1 0 0 0
0 1 0 1 0 0
0 0 -2 0 0 0
0 0 0 1 0 0
0 1 0 1 1 0
0 -1 -1 -1 -1 2
1
Generator of the Alexander module
(0,0,0,0,-t,1+t)
the Blanchfield form on it
-4t^-2+13t^-1-19+13t-4t^2
99
First homology
of the double branched cover of 12a_0643
Z/99
2 2
12a_0644
1

detected by
an unknotting move
8-28t+41t^2-28t^3+8t^4
Seifert matrix of 12a_0644
-1 0 -1 0
0 2 0 0
0 0 -2 0
0 1 -1 2
1 or 2
113
First homology
of the double branched cover of 12a_0644
Z/113
0 0
12a_0645
1

detected by
an unknotting move
-2+11t-30t^2+54t^3-65t^4+54t^5-30t^6+11t^7-2t^8
Seifert matrix of 12a_0645
-1 0 -1 -1 0 -1 0 0
0 1 0 0 0 0 0 0
0 0 -2 -1 0 -2 0 0
0 0 -2 -2 -1 -2 0 -1
0 1 0 0 1 0 0 1
0 0 -1 -1 0 -2 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(8-8t-8t^2+30t^3-40t^4+43t^5-30t^6+14t^7-4t^8,0,0,0,0,0,-1+3t+3t^2-4t^3+9t^4-9t^5+5t^6-2t^7,-1+3t+4t^2-7t^3+5t^4-2t^5)
the Blanchfield form on it
x
259
First homology
of the double branched cover of 12a_0645
Z/259
-2 2
12a_0646
1

detected by
an unknotting move
2-9t+21t^2-33t^3+39t^4-33t^5+21t^6-9t^7+2t^8
Seifert matrix of 12a_0646
-1 0 0 -1 0 0 0 0
0 1 0 0 0 0 1 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 1 0 1 0 1 1 1
0 0 0 0 0 0 1 0
0 1 1 1 0 0 1 1
1
Generator of the Alexander module
(t,0,1,0,-t,0,0,0)
the Blanchfield form on it
2t^-3-5t^-2+9t^-1-10+9t-5t^2+2t^3
169
First homology
of the double branched cover of 12a_0646
Z/169
0 0
12a_0647
4

detected by
the signature
3-10t+20t^2-28t^3+31t^4-28t^5+20t^6-10t^7+3t^8
Seifert matrix of 12a_0647
-1 0 -1 -1 -1 -1 0 -1
0 -1 -1 0 -1 -1 0 0
0 0 -2 -1 -1 -2 0 -1
0 0 -1 -2 -1 -1 0 -2
0 0 -2 -1 -2 -2 0 -1
0 0 -1 -1 -1 -2 0 -1
0 -1 -1 0 -1 -1 -1 0
0 0 -1 -1 -1 -1 0 -2
2
153
First homology
of the double branched cover of 12a_0647
Z/51+Z/3
-8 8
12a_0648
3

detected by
the signature
5-17t+32t^2-39t^3+32t^4-17t^5+5t^6
Seifert matrix of 12a_0648
-1 0 1 -1 0 -1
0 -1 1 0 0 0
0 0 -3 1 0 1
0 0 1 -2 0 -2
0 -1 1 0 -1 0
0 0 1 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
3t^-2-7t^-1+9-7t+3t^2
147
First homology
of the double branched cover of 12a_0648
Z/147
-6 6
12a_0649 1 or 2
-1+7t-17t^2+25t^3-27t^4+25t^5-17t^6+7t^7-t^8
Seifert matrix of 12a_0649
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 1 0 0 1 1 1 1
0 0 0 0 0 0 1 0
0 1 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,t,1+t,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-7t^-1+7-7t+5t^2-t^3
127
First homology
of the double branched cover of 12a_0649
Z/127
2 2
12a_0650
2

detected by
the Lickorish test
-2+15t-39t^2+53t^3-39t^4+15t^5-2t^6
Seifert matrix of 12a_0650
-1 0 0 0 0 0
0 2 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 1 -1 0
0 0 0 0 -1 0
0 -1 0 0 1 1
1
Generator of the Alexander module
(0,0,2-t^2,4+2t-2t^2,0,-1-t)
the Blanchfield form on it
-2t^-2+11t^-1-17+11t-2t^2
165
First homology
of the double branched cover of 12a_0650
Z/165
0 0
12a_0651
2

detected by
the signature
1-7t+15t^2-17t^3+17t^4-17t^5+15t^6-7t^7+t^8
Seifert matrix of 12a_0651
-1 -1 0 0 0 -1 0 -1
0 -1 0 0 0 -1 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 0 1 -1 0 0
0 0 0 0 0 -1 0 0
-1 -1 0 0 0 -1 -1 -1
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1+t,0,2t+2t^2,0,2t^2+t^3,0)
the Blanchfield form on it
t^-3-7t^-2+15t^-1-17+15t-7t^2+t^3
97
First homology
of the double branched cover of 12a_0651
Z/97
-4 4
12a_0652
2

detected by
the Lickorish test
2-15t+37t^2-47t^3+37t^4-15t^5+2t^6
Seifert matrix of 12a_0652
-2 1 0 0 0 1
0 -1 0 0 0 -1
0 0 -1 -1 0 0
0 0 0 1 0 0
0 0 -1 0 1 -1
0 0 0 0 0 -1
1 or 2
155
First homology
of the double branched cover of 12a_0652
Z/155
-2 2
12a_0653
2

detected by
the signature
11-36t+51t^2-36t^3+11t^4
Seifert matrix of 12a_0653
-1 1 0 0
0 -3 -1 1
0 -1 -3 2
0 0 1 -2
1 or 2
145
First homology
of the double branched cover of 12a_0653
Z/145
-4 4
12a_0654
2

detected by
the signature
-3+17t-38t^2+49t^3-38t^4+17t^5-3t^6
Seifert matrix of 12a_0654
-1 0 1 0 0 0
0 1 0 0 0 0
0 1 -3 0 0 0
0 1 -1 -1 0 0
0 -1 1 0 -1 0
0 0 -1 -1 0 -1
1 or 2
165
First homology
of the double branched cover of 12a_0654
Z/165
-4 4
12a_0655
1

detected by
an unknotting move
4-17t+36t^2-45t^3+36t^4-17t^5+4t^6
Seifert matrix of 12a_0655
-1 0 -1 0 0 0
0 2 0 1 0 1
0 0 -2 0 0 0
0 0 1 1 0 0
0 -1 1 0 1 0
0 0 1 1 0 1
1 or 2
159
First homology
of the double branched cover of 12a_0655
Z/159
2 2
12a_0656
1

detected by
an unknotting move
4-22t+55t^2-73t^3+55t^4-22t^5+4t^6
Seifert matrix of 12a_0656
-1 0 0 0 0 0
1 2 1 0 0 0
-1 0 -1 0 0 0
-1 0 -1 1 0 0
1 1 1 -1 2 0
-1 -1 -1 0 0 1
1
Generator of the Alexander module
(0,-7+10t-4t^2,0,0,-5+8t-4t^2,0)
the Blanchfield form on it
478t^-3-2631t^-2+6580t^-1-8736+6580t-2631t^2+478t^3
235
First homology
of the double branched cover of 12a_0656
Z/235
2 2
12a_0657
1

detected by
an unknotting move
2-9t+22t^2-36t^3+43t^4-36t^5+22t^6-9t^7+2t^8
Seifert matrix of 12a_0657
-1 0 0 -1 0 0 0 0
0 1 1 1 0 0 1 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 1 0 1 0 1 1 1
0 0 1 1 0 0 1 0
0 1 1 1 0 0 1 1
1
Generator of the Alexander module
(1-t-t^2,0,-2-t,-t-t^2,t,t^2+t^3,-1-t,0)
the Blanchfield form on it
2t^-3-5t^-2+8t^-1-8+8t-5t^2+2t^3
181
First homology
of the double branched cover of 12a_0657
Z/181
0 0
12a_0658
1

detected by
an unknotting move
4-18t+38t^2-47t^3+38t^4-18t^5+4t^6
Seifert matrix of 12a_0658
-1 0 0 -1 0 0
0 2 -1 -1 0 0
0 0 -1 -1 0 0
0 0 0 -2 0 0
0 0 -1 -1 -1 0
0 -1 0 1 0 1
1 or 2
167
First homology
of the double branched cover of 12a_0658
Z/167
-2 2
12a_0659
3

detected by
the signature
8-30t+58t^2-71t^3+58t^4-30t^5+8t^6
Seifert matrix of 12a_0659
-1 1 -1 -1 -1 0
0 -3 2 1 2 -1
0 1 -2 -1 -2 0
0 1 -1 -2 -1 -1
0 1 -1 -1 -2 0
0 -1 1 0 1 -2
1
Generator of the Alexander module
(1-t+t^2,0,0,t,0,0)
the Blanchfield form on it
-38t^-3+146t^-2-284t^-1+348-284t+146t^2-38t^3
263
First homology
of the double branched cover of 12a_0659
Z/263
-6 6
12a_0660
3

detected by
the signature
-2+10t-21t^2+31t^3-35t^4+31t^5-21t^6+10t^7-2t^8
Seifert matrix of 12a_0660
-1 0 -1 -1 -1 -1 0 -1
0 1 0 0 0 0 0 0
0 0 -2 -1 -1 -2 0 -1
0 -1 -2 -2 -2 -2 0 -2
0 0 -2 -1 -2 -2 0 -1
0 0 -1 -1 -1 -2 0 -1
0 -1 -1 -1 -1 -1 -1 -1
0 -1 -2 -1 -2 -2 0 -2
1
Generator of the Alexander module
(-3+4t-3t^2+t^3,0,0,1-2t+t^2,0,0,0,0)
the Blanchfield form on it
-2t^-3+6t^-2-9t^-1+10-9t+6t^2-2t^3
163
First homology
of the double branched cover of 12a_0660
Z/163
-6 6
12a_0661
2

detected by
the signature
-4+21t-44t^2+55t^3-44t^4+21t^5-4t^6
Seifert matrix of 12a_0661
-1 0 1 -1 0 -1
0 1 0 0 0 0
0 0 -3 1 0 1
0 -1 2 -2 0 -2
0 -1 1 -1 -1 -1
0 -1 2 -1 0 -2
1
Generator of the Alexander module
(-1+2t-5t^3+5t^4-6t^5+4t^7-4t^8,0,-1+t^2-t^3,-1+3t-3t^2-2t^3+13t^4-10t^5+10t^6+2t^7-8t^8+8t^9,2-2t^2+2t^3,1-t^2+t^3)
the Blanchfield form on it
x
193
First homology
of the double branched cover of 12a_0661
Z/193
-4 4
12a_0662
1

detected by
an unknotting move
1-8t+27t^2-52t^3+65t^4-52t^5+27t^6-8t^7+t^8
Seifert matrix of 12a_0662
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 1 -1 0 0 1 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 0 0 0
-1 0 0 -1 1 1 0 1
0 -1 0 0 0 0 -1 0
-1 0 0 -1 1 0 0 1
1
Generator of the Alexander module
(0,6t+3t^2-45t^3+90t^4-277t^5+556t^6-728t^7+517t^8-176t^9-30t^10+40t^11-8t^12,-10t^2-10t^3-2t^4-36t^5+120t^6-238t^7+206t^8-90t^9-6t^10+18t^11-4t^12,t+4t^2+48t^3-72t^4+217t^5-437t^6+625t^7-472t^8+179t^9+21t^10-38t^11+8t^12,-5t+5t^2-18t^3+29t^4-27t^5-7t^6+32t^7-31t^8+13t^9-2t^10,1-10t+17t^2-47t^3+87t^
the Blanchfield form on it
x
241
First homology
of the double branched cover of 12a_0662
Z/241
0 0
12a_0663
1

detected by
an unknotting move
3-17t+41t^2-53t^3+41t^4-17t^5+3t^6
Seifert matrix of 12a_0663
-1 0 0 0 0 0
0 2 0 0 -1 1
-1 0 -1 0 0 0
0 0 0 -1 -1 0
0 0 0 0 -1 0
1 1 1 -1 -1 2
1
Generator of the Alexander module
(0,7+2t,1,0,-7t-2t^2,-1-t)
the Blanchfield form on it
152t^-4-615t^-3+1206t^-2-1631t^-1+1756-1631t+1206t^2-615t^3+152t^4
175
First homology
of the double branched cover of 12a_0663
Z/175
-2 2
12a_0664
3

detected by
the Stoimenow criterion
1-8t+22t^2-34t^3+39t^4-34t^5+22t^6-8t^7+t^8
Seifert matrix of 12a_0664
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 1 -1 1 0 1 1
-1 0 0 -1 0 0 0 0
0 -1 0 0 -1 0 0 -1
-1 1 0 -1 0 1 0 0
0 -1 0 0 -1 0 -1 -1
0 -1 0 0 0 0 0 -1
2
169
First homology
of the double branched cover of 12a_0664
Z/13+Z/13
-4 4
12a_0665
2

detected by
the Lickorish test
2-17t+47t^2-63t^3+47t^4-17t^5+2t^6
Seifert matrix of 12a_0665
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 1 1 -1 -1 0
-1 0 0 -1 0 0
0 1 0 0 -2 0
-1 1 0 -1 0 1
1
Generator of the Alexander module
(-4t^2+2t^3+94t^4-136t^5+64t^6+8t^7-16t^8,-1+2t+35t^2-44t^3+12t^4+12t^5-8t^6,3+t-90t^2-28t^3+132t^4-64t^5-32t^6+32t^7,-2t+39t^3-80t^4+384t^5-400t^6+260t^7-316t^8+352t^9-160t^10-16t^11+32t^12,2-t-47t^2+68t^3-32t^4-4t^5+8t^6,2t-10t^2-70t^3+206t^4-208t^5+80t^6+8t^7-16t^8)
the Blanchfield form on it
x
195
First homology
of the double branched cover of 12a_0665
Z/195
-2 2
12a_0666
1

detected by
an unknotting move
3-20t+49t^2-63t^3+49t^4-20t^5+3t^6
Seifert matrix of 12a_0666
1 0 0 0 0 0
0 -1 0 0 0 0
1 -1 -2 -2 0 -1
1 -1 -1 -2 0 -1
0 0 -1 0 1 -1
1 0 -1 -1 0 -2
1 or 2
207
First homology
of the double branched cover of 12a_0666
Z/207
-2 2
12a_0667
1

detected by
an unknotting move
2-7t+15t^2-23t^3+27t^4-23t^5+15t^6-7t^7+2t^8
Seifert matrix of 12a_0667
-1 0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 0 1 0 1 0 1 0
0 0 1 0 1 1 1 1
0 0 0 0 0 0 1 0
0 0 1 0 1 0 1 1
1
Generator of the Alexander module
(-1,0,0,1,0,0,0,0)
the Blanchfield form on it
2t^-3-5t^-2+9t^-1-10+9t-5t^2+2t^3
121
First homology
of the double branched cover of 12a_0667
Z/121
0 0
12a_0668
1

detected by
an unknotting move
2-9t+23t^2-38t^3+45t^4-38t^5+23t^6-9t^7+2t^8
Seifert matrix of 12a_0668
-1 0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 1 1 1 1 0 1 0
0 -1 -1 0 -1 0 0 0
0 0 1 1 0 1 1 1
0 0 0 0 0 0 1 0
0 1 1 1 1 0 1 1
1
Generator of the Alexander module
(-t+t^2+t^3,-4t+2t^2+t^3-t^5-t^6,0,-1-4t+t^2-t^5-t^6,-1-13t+7t^2+t^3-t^4-3t^5-3t^6,-1+7t^2-5t^3-2t^4+2t^6+2t^7,9t-2t^2-t^3+2t^5+2t^6,-2-11t+6t^2-t^3-2t^4-2t^5-2t^6)
the Blanchfield form on it
x
189
First homology
of the double branched cover of 12a_0668
Z/189
0 2
12a_0669
1

detected by
an unknotting move
3-9t+14t^2-15t^3+14t^4-9t^5+3t^6
Seifert matrix of 12a_0669
-1 1 0 0 0 0
0 -3 0 0 0 0
0 -1 1 0 1 0
0 -1 1 1 1 1
0 0 0 0 1 0
0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-3t^-2+9t^-1-13+9t-3t^2
67
First homology
of the double branched cover of 12a_0669
Z/67
2 2
12a_0670
1

detected by
an unknotting move
2-11t+29t^2-48t^3+57t^4-48t^5+29t^6-11t^7+2t^8
Seifert matrix of 12a_0670
-1 0 0 -1 0 0 0 0
0 1 1 1 1 1 0 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 0 1 1 1 1 0 0
0 0 -1 -1 0 -1 0 0
0 1 0 1 1 0 1 1
0 1 1 1 1 0 0 1
1
Generator of the Alexander module
(t-t^3+2t^4-t^5,0,1+t^4,t^2-2t^3+t^4+t^5,2t-2t^2+t^5,1+t^4,t^2-2t^3+t^5-t^6,-t^4)
the Blanchfield form on it
x
237
First homology
of the double branched cover of 12a_0670
Z/237
0 2
12a_0671
2

detected by
the signature
2-9t+22t^2-34t^3+39t^4-34t^5+22t^6-9t^7+2t^8
Seifert matrix of 12a_0671
-1 0 0 -1 0 0 0 0
0 -1 -1 -1 0 -1 0 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 -1 -1 -1 -1 -1 0 0
0 0 -1 -1 0 -1 0 0
0 0 0 1 0 0 1 1
0 1 1 1 0 1 0 1
1
Generator of the Alexander module
(1-t,0,4-2t+2t^3,2-t+t^3,t+t^3,1,-2t+t^2-t^4,2-t+t^3)
the Blanchfield form on it
34t^-3-161t^-2+378t^-1-490+378t-161t^2+34t^3
173
First homology
of the double branched cover of 12a_0671
Z/173
-4 4
12a_0672
1

detected by
an unknotting move
-2+11t-29t^2+50t^3-59t^4+50t^5-29t^6+11t^7-2t^8
Seifert matrix of 12a_0672
-1 0 0 -1 0 0 0 0
0 -1 -1 -1 -1 -1 0 -1
0 0 1 0 0 0 0 1
0 0 0 -2 0 -1 0 0
0 0 -1 -1 -1 -1 0 0
0 0 1 0 0 1 0 1
0 -1 0 -1 -1 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(-t,0,0,1,2-3t+5t^2-2t^3,0,0,0)
the Blanchfield form on it
-6t^-3+29t^-2-61t^-1+79-61t+29t^2-6t^3
243
First homology
of the double branched cover of 12a_0672
Z/243
-2 2
12a_0673
1

detected by
an unknotting move
-1+8t-25t^2+43t^3-49t^4+43t^5-25t^6+8t^7-t^8
Seifert matrix of 12a_0673
-1 0 0 0 0 -1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 -1 0 1 -1 -1 0 1
-1 0 0 0 -1 -1 0 0
0 0 0 0 0 -1 0 0
-1 0 0 0 -1 -1 -1 0
0 0 0 0 -1 0 0 1
1
Generator of the Alexander module
(0,-2-2t+6t^2-4t^3+t^4,0,-2t-2t^2+6t^3-4t^4+t^5,-1+4t-3t^2+t^3,0,2t-12t^2+13t^3-6t^4+t^5,0)
the Blanchfield form on it
x
203
First homology
of the double branched cover of 12a_0673
Z/203
-2 2
12a_0674
2

detected by
the Lickorish test
1-8t+25t^2-47t^3+59t^4-47t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_0674
-1 0 0 0 0 -1 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
-1 -1 0 1 1 -1 0 1
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
-1 0 0 0 0 -1 -1 0
-1 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,-1,0,-2t+t^2,0,0,-2t^2+t^3,0)
the Blanchfield form on it
2t^-3-15t^-2+39t^-1-51+39t-15t^2+2t^3
221
First homology
of the double branched cover of 12a_0674
Z/221
0 0
12a_0675
2

detected by
the signature
2-10t+26t^2-42t^3+49t^4-42t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_0675
-1 0 -1 -1 -1 0 0 0
0 -1 -1 -1 -1 0 0 0
0 0 -2 -1 -2 0 0 0
0 0 -2 -2 -2 0 0 0
0 0 -1 -1 -2 0 0 0
0 -1 -1 -1 -1 -1 0 0
0 0 1 1 1 0 1 1
0 1 1 1 1 0 0 1
1
Generator of the Alexander module
(1-t,0,-t,-t,-t,-1,t^2,-t)
the Blanchfield form on it
-2t^-3+7t^-2-12t^-1+14-12t+7t^2-2t^3
209
First homology
of the double branched cover of 12a_0675
Z/209
-4 4
12a_0676
1

detected by
an unknotting move
3-14t+32t^2-41t^3+32t^4-14t^5+3t^6
Seifert matrix of 12a_0676
-1 0 1 0 0 0
0 -1 1 0 0 0
0 0 -3 0 0 0
0 -1 1 -1 0 0
0 0 -1 0 1 1
0 1 -1 0 0 1
1
Generator of the Alexander module
(0,0,0,-1,1,0)
the Blanchfield form on it
3t^-2-11t^-1+16-11t+3t^2
139
First homology
of the double branched cover of 12a_0676
Z/139
-2 2
12a_0677
2

detected by
the Lickorish test
4-18t+40t^2-51t^3+40t^4-18t^5+4t^6
Seifert matrix of 12a_0677
-1 -1 0 0 0 0
0 -2 0 0 0 0
0 -1 -1 1 0 0
0 1 0 -2 0 0
0 1 0 0 1 1
0 1 0 -1 0 1
1
Generator of the Alexander module
(t,0,0,0,-t,1)
the Blanchfield form on it
-4t^-2+12t^-1-16+12t-4t^2
175
First homology
of the double branched cover of 12a_0677
Z/175
-2 2
12a_0678
1

detected by
an unknotting move
4-19t+41t^2-51t^3+41t^4-19t^5+4t^6
Seifert matrix of 12a_0678
-1 0 0 -1 0 0
0 2 -1 -1 0 1
0 0 -1 -1 0 0
0 0 0 -2 0 0
0 0 -1 -1 -1 0
0 0 -1 0 0 1
1 or 2
179
First homology
of the double branched cover of 12a_0678
Z/179
-2 2
12a_0679
2

detected by
the Nakanishi index
7-20t+27t^2-20t^3+7t^4
Seifert matrix of 12a_0679
-1 -1 -1 -1
0 -2 -1 -2
0 -1 -4 -1
0 -1 -1 -2
2
81
First homology
of the double branched cover of 12a_0679
Z/27+Z/3
-4 4
12a_0680
1

detected by
an unknotting move
-2+10t-24t^2+40t^3-47t^4+40t^5-24t^6+10t^7-2t^8
Seifert matrix of 12a_0680
-1 0 -1 -1 -1 0 0 0
0 -1 -1 -1 -1 0 0 0
0 0 -2 -1 -2 0 0 0
0 0 -2 -2 -2 0 0 0
0 0 -1 -1 -2 0 0 0
0 1 1 1 1 1 0 0
0 0 1 1 1 1 1 1
0 0 1 1 1 1 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0,1,0)
the Blanchfield form on it
-2t^-1+4-2t
199
First homology
of the double branched cover of 12a_0680
Z/199
-2 2
12a_0681
2

detected by
the signature
1-7t+18t^2-29t^3+35t^4-29t^5+18t^6-7t^7+t^8
Seifert matrix of 12a_0681
-1 0 0 0 0 0 -1 0
0 -1 -1 -1 -1 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 -1 -1 0 -1 1 -1 0
0 0 0 0 0 0 -1 0
-1 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-3-7t^-2+16t^-1-19+16t-7t^2+t^3
145
First homology
of the double branched cover of 12a_0681
Z/145
-4 4
12a_0682
1

detected by
an unknotting move
2-12t+25t^2-29t^3+25t^4-12t^5+2t^6
Seifert matrix of 12a_0682
-1 0 0 0 -1 0
0 1 0 0 0 0
0 1 -2 0 0 0
0 0 1 1 -1 0
0 0 0 0 -1 0
-1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1+t,0,t^2)
the Blanchfield form on it
2t^-2-12t^-1+21-12t+2t^2
107
First homology
of the double branched cover of 12a_0682
Z/107
-2 2
12a_0683
3

detected by
the new u==2 criterion
1-7t+16t^2-22t^3+25t^4-22t^5+16t^6-7t^7+t^8
Seifert matrix of 12a_0683
-1 -1 0 0 0 -1 -1 0
0 -1 0 0 0 0 -1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 -1 0 1 -1 -1 0
0 -1 0 0 0 -1 -1 0
0 0 0 0 0 0 -1 0
-1 -1 0 0 0 -1 -1 -1
2
117
First homology
of the double branched cover of 12a_0683
Z/39+Z/3
-4 4
12a_0684
2

detected by
the Lickorish test
2-14t+32t^2-39t^3+32t^4-14t^5+2t^6
Seifert matrix of 12a_0684
-1 1 0 0 0 0
0 -2 0 0 0 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 1 -1 0 1 0
-1 1 0 0 0 -1
1
Generator of the Alexander module
(0,1-t,-1+2t,-1,t^2,-1+t)
the Blanchfield form on it
2t^-2-13t^-1+23-13t+2t^2
135
First homology
of the double branched cover of 12a_0684
Z/135
-2 2
12a_0685
2

detected by
the signature
-4+21t-46t^2+59t^3-46t^4+21t^5-4t^6
Seifert matrix of 12a_0685
-1 0 -1 0 0 0
0 -1 0 0 -1 0
0 0 -2 0 0 0
0 0 -1 -1 1 0
0 0 1 0 -2 0
0 1 1 0 0 1
1 or 2
201
First homology
of the double branched cover of 12a_0685
Z/201
-4 4
12a_0686
2

detected by
the signature
-5+23t-47t^2+59t^3-47t^4+23t^5-5t^6
Seifert matrix of 12a_0686
1 0 0 0 0 0
0 -1 0 0 0 0
1 -1 -2 -1 0 -2
1 0 -1 -2 1 -1
0 -1 -1 0 -2 -1
1 -1 -1 -1 0 -2
1 or 2
209
First homology
of the double branched cover of 12a_0686
Z/209
-4 4
12a_0687
1

detected by
an unknotting move
3-21t+53t^2-69t^3+53t^4-21t^5+3t^6
Seifert matrix of 12a_0687
-2 1 1 0 0 -1
0 -1 -1 0 0 0
0 0 1 0 0 0
-1 0 0 -1 0 -1
1 -1 0 0 1 0
-1 1 1 0 0 -2
1
Generator of the Alexander module
(-3-16t+27t^2+6t^3-104t^4+148t^5-104t^6+32t^7,1+3t-6t^2-2t^3+26t^4-37t^5+26t^6-8t^7,-2+5t-5t^2+2t^3,-1-3t+8t^2-9t^3-2t^4+10t^5-10t^6+4t^7,1-2t+8t^2-3t^3-7t^4+17t^5-2t^6-10t^7+10t^8-4t^9,-5+5t^2+6t^3-52t^4+74t^5-52t^6+16t^7)
the Blanchfield form on it
x
223
First homology
of the double branched cover of 12a_0687
Z/223
-2 2
12a_0688
2

detected by
the signature
2-10t+26t^2-42t^3+49t^4-42t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_0688
-1 0 -1 -1 -1 0 0 0
0 1 0 0 0 0 0 0
0 0 -2 -1 -2 0 -1 0
0 0 -2 -2 -2 0 -1 0
0 0 -1 -1 -2 0 -1 0
0 -1 -1 -1 -1 -1 -1 0
0 1 0 0 0 0 1 0
0 -1 -1 -1 -1 -1 -1 -1
1
Generator of the Alexander module
(-2t^2-t^4+t^5,0,-2-t^2+t^3,-2+2t^2+t^3-t^4,4+4t-4t^2,-1-t+t^2-4t^3-2t^5+2t^6,-2t^2-t^4+t^5,-4t^2-2t^3-2t^4+t^5+t^6)
the Blanchfield form on it
x
209
First homology
of the double branched cover of 12a_0688
Z/209
-4 4
12a_0689
2

detected by
the Lickorish test
2-13t+29t^2-35t^3+29t^4-13t^5+2t^6
Seifert matrix of 12a_0689
-2 0 0 0 0 0
0 -1 -1 -1 -1 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 0 -1 -1 -1 0
1 -1 -1 0 -1 1
1
Generator of the Alexander module
(0,0,4-4t+4t^2-t^3,0,0,-3+t)
the Blanchfield form on it
-2t^-2+5t^-1-5+5t-2t^2
123
First homology
of the double branched cover of 12a_0689
Z/123
-2 2
12a_0690
1

detected by
an unknotting move
4-22t+37t^2-22t^3+4t^4
Seifert matrix of 12a_0690
-2 0 0 0
0 1 0 0
0 1 -2 0
1 0 1 1
1 or 2
89
First homology
of the double branched cover of 12a_0690
Z/89
0 0
12a_0691
1

detected by
an unknotting move
3-19t+33t^2-19t^3+3t^4
Seifert matrix of 12a_0691
-1 -1 0 0
0 1 0 0
-1 0 1 -1
0 0 0 -3
1 or 2
77
First homology
of the double branched cover of 12a_0691
Z/77
0 0
12a_0692
2

detected by
the Nakanishi index
2-8t+19t^2-30t^3+35t^4-30t^5+19t^6-8t^7+2t^8
Seifert matrix of 12a_0692
-1 0 0 0 0 0 0 0
0 1 0 1 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
-1 0 0 0 -1 0 0 0
0 0 0 0 0 1 0 1
1 -1 1 -1 1 1 2 1
0 0 0 0 0 0 0 1
2
153
First homology
of the double branched cover of 12a_0692
Z/51+Z/3
4 4
12a_0693
2

detected by
the signature
1-7t+18t^2-28t^3+33t^4-28t^5+18t^6-7t^7+t^8
Seifert matrix of 12a_0693
1 0 1 0 0 0 0 0
0 -1 0 0 0 -1 -1 -1
0 0 1 0 0 0 0 0
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
1 0 1 -1 0 1 0 0
1 0 1 -1 0 1 1 1
1 0 1 -1 0 1 0 1
2
141
First homology
of the double branched cover of 12a_0693
Z/141
4 4
12a_0694
3

detected by
the signature
-2+10t-21t^2+30t^3-33t^4+30t^5-21t^6+10t^7-2t^8
Seifert matrix of 12a_0694
1 0 0 0 0 0 0 0
0 -1 0 -1 0 0 0 0
1 -1 -2 -1 1 0 -1 0
0 0 0 -1 0 0 0 0
-1 0 0 0 -1 0 0 0
0 0 -1 0 0 -1 -1 -1
1 -1 -2 -1 1 0 -2 0
0 0 -1 0 0 0 -1 -1
2
159
First homology
of the double branched cover of 12a_0694
Z/159
-6 6
12a_0695
1

detected by
an unknotting move
-1+8t-29t^2+61t^3-77t^4+61t^5-29t^6+8t^7-t^8
Seifert matrix of 12a_0695
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
0 -1 -1 0 -1 0 0 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 0 1 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 1 1 0
0 -1 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,-t+t^2+2t^3+2t^4,1-4t+4t^3,-1+t+t^2,-t+t^2+2t^3+2t^4,1-t-2t^2-2t^3,-1-2t+t^2+2t^3+2t^4,-4+t+3t^2+4t^3)
the Blanchfield form on it
t^-3-7t^-2+18t^-1-24+18t-7t^2+t^3
275
First homology
of the double branched cover of 12a_0695
Z/275
-2 2
12a_0696
1

detected by
an unknotting move
1-8t+29t^2-61t^3+79t^4-61t^5+29t^6-8t^7+t^8
Seifert matrix of 12a_0696
-1 -1 -1 -1 1 0 -1 1
0 -1 -1 -1 0 0 0 1
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 -1 0 0 0 1 -1 0
0 -1 -1 -1 1 0 -1 1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(t-7t^2+26t^3-25t^4-13t^5+28t^6-13t^7+2t^8,0,7-13t+16t^2+10t^3-2t^4-17t^5+11t^6-2t^7,1+7t-31t^2+51t^3-17t^4-15t^5+11t^6-2t^7,1-7t+26t^2-25t^3-13t^4+28t^5-13t^6+2t^7,-3t-5t^2+36t^3-82t^4+73t^5-28t^6+4t^7,-2+5t^2-26t^3+30t^4-13t^5+2t^6,-1-7t+31t^2-51t^3+17t^4+15t^5-11t^6+2t^7)
the Blanchfield form on it
x
277
First homology
of the double branched cover of 12a_0696
Z/277
0 0
12a_0697
1

detected by
an unknotting move
-1+9t-33t^2+66t^3-83t^4+66t^5-33t^6+9t^7-t^8
Seifert matrix of 12a_0697
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
0 0 -1 0 0 0 -1 0
-1 0 0 -1 -1 -1 0 0
0 0 0 0 1 1 -1 1
0 0 0 0 0 1 -1 1
0 0 0 0 0 0 -1 0
0 0 -1 0 0 0 -1 1
1
Generator of the Alexander module
(-2+t,6-7t+6t^2-2t^3,-2+t,1+4t-2t^2,-2+3t-3t^2+t^3,-2+5t-4t^2+t^3,-2t+t^2,0)
the Blanchfield form on it
-27t^-3+181t^-2-434t^-1+583-434t+181t^2-27t^3
301
First homology
of the double branched cover of 12a_0697
Z/301
0 0
12a_0698
1

detected by
an unknotting move
1-8t+28t^2-55t^3+67t^4-55t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0698
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 -1 -1 -1
0 0 -1 0 0 0 0 0
0 0 -1 1 0 0 0 0
-1 0 0 0 -1 -1 -1 0
0 0 0 1 0 1 1 1
0 0 0 1 0 0 1 1
0 0 -1 1 0 0 0 1
1
Generator of the Alexander module
(0,1-t+t^2,0,0,2-2t+t^2,0,0,0)
the Blanchfield form on it
-2t^-3+15t^-2-42t^-1+51-42t+15t^2-2t^3
251
First homology
of the double branched cover of 12a_0698
Z/251
2 2
12a_0699
1

detected by
an unknotting move
1-8t+28t^2-57t^3+73t^4-57t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0699
-1 0 0 1 -1 0 -1 0
-1 1 -1 0 0 -1 -1 1
-1 0 -1 0 -1 -1 -1 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
-1 0 0 1 -1 -1 -1 0
0 0 0 1 -1 0 -1 0
0 0 -1 0 0 -1 0 1
1
Generator of the Alexander module
(0,-2t+22t^2-26t^3+20t^4-66t^5+118t^6-121t^7+74t^8-26t^9+4t^10,3+7t+2t^2-13t^3-14t^4+48t^5-56t^6+36t^7-13t^8+2t^9,5+6t-3t^2-4t^3+7t^5-11t^6+7t^7-2t^8,-3-2t-2t^2+6t^3-7t^5+11t^6-7t^7+2t^8,6t-t^2+5t^3-39t^4+68t^5-65t^6+38t^7-13t^8+2t^9,-6t^2+t^3-5t^4+39t^5-68t^6+65t^7-38t^8+13t^9-2t^10,6t^2+2t^3+6t^4-
the Blanchfield form on it
x
261
First homology
of the double branched cover of 12a_0699
Z/261
0 0
12a_0700
1

detected by
an unknotting move
1-7t+26t^2-56t^3+73t^4-56t^5+26t^6-7t^7+t^8
Seifert matrix of 12a_0700
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
-1 1 1 -1 1 0 1 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 0 1 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 1 1 0
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(1+3t-9t^2+7t^3+t^4-3t^5+t^6,-3+4t+2t^2-9t^3+4t^4+t^5-t^6,1-4t+13t^2-19t^3+16t^4-2t^5-4t^6+2t^7,6t^2-20t^3+43t^4-46t^5+29t^6-9t^8+4t^9,-3+3t+7t^2-18t^3+12t^4-3t^6+t^7,-2+6t-7t^2+t^3+2t^4-t^5,1+3t-9t^2+7t^3+t^4-3t^5+t^6,-3+10t-13t^2+13t^3-31t^4+43t^5-31t^6+t^7+9t^8-4t^9)
the Blanchfield form on it
x
253
First homology
of the double branched cover of 12a_0700
Z/253
0 0
12a_0701
2

detected by
the Nakanishi index
2-10t+27t^2-46t^3+55t^4-46t^5+27t^6-10t^7+2t^8
Seifert matrix of 12a_0701
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 1 -1 0 -1 0 1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 1 0
0 1 0 0 1 2 1 0
0 0 0 0 0 0 1 0
-1 0 0 -1 0 -1 0 1
2
225
First homology
of the double branched cover of 12a_0701
Z/75+Z/3
4 4
12a_0702
2

detected by
the signature
1-7t+20t^2-34t^3+41t^4-34t^5+20t^6-7t^7+t^8
Seifert matrix of 12a_0702
-1 0 -1 0 0 -1 -1 0
0 1 1 -1 0 1 1 1
0 0 1 0 0 0 0 0
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 0 1 -1 0 1 1 0
0 0 1 0 0 0 1 0
0 0 1 -1 0 1 1 1
1
Generator of the Alexander module
(-1,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+7t^-2-17t^-1+21-17t+7t^2-t^3
165
First homology
of the double branched cover of 12a_0702
Z/165
4 4
12a_0703
2

detected by
the Lickorish test
-1+9t-32t^2+64t^3-79t^4+64t^5-32t^6+9t^7-t^8
Seifert matrix of 12a_0703
-1 0 0 1 -1 0 -1 0
-1 1 -1 0 0 0 -1 1
-1 0 -1 1 -1 1 -1 0
0 0 0 1 0 1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 1 -1 0 -1 0
0 0 -1 0 0 0 0 1
2
291
First homology
of the double branched cover of 12a_0703
Z/291
2 2
12a_0704
2

detected by
the Lickorish test
-1+8t-24t^2+43t^3-51t^4+43t^5-24t^6+8t^7-t^8
Seifert matrix of 12a_0704
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
-1 1 1 -1 0 0 1 1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 -1 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 1 1 0
-1 1 0 -1 0 0 1 1
1
Generator of the Alexander module
(0,-4t,-2,0,0,0,-2,1)
the Blanchfield form on it
-15t^-3-53t^-2+239t^-1-401+239t-53t^2-15t^3
203
First homology
of the double branched cover of 12a_0704
Z/203
2 2
12a_0705
1

detected by
an unknotting move
-1+9t-33t^2+68t^3-87t^4+68t^5-33t^6+9t^7-t^8
Seifert matrix of 12a_0705
1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 -1
-1 0 -1 -1 0 -1 0 -1
0 0 0 1 1 0 -1 1
0 0 0 0 1 0 0 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 1 0 -1 1
1
Generator of the Alexander module
(0,-3t^3+t^4-6t^5,1-t+t^2+3t^3-5t^5+5t^6-11t^7-6t^8,-t+3t^2-9t^3+9t^4-14t^5+14t^6-12t^7,t-3t^3-t^4-2t^5-5t^6-6t^7,-t+3t^2-4t^3+9t^4-8t^5+12t^6,-3t^3-5t^4-4t^5-12t^6,0)
the Blanchfield form on it
x
309
First homology
of the double branched cover of 12a_0705
Z/309
0 0
12a_0706
1

detected by
an unknotting move
1-7t+24t^2-46t^3+57t^4-46t^5+24t^6-7t^7+t^8
Seifert matrix of 12a_0706
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
0 0 -1 0 -1 0 0 -1
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 0 1 1
0 0 0 0 0 -1 0 0
0 0 0 0 0 1 1 0
0 1 0 0 0 1 1 1
1
Generator of the Alexander module
(0,0,-2,1,2,0,1,0)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
213
First homology
of the double branched cover of 12a_0706
Z/213
0 2
12a_0707
1

detected by
an unknotting move
1-8t+29t^2-59t^3+75t^4-59t^5+29t^6-8t^7+t^8
Seifert matrix of 12a_0707
-1 -1 -1 -1 1 0 -1 0
0 -1 -1 -1 1 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 -1 -1 0 0 1 -1 1
0 -1 -1 -1 1 0 -1 0
0 -1 0 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,1+t+t^2,0,-t,0,0,-1-2t^2)
the Blanchfield form on it
t^-3-6t^-2+15t^-1-20+15t-6t^2+t^3
269
First homology
of the double branched cover of 12a_0707
Z/269
0 0
12a_0708
1

detected by
an unknotting move
-1+7t-22t^2+42t^3-51t^4+42t^5-22t^6+7t^7-t^8
Seifert matrix of 12a_0708
-1 -1 -1 -1 1 0 -1 -1
0 -1 -1 -1 1 0 0 -1
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 -1 0 0 0 1 -1 -1
0 -1 -1 -1 1 0 -1 -1
0 0 -1 -1 0 0 0 -1
1
Generator of the Alexander module
(2,0,1,0,0,-1,0,0)
the Blanchfield form on it
-3t^-3+26t^-2-68t^-1+95-68t+26t^2-3t^3
195
First homology
of the double branched cover of 12a_0708
Z/195
-2 2
12a_0709
2

detected by
the Lickorish test
1-8t+28t^2-57t^3+71t^4-57t^5+28t^6-8t^7+t^8
Seifert matrix of 12a_0709
1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 -1
-1 0 -1 -1 0 -1 0 0
0 0 0 1 1 1 -1 1
0 0 0 0 1 0 0 0
0 0 0 0 1 1 -1 1
0 0 0 0 0 0 -1 0
0 0 0 0 1 0 -1 1
1
Generator of the Alexander module
(0,-3+9t-20t^2+28t^3-28t^4+19t^5-7t^6+t^7,-2-t+3t^2-7t^3+5t^4-t^5,0,0,-3t+9t^2-20t^3+28t^4-28t^5+19t^6-7t^7+t^8,-3+12t-23t^2+27t^3-19t^4+7t^5-t^6,0)
the Blanchfield form on it
x
259
First homology
of the double branched cover of 12a_0709
Z/259
2 2
12a_0710
2

detected by
the Lickorish test
-1+9t-33t^2+66t^3-81t^4+66t^5-33t^6+9t^7-t^8
Seifert matrix of 12a_0710
-1 0 0 1 -1 0 -1 0
-1 1 -1 0 0 1 -1 1
-1 0 -1 0 -1 0 -1 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 -1 0 0 1 0 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 1 0 1
1
Generator of the Alexander module
(0,1-3t+t^2,0,0,0,0,0,3-t)
the Blanchfield form on it
2t^-3-11t^-2+26t^-1-33+26t-11t^2+2t^3
299
First homology
of the double branched cover of 12a_0710
Z/299
2 2
12a_0711
1

detected by
an unknotting move
-1+8t-27t^2+53t^3-65t^4+53t^5-27t^6+8t^7-t^8
Seifert matrix of 12a_0711
-1 0 -1 0 0 0 -1 -1
0 1 1 -1 0 1 1 0
0 0 1 0 0 0 0 0
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 0 1 -1 0 1 1 0
0 0 1 0 0 0 1 0
0 0 -1 0 0 -1 -1 -1
1
Generator of the Alexander module
(-1-3t+5t^2-2t^3,-2-6t+9t^2-2t^3-t^4,0,t-2t^2+t^3,0,0,1-2t+t^2,-4-12t+18t^2-4t^3-2t^4)
the Blanchfield form on it
894t^-3-4417t^-2+10188t^-1-13328+10188t-4417t^2+894t^3
243
First homology
of the double branched cover of 12a_0711
Z/243
2 2
12a_0712
2

detected by
the Nakanishi index
-1+9t-34t^2+70t^3-87t^4+70t^5-34t^6+9t^7-t^8
Seifert matrix of 12a_0712
-1 0 0 -1 0 -1 -1 0
0 1 0 0 0 0 0 0
0 0 1 -1 0 0 -1 1
0 1 0 -1 1 -1 -1 0
0 1 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 1 -1 -1 0
0 0 0 -1 0 0 0 1
2
315
First homology
of the double branched cover of 12a_0712
Z/105+Z/3
2 2
12a_0713
1

detected by
an unknotting move
-2+8t-17t^2+27t^3-31t^4+27t^5-17t^6+8t^7-2t^8
Seifert matrix of 12a_0713
-1 0 0 0 -1 0 0 0
0 -1 0 0 -1 0 -1 0
0 0 1 0 0 0 0 0
0 0 1 1 0 0 0 1
0 0 0 0 -2 0 0 0
0 -1 0 0 -1 -1 -1 0
0 0 -1 -1 -1 0 -1 -1
0 0 1 0 0 0 0 1
1
Generator of the Alexander module
(-t+t^2+t^4,0,0,1+t+t^2+t^3,1+t^2,-t-t^2-t^3-t^4,-t^3,0)
the Blanchfield form on it
t^-2-t^-1+2-t+t^2
139
First homology
of the double branched cover of 12a_0713
Z/139
-2 2
12a_0714
1

detected by
an unknotting move
-2+8t-15t^2+19t^3-19t^4+19t^5-15t^6+8t^7-2t^8
Seifert matrix of 12a_0714
-1 0 0 0 -1 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 1 0
0 1 1 1 0 0 1 1
0 0 0 0 -2 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 1 0
0 1 1 0 0 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-3t^-1+3-3t+3t^2-t^3
107
First homology
of the double branched cover of 12a_0714
Z/107
2 2
12a_0715
1

detected by
an unknotting move
-4+18t-38t^2+49t^3-38t^4+18t^5-4t^6
Seifert matrix of 12a_0715
-1 0 0 0 -1 0
0 1 0 0 0 0
0 -1 2 0 0 0
0 1 -1 1 0 0
0 0 0 0 -2 0
0 -1 1 -1 -1 -1
1 or 2
169
First homology
of the double branched cover of 12a_0715
Z/169
0 0
12a_0716
3

detected by
the signature
1-3t+5t^2-5t^3+5t^4-5t^5+5t^6-5t^7+5t^8-3t^9+t^10
Seifert matrix of 12a_0716
-1 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0 0 0
0 1 1 0 0 0 1 1 0 0
0 1 1 1 0 0 1 1 1 0
-1 0 0 0 -1 0 0 0 0 0
-1 1 1 1 -1 1 1 1 1 1
0 0 0 0 0 0 1 0 0 0
0 1 0 0 0 0 1 1 0 0
0 1 1 0 0 0 1 1 1 0
0 1 1 1 0 0 1 1 1 1
1
Generator of the Alexander module
(0,0,0,0,t,1+t,0,0,0,0)
the Blanchfield form on it
t^-4-t^-3+t^-2-t^-1+1-t+t^2-t^3+t^4
43
First homology
of the double branched cover of 12a_0716
Z/43
6 6
12a_0717
2

detected by
the signature
2-7t+13t^2-15t^3+15t^4-15t^5+13t^6-7t^7+2t^8
Seifert matrix of 12a_0717
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
0 1 1 0 0 0 1 1
0 -1 -1 2 0 0 -1 -1
-1 0 0 0 -1 0 0 0
-1 1 1 -1 -1 1 1 1
0 0 0 0 0 0 1 0
0 1 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,t,1+t,0,0)
the Blanchfield form on it
2t^-3-3t^-2+3t^-1-3+3t-3t^2+2t^3
89
First homology
of the double branched cover of 12a_0717
Z/89
4 4
12a_0718
2

detected by
the signature
2-8t+18t^2-27t^3+31t^4-27t^5+18t^6-8t^7+2t^8
Seifert matrix of 12a_0718
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
0 -1 2 1 0 0 -1 1
0 -1 2 2 0 0 -1 2
-1 0 0 0 -1 0 0 0
-1 1 -1 -1 -1 1 1 -1
0 0 0 0 0 0 1 0
0 -1 2 1 0 0 -1 2
1
Generator of the Alexander module
(0,0,0,0,t,1+t,0,0)
the Blanchfield form on it
2t^-3-4t^-2+6t^-1-7+6t-4t^2+2t^3
141
First homology
of the double branched cover of 12a_0718
Z/141
4 4
12a_0719
1

detected by
an unknotting move
4-16t+33t^2-41t^3+33t^4-16t^5+4t^6
Seifert matrix of 12a_0719
-1 0 0 0 0 0
0 2 0 0 0 0
0 -1 1 0 0 0
0 1 -1 2 0 0
-1 0 0 0 -1 0
-1 -1 1 -1 -1 1
1 or 2
147
First homology
of the double branched cover of 12a_0719
Z/147
2 2
12a_0720
2

detected by
the signature
-2+8t-16t^2+20t^3-21t^4+20t^5-16t^6+8t^7-2t^8
Seifert matrix of 12a_0720
-1 0 0 0 0 0 0 0
0 2 1 1 0 0 1 1
0 2 2 1 0 0 2 1
0 2 2 2 0 0 2 2
-1 0 0 0 -1 0 0 0
-1 -1 -1 -1 -1 1 -1 -1
0 2 1 1 0 0 2 1
0 2 2 1 0 0 2 2
1
Generator of the Alexander module
(0,0,0,0,t,1+t,0,0)
the Blanchfield form on it
-2t^-3+4t^-2-5t^-1+5-5t+4t^2-2t^3
113
First homology
of the double branched cover of 12a_0720
Z/113
4 4
12a_0721
1

detected by
an unknotting move
4-18t+39t^2-49t^3+39t^4-18t^5+4t^6
Seifert matrix of 12a_0721
-1 0 0 0 0 0
0 2 -1 1 0 0
0 -2 3 -1 0 0
0 2 -2 2 0 0
-1 0 0 0 -1 0
-1 -1 1 -1 -1 1
1 or 2
171
First homology
of the double branched cover of 12a_0721
Z/171
2 2
12a_0722
4

detected by
the signature
1-3t+3t^2-3t^3+3t^4-3t^5+3t^6-3t^7+3t^8-3t^9+t^10
Seifert matrix of 12a_0722
1 0 0 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 0 -1 -1 -1 -1 0 -1 -1 -1
-1 0 0 -1 -1 -1 0 0 -1 -1
-1 0 0 0 -1 -1 0 0 0 -1
-1 0 0 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1 -1 -1
-1 0 0 -1 -1 -1 0 -1 -1 -1
-1 0 0 0 -1 -1 0 0 -1 -1
-1 0 0 0 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,t,1,0,0,0,0)
the Blanchfield form on it
2t^-4-7t^-3+9t^-2-8t^-1+6-8t+9t^2-7t^3+2t^4
29
First homology
of the double branched cover of 12a_0722
Z/29
-8 8
12a_0723
3

detected by
the signature
-2+7t-9t^2+9t^3-9t^4+9t^5-9t^6+7t^7-2t^8
Seifert matrix of 12a_0723
1 0 0 0 0 0 0 0
-1 -1 -1 -1 1 -1 -1 -1
-1 0 -1 -1 1 -1 0 -1
-1 0 0 -1 1 -1 0 0
1 0 0 0 -2 1 0 0
-1 0 0 0 0 -1 0 0
-1 0 -1 -1 1 -1 -1 -1
-1 0 0 -1 1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+6t^-2-6t^-1+6-6t+6t^2-4t^3+t^4
63
First homology
of the double branched cover of 12a_0723
Z/63
-6 6
12a_0724
3

detected by
the signature
-2+8t-14t^2+19t^3-21t^4+19t^5-14t^6+8t^7-2t^8
Seifert matrix of 12a_0724
1 0 0 0 0 0 0 0
-1 -1 -1 1 1 -1 -1 1
-1 0 -1 1 1 -1 0 1
1 0 0 -2 -2 1 0 -2
1 0 0 -1 -2 1 0 -1
-1 0 0 0 0 -1 0 0
-1 0 -1 1 1 -1 -1 1
1 0 0 -1 -2 1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-9t^-1+9-9t+7t^2-2t^3
107
First homology
of the double branched cover of 12a_0724
Z/107
-6 6
12a_0725
3

detected by
the new u==2 criterion
-4+16t-25t^2+27t^3-25t^4+16t^5-4t^6
Seifert matrix of 12a_0725
1 0 0 0 0 0
-1 -1 1 -1 1 -1
1 0 -2 1 -1 1
-1 0 0 -1 1 -1
1 0 0 0 -2 1
-1 0 0 0 0 -1
2
117
First homology
of the double branched cover of 12a_0725
Z/39+Z/3
-4 4
12a_0726
3

detected by
the signature
-2+8t-14t^2+18t^3-19t^4+18t^5-14t^6+8t^7-2t^8
Seifert matrix of 12a_0726
1 0 0 0 0 0 0 0
-1 -1 1 1 1 -1 1 1
1 0 -2 -2 -2 1 -2 -2
1 0 -1 -2 -2 1 -1 -2
1 0 -1 -1 -2 1 -1 -1
-1 0 0 0 0 -1 0 0
1 0 -1 -2 -2 1 -2 -2
1 0 -1 -1 -2 1 -1 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+8t^-2-14t^-1+17-14t+8t^2-2t^3
103
First homology
of the double branched cover of 12a_0726
Z/103
-6 6
12a_0727
2

detected by
the signature
-4+18t-35t^2+43t^3-35t^4+18t^5-4t^6
Seifert matrix of 12a_0727
1 0 0 0 0 0
-1 -1 1 -1 1 -1
1 0 -2 2 -2 1
-1 0 1 -3 2 -1
1 0 -1 1 -2 1
-1 0 0 0 0 -1
1 or 2
157
First homology
of the double branched cover of 12a_0727
Z/157
-4 4
12a_0728 1 or 2
2-8t+17t^2-25t^3+29t^4-25t^5+17t^6-8t^7+2t^8
Seifert matrix of 12a_0728
-1 0 0 0 -1 0 0 0
0 1 0 0 0 0 0 -1
0 1 1 0 0 1 0 -1
0 0 0 -1 -1 0 0 0
0 0 0 0 -2 0 0 0
0 1 0 0 0 1 0 -1
0 1 1 0 0 1 1 -1
0 0 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-5+5t-3t^2+t^3
133
First homology
of the double branched cover of 12a_0728
Z/133
0 2
12a_0729
1

detected by
an unknotting move
4-18t+38t^2-47t^3+38t^4-18t^5+4t^6
Seifert matrix of 12a_0729
-1 0 0 0 -1 0
0 1 0 0 0 -1
0 -1 2 0 0 1
0 0 0 -1 -1 0
0 0 0 0 -2 0
0 0 0 -1 -1 -1
1 or 2
167
First homology
of the double branched cover of 12a_0729
Z/167
-2 2
12a_0730
2

detected by
the signature
-4+18t-34t^2+41t^3-34t^4+18t^5-4t^6
Seifert matrix of 12a_0730
1 0 0 0 0 0
-1 -1 1 1 1 1
1 0 -2 -2 -2 -1
1 0 -1 -2 -1 -1
1 0 -1 -2 -2 -1
1 0 0 0 0 -2
1
Generator of the Alexander module
(-1-t,-1-t,1+t+t^2,2+t+t^2,1+t-t^2-2t^3,4t^2)
the Blanchfield form on it
-14t^-5+64t^-4-67t^-3-138t^-2+484t^-1-658+484t-138t^2-67t^3+64t^4-14t^5
153
First homology
of the double branched cover of 12a_0730
Z/153
-4 4
12a_0731
2

detected by
the signature
-4+14t-22t^2+25t^3-22t^4+14t^5-4t^6
Seifert matrix of 12a_0731
-1 0 -1 0 0 0
0 -1 -1 0 -1 0
0 0 -2 0 0 0
0 -1 -1 -1 -1 0
0 0 -1 0 -1 1
0 0 0 0 0 2
1 or 2
105
First homology
of the double branched cover of 12a_0731
Z/105
-4 4
12a_0732
1

detected by
an unknotting move
3-11t+21t^2-25t^3+21t^4-11t^5+3t^6
Seifert matrix of 12a_0732
-1 0 0 0 0 0
0 1 0 0 1 0
-1 0 -1 0 0 0
-1 1 -1 1 1 1
0 0 0 0 1 0
0 1 0 0 1 3
1
Generator of the Alexander module
(0,0,t,1+t,0,0)
the Blanchfield form on it
3t^-2-5t^-1+5-5t+3t^2
95
First homology
of the double branched cover of 12a_0732
Z/95
2 2
12a_0733
2

detected by
the signature
-3+11t-15t^2+15t^3-15t^4+11t^5-3t^6
Seifert matrix of 12a_0733
1 0 0 0 0 0
-1 -1 -1 -1 -1 -1
-1 0 -1 -1 0 -1
-1 0 0 -1 0 0
-1 0 -1 -1 -1 -1
-1 0 0 -1 0 -3
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-4t^-2+6t^-1-6+6t-4t^2+t^3
73
First homology
of the double branched cover of 12a_0733
Z/73
-4 4
12a_0734
1

detected by
an unknotting move
-2+10t-26t^2+46t^3-55t^4+46t^5-26t^6+10t^7-2t^8
Seifert matrix of 12a_0734
-1 0 0 0 -1 0 0 0
0 1 0 0 0 0 0 0
0 0 -1 -1 -1 0 -1 0
0 1 0 1 0 0 1 0
0 0 0 0 -2 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 1 0
0 0 -1 -1 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,-3+12t-9t^2+6t^3-t^4,-2-3t+t^2-2t^3,-4+2t-2t^2,8t-4t^2+4t^3,0,4t-2t^2+2t^3)
the Blanchfield form on it
-2t^-2+6t^-1-8+6t-2t^2
223
First homology
of the double branched cover of 12a_0734
Z/223
-2 2
12a_0735
2

detected by
the Lickorish test
-6+25t-37t^2+25t^3-6t^4
Seifert matrix of 12a_0735
1 0 0 0
-1 -1 1 -1
1 0 -2 1
-1 0 0 -3
1
Generator of the Alexander module
(0,0,2,1)
the Blanchfield form on it
16t^-2-71t^-1+110-71t+16t^2
99
First homology
of the double branched cover of 12a_0735
Z/99
-2 2
12a_0736
1

detected by
an unknotting move
-4+16t-31t^2+39t^3-31t^4+16t^5-4t^6
Seifert matrix of 12a_0736
-1 0 -1 0 0 0
0 1 0 0 0 1
0 0 -2 0 0 0
0 0 -1 -1 1 0
0 1 0 0 2 1
0 0 0 0 0 1
1 or 2
141
First homology
of the double branched cover of 12a_0736
Z/141
0 2
12a_0737
2

detected by
the signature
2-9t+21t^2-32t^3+37t^4-32t^5+21t^6-9t^7+2t^8
Seifert matrix of 12a_0737
-1 0 0 0 0 0 0 0
0 2 1 1 0 0 1 1
0 2 2 1 0 0 1 2
0 0 0 1 0 0 0 0
-1 0 0 0 -1 0 0 0
-1 -1 -1 0 -1 1 0 -1
0 0 0 1 0 0 1 0
0 2 1 1 0 0 1 2
1
Generator of the Alexander module
(0,-t-t^2,1+t,-1,-t+t^2-3t^3+t^4,-3+t-4t^3+t^4,0,0)
the Blanchfield form on it
2t^-2-3t^-1+4-3t+2t^2
165
First homology
of the double branched cover of 12a_0737
Z/165
4 4
12a_0738
2

detected by
the Lickorish test
3-13t+27t^2-33t^3+27t^4-13t^5+3t^6
Seifert matrix of 12a_0738
-1 0 0 0 0 0
0 1 0 0 0 1
-1 0 -1 0 0 0
-1 0 -1 1 1 0
0 1 0 0 3 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,t,1+t,0,0)
the Blanchfield form on it
3t^-2-7t^-1+9-7t+3t^2
119
First homology
of the double branched cover of 12a_0738
Z/119
2 2
12a_0739
3

detected by
the signature
-2+9t-19t^2+28t^3-31t^4+28t^5-19t^6+9t^7-2t^8
Seifert matrix of 12a_0739
1 0 0 0 0 0 0 0
-1 -1 1 1 0 -1 0 1
1 0 -2 -2 -1 1 -1 -2
1 0 -1 -2 -1 1 -1 -1
0 0 0 0 -1 0 0 0
-1 0 0 0 0 -1 0 0
0 0 0 0 -1 0 -1 0
1 0 -1 -2 -1 1 -1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-2t^-3+8t^-2-14t^-1+17-14t+8t^2-2t^3
147
First homology
of the double branched cover of 12a_0739
Z/147
-6 6
12a_0740
2

detected by
the signature
-3+13t-25t^2+31t^3-25t^4+13t^5-3t^6
Seifert matrix of 12a_0740
1 0 0 0 0 0
-1 -1 0 -1 -1 0
0 0 -1 0 -1 0
-1 0 0 -1 0 0
-1 0 0 -1 -3 0
0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-3t^-2+11t^-1-15+11t-3t^2
113
First homology
of the double branched cover of 12a_0740
Z/113
-4 4
12a_0741
2

detected by
the signature
-5+25t-54t^2+69t^3-54t^4+25t^5-5t^6
Seifert matrix of 12a_0741
1 0 0 0 0 0
-1 -1 1 1 1 1
1 0 -2 -1 -1 -1
1 0 -1 -2 -2 -1
1 0 -1 -1 -2 -1
1 0 0 -1 -1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
3t^-3-17t^-2+40t^-1-52+40t-17t^2+3t^3
237
First homology
of the double branched cover of 12a_0741
Z/237
-4 4
12a_0742
2

detected by
the Nakanishi index
-2+8t-17t^2+26t^3-29t^4+26t^5-17t^6+8t^7-2t^8
Seifert matrix of 12a_0742
-1 0 0 0 -1 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1
0 1 1 1 0 0 1 1
0 0 0 0 -2 0 0 0
0 0 -1 -1 -1 -1 -1 0
0 1 1 0 0 0 1 1
0 1 0 0 0 0 0 1
2
135
First homology
of the double branched cover of 12a_0742
Z/45+Z/3
2 2
12a_0743
1

detected by
an unknotting move
-6+20t-27t^2+20t^3-6t^4
Seifert matrix of 12a_0743
-1 0 -1 0
0 3 0 0
0 0 -2 0
0 -1 -1 -1
1 or 2
79
First homology
of the double branched cover of 12a_0743
Z/79
-2 2
12a_0744
1

detected by
an unknotting move
4-15t+23t^2-15t^3+4t^4
Seifert matrix of 12a_0744
-1 0 0 0
0 4 0 0
-1 0 -1 0
-1 -1 -1 1
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
1
61
First homology
of the double branched cover of 12a_0744
Z/61
0 0
12a_0745
1

detected by
an unknotting move
-4+15t-21t^2+15t^3-4t^4
Seifert matrix of 12a_0745
1 0 0 0
-1 -1 1 -1
1 0 -4 1
-1 0 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
59
First homology
of the double branched cover of 12a_0745
Z/59
-2 2
12a_0746
1

detected by
an unknotting move
2-10t+26t^2-44t^3+53t^4-44t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_0746
-1 0 0 0 -1 0 0 0
0 1 0 0 0 0 0 0
0 0 -1 -1 -1 0 -1 0
0 1 0 1 0 0 1 1
0 0 0 0 -2 0 0 0
0 0 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 1 1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(0,-1-t^2+3t^3-t^4,-t-t^3+3t^4-t^5,2+t+t^2-2t^3-7t^4+8t^5-2t^6,1+t^2-3t^3+t^4,-t-t^3+3t^4-t^5,3+t+2t^2-5t^3-6t^4+8t^5-2t^6,-t+3t^2-t^3)
the Blanchfield form on it
x
217
First homology
of the double branched cover of 12a_0746
Z/217
0 0
12a_0747
1

detected by
an unknotting move
-1+8t-25t^2+45t^3-53t^4+45t^5-25t^6+8t^7-t^8
Seifert matrix of 12a_0747
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 1 0 -1 0 0 0
-1 1 1 1 -1 0 1 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 1 0 1
-1 1 1 0 -1 0 1 0
-1 1 0 0 -1 0 0 1
1 or 2
211
First homology
of the double branched cover of 12a_0747
Z/211
2 2
12a_0748
1

detected by
an unknotting move
-4+16t-30t^2+37t^3-30t^4+16t^5-4t^6
Seifert matrix of 12a_0748
-1 0 0 -1 0 0
0 -2 0 0 0 -1
0 0 1 0 1 0
0 -1 0 -2 0 -1
0 0 0 0 1 0
0 0 1 0 1 1
1
Generator of the Alexander module
(-t,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+5t^-1-5+5t-2t^2
137
First homology
of the double branched cover of 12a_0748
Z/137
0 2
12a_0749
2

detected by
the Lickorish test
4-16t+32t^2-39t^3+32t^4-16t^5+4t^6
Seifert matrix of 12a_0749
-1 0 0 0 0 0
1 2 0 1 0 0
0 0 1 0 1 0
-1 0 0 -1 0 0
0 0 0 0 1 0
1 1 1 1 1 2
1
Generator of the Alexander module
(0,-2+4t-4t^2+2t^3,0,0,0,1)
the Blanchfield form on it
-10t^-6+76t^-5-292t^-4+742t^-3-1381t^-2+1975t^-1-2220+1975t-1381t^2+742t^3-292t^4+76t^5-10t^6
143
First homology
of the double branched cover of 12a_0749
Z/143
2 2
12a_0750
3

detected by
the Nakanishi index
-8+34t-51t^2+34t^3-8t^4
Seifert matrix of 12a_0750
1 0 0 0
1 -2 0 -1
1 -1 -2 -1
1 0 0 -2
3
135
First homology
of the double branched cover of 12a_0750
Z/15+Z/3+Z/3
-2 2
12a_0751
1

detected by
an unknotting move
-2+14t-38t^2+53t^3-38t^4+14t^5-2t^6
Seifert matrix of 12a_0751
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 1 0 1
1 -1 1 0 2 0
-1 1 -1 0 0 1
1
Generator of the Alexander module
(0,0,-5+2t,-10+4t,5-2t,-7+2t)
the Blanchfield form on it
-2t^-2+10t^-1-15+10t-2t^2
161
First homology
of the double branched cover of 12a_0751
Z/161
0 0
12a_0752
2

detected by
the Lickorish test
-8+29t-41t^2+29t^3-8t^4
Seifert matrix of 12a_0752
-1 0 0 -1
0 -2 1 0
0 0 2 0
0 -1 1 -2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
-4t^-1+9-4t
115
First homology
of the double branched cover of 12a_0752
Z/115
-2 2
12a_0753
2

detected by
the Lickorish test
6-21t+31t^2-21t^3+6t^4
Seifert matrix of 12a_0753
-1 0 0 0
1 2 0 1
-1 -1 3 -1
-1 0 0 -1
1
Generator of the Alexander module
(0,-t,1-t,0)
the Blanchfield form on it
-3t^-3+18t^-2-45t^-1+60-45t+18t^2-3t^3
85
First homology
of the double branched cover of 12a_0753
Z/85
0 0
12a_0754
1

detected by
an unknotting move
-1+9t-30t^2+57t^3-69t^4+57t^5-30t^6+9t^7-t^8
Seifert matrix of 12a_0754
-1 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 -1
0 0 -1 0 0 0 0 0
-1 1 1 1 -1 0 0 1
-1 0 0 0 -1 0 0 0
-1 0 1 0 -1 1 1 1
-1 1 1 0 -1 0 1 1
0 0 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,1+7t-47t^2+63t^3-34t^4+8t^5,0,30-87t+79t^2+7t^3-55t^4+34t^5-8t^6,5-11t+7t^2-2t^3,t+7t^2-47t^3+63t^4-34t^5+8t^6,-1+23t-39t^2+23t^3-6t^4,0)
the Blanchfield form on it
x
263
First homology
of the double branched cover of 12a_0754
Z/263
-2 2
12a_0755
1

detected by
an unknotting move
-2+11t-31t^2+57t^3-69t^4+57t^5-31t^6+11t^7-2t^8
Seifert matrix of 12a_0755
-1 0 -1 0 -1 -1 0 0
0 1 0 0 0 0 0 0
0 0 -2 -1 -1 -2 0 -1
0 1 0 1 0 0 0 1
0 0 -2 -1 -2 -2 0 -1
0 0 -1 0 -1 -2 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(t,0,t+2t^3,1+2t+2t^2,1+2t,1+2t,-2t-4t^2,0)
the Blanchfield form on it
2t^-3-7t^-2+15t^-1-18+15t-7t^2+2t^3
271
First homology
of the double branched cover of 12a_0755
Z/271
-2 2
12a_0756
1

detected by
an unknotting move
-1+8t-23t^2+39t^3-45t^4+39t^5-23t^6+8t^7-t^8
Seifert matrix of 12a_0756
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
0 0 -1 0 0 0 0 0
-1 0 1 1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 1 0 0 -1 1 1 1
0 0 0 0 0 0 1 0
-1 1 1 0 -1 0 1 1
1
Generator of the Alexander module
(-6+4t-2t^3+4t^4-2t^5,1+t+3t^3-3t^4+3t^5-2t^6,-1-2t+2t^2-3t^3+2t^4,-3+2t-t^3+2t^4-t^5,11-9t-t^2-t^3-3t^4-2t^5+4t^6,-1-2t+t^5,3+3t-t^2+7t^3-7t^4+6t^5-4t^6,5+t+2t^2+3t^4-4t^5+3t^6-2t^7)
the Blanchfield form on it
x
187
First homology
of the double branched cover of 12a_0756
Z/187
2 2
12a_0757
1

detected by
an unknotting move
-2+9t-20t^2+32t^3-37t^4+32t^5-20t^6+9t^7-2t^8
Seifert matrix of 12a_0757
-1 0 0 -1 -1 -1 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1
0 0 0 -2 -1 -2 0 0
0 0 0 -2 -2 -2 0 0
0 0 0 -1 -1 -2 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,1,0,0,0,-2,0)
the Blanchfield form on it
2t^-3-5t^-2+9t^-1-10+9t-5t^2+2t^3
163
First homology
of the double branched cover of 12a_0757
Z/163
-2 2
12a_0758
1

detected by
an unknotting move
-3+13t-25t^2+31t^3-25t^4+13t^5-3t^6
Seifert matrix of 12a_0758
-1 0 0 1 0 0
0 1 0 0 0 0
0 1 1 0 0 1
0 0 0 -3 0 0
0 -1 -1 1 -1 -1
0 1 0 0 0 1
1
Generator of the Alexander module
(0,0,-1,0,1,0)
the Blanchfield form on it
-2t^-1+3-2t
113
First homology
of the double branched cover of 12a_0758
Z/113
0 2
12a_0759
2

detected by
the signature
2-6t+9t^2-9t^3+9t^4-9t^5+9t^6-6t^7+2t^8
Seifert matrix of 12a_0759
-1 0 0 -1 0 0 0 0
0 1 0 0 0 1 0 0
0 1 1 0 0 1 1 0
0 0 0 -2 0 0 0 0
0 1 1 1 1 1 1 1
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
0 1 1 0 0 1 1 1
1
Generator of the Alexander module
(1+t-4t^4+3t^5,0,0,0,0,0,4t-3t^2+4t^3-4t^4+3t^5-4t^6+3t^7,0)
the Blanchfield form on it
x
61
First homology
of the double branched cover of 12a_0759
Z/61
4 4
12a_0760
2

detected by
the Lickorish test
4-14t+24t^2-27t^3+24t^4-14t^5+4t^6
Seifert matrix of 12a_0760
-1 0 0 -1 0 0
0 1 0 0 0 1
0 -1 2 0 0 -1
0 0 0 -2 0 0
0 1 -1 1 1 1
0 0 0 0 0 1
1 or 2
111
First homology
of the double branched cover of 12a_0760
Z/111
2 2
12a_0761
1

detected by
an unknotting move
4-16t+31t^2-37t^3+31t^4-16t^5+4t^6
Seifert matrix of 12a_0761
-1 0 0 -1 0 0
0 2 1 0 0 1
0 2 2 0 0 2
0 0 0 -2 0 0
0 -1 -1 1 1 -1
0 2 1 0 0 2
1 or 2
139
First homology
of the double branched cover of 12a_0761
Z/139
2 2
12a_0762
3

detected by
the signature
-2+6t-7t^2+7t^3-7t^4+7t^5-7t^6+6t^7-2t^8
Seifert matrix of 12a_0762
1 0 0 0 0 0 0 0
0 -1 -1 -1 0 -1 -1 -1
0 0 -1 -1 0 0 -1 -1
0 0 0 -1 0 0 0 -1
1 -1 -1 -1 -2 -1 -1 -1
0 0 -1 -1 0 -1 -1 -1
0 0 0 -1 0 0 -1 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-4-3t^-3+4t^-2-4t^-1+4-4t+4t^2-3t^3+t^4
51
First homology
of the double branched cover of 12a_0762
Z/51
-6 6
12a_0763
2

detected by
the signature
-4+14t-20t^2+21t^3-20t^4+14t^5-4t^6
Seifert matrix of 12a_0763
1 0 0 0 0 0
0 -1 -1 1 0 -1
0 0 -1 1 0 0
0 0 0 -2 0 0
1 -1 -1 1 -2 -1
0 0 -1 1 0 -1
1 or 2
97
First homology
of the double branched cover of 12a_0763
Z/97
-4 4
12a_0764
2

detected by
the signature
-4+16t-29t^2+35t^3-29t^4+16t^5-4t^6
Seifert matrix of 12a_0764
1 0 0 0 0 0
0 -1 1 1 0 1
0 0 -2 -2 0 -2
0 0 -1 -2 0 -1
1 -1 1 1 -2 1
0 0 -1 -2 0 -2
1 or 2
133
First homology
of the double branched cover of 12a_0764
Z/133
-4 4
12a_0765
1

detected by
an unknotting move
1-9t+31t^2-60t^3+75t^4-60t^5+31t^6-9t^7+t^8
Seifert matrix of 12a_0765
-1 0 0 0 0 0 0 0
0 1 0 -1 0 0 0 0
-1 1 1 -1 -1 0 -1 1
0 0 0 -1 0 0 -1 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 1 -1 0
0 0 0 0 0 0 -1 0
-1 1 0 -1 -1 0 -1 1
1
Generator of the Alexander module
(0,-4t+4t^2-5t^3+8t^4-5t^5+t^6,4t-3t^3+5t^4-8t^5+5t^6-t^7,4-4t+t^2+4t^3-8t^4+5t^5-t^6,-18+32t-28t^2+20t^3+10t^4-6t^5-27t^6+23t^7-5t^8,13-20t+15t^2-6t^3-11t^4+8t^5+9t^6-9t^7+2t^8,0,-4+7t^2-5t^3+t^4)
the Blanchfield form on it
x
277
First homology
of the double branched cover of 12a_0765
Z/277
0 0
12a_0766
1

detected by
an unknotting move
1-8t+25t^2-45t^3+55t^4-45t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_0766
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
0 0 -1 0 0 0 0 0
-1 0 1 1 -1 0 0 1
-1 0 0 0 -1 0 0 0
-1 1 1 0 -1 1 1 0
0 0 0 0 0 0 1 0
0 0 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1-t^2,t-t^2,2-t^2,0,0)
the Blanchfield form on it
t^-3-6t^-2+12t^-1-15+12t-6t^2+t^3
213
First homology
of the double branched cover of 12a_0766
Z/213
0 2
12a_0767
2

detected by
the Lickorish test
-8+31t-45t^2+31t^3-8t^4
Seifert matrix of 12a_0767
1 0 0 0
0 -2 -1 0
1 0 -2 0
0 -1 -1 -2
1
Generator of the Alexander module
(-21t^2+30t^3,1-2t,-1+2t-3t^2+6t^3,5-6t)
the Blanchfield form on it
-237t^-4+5876t^-3-29517t^-2+68513t^-1-89204+68513t-29517t^2+5876t^3-237t^4
123
First homology
of the double branched cover of 12a_0767
Z/123
-2 2
12a_0768
2

detected by
the Lickorish test
-1+8t-23t^2+38t^3-43t^4+38t^5-23t^6+8t^7-t^8
Seifert matrix of 12a_0768
-1 0 0 0 0 0 0 0
-1 1 1 0 -1 0 1 0
0 0 -1 0 0 0 0 0
-1 0 1 1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 1 0 0 -1 1 1 1
-1 0 1 0 -1 0 1 0
-1 1 1 0 -1 0 1 1
1 or 2
183
First homology
of the double branched cover of 12a_0768
Z/183
2 2
12a_0769
2

detected by
the Nakanishi index
-2+16t-45t^2+63t^3-45t^4+16t^5-2t^6
Seifert matrix of 12a_0769
-1 0 0 0 0 0
1 2 -1 0 1 0
0 0 -1 0 0 0
-1 0 1 1 -1 0
-1 0 0 0 -1 0
-1 -1 0 0 -1 1
2
189
First homology
of the double branched cover of 12a_0769
Z/63+Z/3
0 0
12a_0770
1

detected by
an unknotting move
2-17t+48t^2-65t^3+48t^4-17t^5+2t^6
Seifert matrix of 12a_0770
-1 0 -1 0 0 0
0 1 0 0 0 0
0 -1 -2 0 0 -1
0 1 0 -1 0 1
0 -1 -1 0 -1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(-t+t^2,0,0,1,1,0)
the Blanchfield form on it
3t^-4-33t^-3+139t^-2-305t^-1+392-305t+139t^2-33t^3+3t^4
199
First homology
of the double branched cover of 12a_0770
Z/199
-2 2
12a_0771
1

detected by
an unknotting move
5-23t+50t^2-63t^3+50t^4-23t^5+5t^6
Seifert matrix of 12a_0771
-1 0 0 0 0 0
0 1 0 0 0 0
1 0 2 1 1 1
0 1 0 2 0 1
-1 0 0 0 -1 0
1 1 1 1 1 2
1 or 2
219
First homology
of the double branched cover of 12a_0771
Z/219
2 2
12a_0772
2

detected by
the signature
-4+16t-28t^2+33t^3-28t^4+16t^5-4t^6
Seifert matrix of 12a_0772
-1 -1 -1 -1 0 0
0 -2 -1 -2 0 0
0 -2 -2 -2 0 0
0 -1 -1 -2 0 0
0 -1 -1 -1 -1 1
0 0 0 0 0 2
1 or 2
129
First homology
of the double branched cover of 12a_0772
Z/129
-4 4
12a_0773
1

detected by
an unknotting move
-6+23t-33t^2+23t^3-6t^4
Seifert matrix of 12a_0773
-1 1 0 0
0 -3 0 0
0 1 -1 1
0 0 0 2
1 or 2
91
First homology
of the double branched cover of 12a_0773
Z/91
-2 2
12a_0774
1

detected by
an unknotting move
6-22t+33t^2-22t^3+6t^4
Seifert matrix of 12a_0774
-1 -1 0 0
0 -2 0 0
0 1 1 1
0 0 0 3
1 or 2
89
First homology
of the double branched cover of 12a_0774
Z/89
0 0
12a_0775
2

detected by
the Lickorish test
-6+22t-31t^2+22t^3-6t^4
Seifert matrix of 12a_0775
1 0 0 0
0 -1 0 -1
1 -1 -2 -1
0 0 0 -3
1
Generator of the Alexander module
(0,-1,1,0)
the Blanchfield form on it
-3t^-1+8-3t
87
First homology
of the double branched cover of 12a_0775
Z/87
-2 2
12a_0776
2

detected by
the Lickorish test
-1+8t-25t^2+46t^3-55t^4+46t^5-25t^6+8t^7-t^8
Seifert matrix of 12a_0776
-1 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 -1
0 0 -1 0 0 0 0 0
-1 1 1 1 -1 1 0 1
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 1 0 0
-1 1 1 0 -1 0 1 1
0 0 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,-1+t-t^2,0,0,2-2t+t^2,0)
the Blanchfield form on it
t^-3-7t^-2+16t^-1-19+16t-7t^2+t^3
215
First homology
of the double branched cover of 12a_0776
Z/215
-2 2
12a_0777
2

detected by
the signature
1-8t+23t^2-36t^3+41t^4-36t^5+23t^6-8t^7+t^8
Seifert matrix of 12a_0777
-1 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 -1
0 0 -1 0 0 0 0 0
-1 1 1 1 -1 0 1 1
-1 0 0 0 -1 0 0 0
-1 1 1 0 -1 1 0 1
0 -1 -1 0 0 0 -1 -1
0 0 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,-t,-t,2-3t+t^2,-1,1-t,-t,-t)
the Blanchfield form on it
t^-3-8t^-2+22t^-1-29+22t-8t^2+t^3
177
First homology
of the double branched cover of 12a_0777
Z/177
-4 4
12a_0778
1

detected by
an unknotting move
1-9t+30t^2-57t^3+71t^4-57t^5+30t^6-9t^7+t^8
Seifert matrix of 12a_0778
-1 0 0 0 0 0 0 0
-1 1 1 0 -1 0 1 1
0 0 -1 0 0 0 0 0
-1 0 1 1 -1 0 0 1
-1 0 0 0 -1 0 0 0
-1 1 1 0 -1 1 1 0
-1 0 1 0 -1 0 1 1
0 0 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,-6t+3t^2-2t^3+7t^4+t^5-6t^6+4t^7-3t^8+t^9,-2-7t+14t^3-8t^4+11t^5-5t^6+2t^7-t^8,3-9t+8t^2+40t^3-29t^4+24t^5-12t^6+3t^7-t^8,2+13t+7t^2+3t^3+5t^4-3t^5+t^6-t^7,-4-16t+5t^2+12t^3-9t^4+12t^5-11t^6+5t^7-3t^8+t^9,-4t+16t^2+13t^3+13t^5-7t^6+3t^7-2t^8,2+7t+10t^2+9t^3+2t^4+5t^5-3t^6+t^7-t^8)
the Blanchfield form on it
x
265
First homology
of the double branched cover of 12a_0778
Z/265
0 0
12a_0779
2

detected by
the Lickorish test
-2+16t-44t^2+61t^3-44t^4+16t^5-2t^6
Seifert matrix of 12a_0779
-1 0 0 0 0 0
0 -1 0 0 0 0
0 1 1 0 0 0
-1 0 0 -1 0 0
-1 1 0 -1 1 0
1 0 1 1 0 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+8t^-2-22t^-1+30-22t+8t^2-t^3
185
First homology
of the double branched cover of 12a_0779
Z/185
0 0
12a_0780
3

detected by
the new u==2 criterion
-5+24t-51t^2+65t^3-51t^4+24t^5-5t^6
Seifert matrix of 12a_0780
1 0 0 0 0 0
0 -1 0 0 0 0
1 -1 -2 0 -1 -1
0 0 -1 -1 0 -1
1 -1 -1 0 -2 -1
1 0 -1 0 0 -2
2
225
First homology
of the double branched cover of 12a_0780
Z/45+Z/5
-4 4
12a_0781
1

detected by
an unknotting move
-2+14t-37t^2+51t^3-37t^4+14t^5-2t^6
Seifert matrix of 12a_0781
-1 0 0 0 0 0
-1 1 -1 1 0 -1
-1 0 -1 0 0 0
-1 0 -1 1 0 0
-1 0 -1 0 1 -1
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,2t^2,t+t^2,t^2,1+t+t^2,t)
the Blanchfield form on it
2t^-2-12t^-1+21-12t+2t^2
157
First homology
of the double branched cover of 12a_0781
Z/157
0 0
12a_0782
1

detected by
an unknotting move
2-14t+36t^2-47t^3+36t^4-14t^5+2t^6
Seifert matrix of 12a_0782
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 0 -1 0 0 0
-1 1 -1 1 0 0
1 -1 1 0 2 -1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,-2+t,1,0)
the Blanchfield form on it
-4t^-2+16t^-1-21+16t-4t^2
151
First homology
of the double branched cover of 12a_0782
Z/151
-2 2
12a_0783
2

detected by
the Lickorish test
2-16t+45t^2-61t^3+45t^4-16t^5+2t^6
Seifert matrix of 12a_0783
-1 0 0 0 0 0
-1 1 -1 0 1 -1
-1 0 -1 0 0 0
-1 0 -1 1 0 -1
0 0 0 0 -1 1
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,2t,1+t,1+t,-1,1)
the Blanchfield form on it
-2t^-2+6t^-1-7+6t-2t^2
187
First homology
of the double branched cover of 12a_0783
Z/187
-2 2
12a_0784
1

detected by
an unknotting move
2-9t+23t^2-39t^3+47t^4-39t^5+23t^6-9t^7+2t^8
Seifert matrix of 12a_0784
-1 0 0 -1 0 0 0 0
0 1 1 1 0 0 1 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 1 0 1 0 1 1 1
0 0 0 0 0 0 1 0
0 1 1 1 0 0 1 1
1
Generator of the Alexander module
(-5+14t-t^2-38t^3+70t^4-61t^5+29t^6-6t^7,0,5-9t+7t^2-2t^3,-5-6t+40t^2-70t^3+61t^4-29t^5+6t^6,-5t+9t^2-7t^3+2t^4,2-6t+9t^2-12t^3+11t^4-7t^5+2t^6,0,0)
the Blanchfield form on it
x
193
First homology
of the double branched cover of 12a_0784
Z/193
0 0
12a_0785
2

detected by
the signature
1-9t+32t^2-62t^3+77t^4-62t^5+32t^6-9t^7+t^8
Seifert matrix of 12a_0785
-1 0 0 0 0 0 0 0
0 1 0 -1 0 0 0 0
0 -1 -1 0 0 -1 0 0
0 0 0 -1 0 0 -1 0
-1 0 0 0 -1 0 0 0
-1 1 0 -1 -1 1 -1 0
0 0 0 0 0 0 -1 0
0 -1 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,5t+7t^2-55t^3+53t^4-18t^5+2t^6,4-5t-11t^2+10t^3-2t^4,4+11t-27t^2+14t^3-2t^4,1+4t-2t^2,0,0,4+11t-32t^2+7t^3+53t^4-53t^5+18t^6-2t^7)
the Blanchfield form on it
x
285
First homology
of the double branched cover of 12a_0785
Z/285
-4 4
12a_0786
2

detected by
the Lickorish test
-2+15t-40t^2+55t^3-40t^4+15t^5-2t^6
Seifert matrix of 12a_0786
-1 0 0 -1 0 0
0 -1 0 0 0 0
0 1 1 1 0 0
0 0 0 -2 0 0
0 0 0 1 1 1
0 1 0 1 0 1
1
Generator of the Alexander module
(t,0,0,0,-t,1)
the Blanchfield form on it
2t^-2-11t^-1+18-11t+2t^2
169
First homology
of the double branched cover of 12a_0786
Z/169
0 0
12a_0787
2

detected by
the Nakanishi index
8-29t+43t^2-29t^3+8t^4
Seifert matrix of 12a_0787
-1 0 -1 0
0 2 -1 0
0 0 -2 0
0 1 -1 2
2
117
First homology
of the double branched cover of 12a_0787
Z/39+Z/3
0 0
12a_0788
1

detected by
an unknotting move
-1+8t-31t^2+67t^3-85t^4+67t^5-31t^6+8t^7-t^8
Seifert matrix of 12a_0788
-1 0 0 0 0 0 0 0
0 1 0 -1 0 0 0 0
-1 1 1 -1 -1 1 -1 0
0 0 0 -1 0 0 -1 0
-1 0 0 0 -1 0 0 0
-1 1 0 -1 -1 1 -1 0
0 0 0 0 0 0 -1 0
0 -1 0 0 0 -1 0 -1
1 or 2
299
First homology
of the double branched cover of 12a_0788
Z/299
-2 2
12a_0789
1

detected by
an unknotting move
2-7t+14t^2-20t^3+23t^4-20t^5+14t^6-7t^7+2t^8
Seifert matrix of 12a_0789
-1 0 0 -1 0 0 0 0
0 1 0 0 0 0 1 0
0 0 -1 -1 0 0 0 0
0 0 0 -2 0 0 0 0
0 0 -1 -1 -1 0 0 0
0 1 0 1 0 1 1 1
0 0 0 0 0 0 1 0
0 1 0 0 0 0 1 1
1
Generator of the Alexander module
(1,0,0,0,-1,0,0,0)
the Blanchfield form on it
2t^-3-5t^-2+8t^-1-8+8t-5t^2+2t^3
109
First homology
of the double branched cover of 12a_0789
Z/109
0 2
12a_0790
2

detected by
the Lickorish test
4-16t+32t^2-39t^3+32t^4-16t^5+4t^6
Seifert matrix of 12a_0790
-1 0 0 -1 0 0
0 2 0 0 0 0
0 0 -1 -1 0 0
0 0 0 -2 0 0
0 0 -1 -1 -1 0
0 -1 0 1 0 1
1 or 2
143
First homology
of the double branched cover of 12a_0790
Z/143
-2 2
12a_0791 1 or 2
3-9t+13t^2-13t^3+13t^4-9t^5+3t^6
Seifert matrix of 12a_0791
-1 0 1 0 0 0
0 1 0 0 1 0
0 0 -3 0 0 0
0 1 -1 1 1 1
0 0 0 0 1 0
0 1 0 0 1 1
1
Generator of the Alexander module
(1,0,1,0,0,0)
the Blanchfield form on it
-5t^-3+16t^-2-22t^-1+22-22t+16t^2-5t^3
63
First homology
of the double branched cover of 12a_0791
Z/63
2 2
12a_0792
2

detected by
the Lickorish test
6-21t+31t^2-21t^3+6t^4
Seifert matrix of 12a_0792
-1 0 1 0
0 2 0 0
0 0 -3 0
0 -1 -1 1
1 or 2
85
First homology
of the double branched cover of 12a_0792
Z/85
0 0
12a_0793
1

detected by
an unknotting move
1-9t+32t^2-62t^3+77t^4-62t^5+32t^6-9t^7+t^8
Seifert matrix of 12a_0793
-1 0 0 0 0 -1 -1 -1
0 1 -1 0 1 0 1 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 -1 0 1 0 1 0
0 -1 0 0 -1 -1 -1 0
0 0 0 0 0 0 1 0
0 0 0 0 -1 -1 -1 -1
1 or 2
285
First homology
of the double branched cover of 12a_0793
Z/285
0 2
12a_0794
3

detected by
the signature
-2+7t-12t^2+16t^3-17t^4+16t^5-12t^6+7t^7-2t^8
Seifert matrix of 12a_0794
1 0 0 0 0 0 0 0
0 -1 -1 0 0 0 -1 -1
0 0 -1 0 0 0 0 -1
0 0 0 -1 0 -1 0 0
0 0 0 -1 -1 -1 0 0
1 -1 -1 0 0 -2 -1 -1
0 0 -1 0 0 0 -1 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-2t^-3+6t^-2-7t^-1+7-7t+6t^2-2t^3
91
First homology
of the double branched cover of 12a_0794
Z/91
-6 6
12a_0795
2

detected by
the signature
-4+16t-30t^2+37t^3-30t^4+16t^5-4t^6
Seifert matrix of 12a_0795
1 0 0 0 0 0
0 -1 1 0 0 0
0 0 -2 0 0 0
0 0 0 -1 0 -1
0 0 0 -1 -1 -1
1 -1 1 0 0 -2
1 or 2
137
First homology
of the double branched cover of 12a_0795
Z/137
-4 4
12a_0796
2

detected by
the signature
-3+9t-11t^2+11t^3-11t^4+9t^5-3t^6
Seifert matrix of 12a_0796
1 0 0 0 0 0
0 -1 -1 0 -1 -1
0 0 -1 0 0 -1
-1 1 1 -3 1 1
0 0 -1 0 -1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-4+4t-3t^2+t^3
57
First homology
of the double branched cover of 12a_0796
Z/57
-4 4
12a_0797
1

detected by
an unknotting move
-6+21t-29t^2+21t^3-6t^4
Seifert matrix of 12a_0797
1 0 0 0
0 -1 1 0
0 0 -2 0
-1 1 -1 -3
1 or 2
83
First homology
of the double branched cover of 12a_0797
Z/83
-2 2
12a_0798
2

detected by
the signature
-5+23t-48t^2+61t^3-48t^4+23t^5-5t^6
Seifert matrix of 12a_0798
1 0 0 0 0 0
0 -1 0 0 0 0
1 0 -2 1 -1 -1
0 -1 0 -2 0 -1
1 0 -2 1 -2 -1
1 -1 -1 0 -1 -2
1
Generator of the Alexander module
(0,1+t-2t^2+t^3,-2-t+6t^2-5t^3+t^4,2+t-5t^2+4t^3-t^4,t+t^2-2t^3+t^4,-t-t^2+2t^3-t^4)
the Blanchfield form on it
-10t^-2+31t^-1-42+31t-10t^2
213
First homology
of the double branched cover of 12a_0798
Z/213
-4 4
12a_0799
1

detected by
an unknotting move
2-15t+42t^2-57t^3+42t^4-15t^5+2t^6
Seifert matrix of 12a_0799
-1 0 0 -1 0 0
0 -1 0 0 0 0
0 1 1 1 0 1
0 0 0 -2 0 0
0 1 0 1 1 0
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,-t,0,0,1,0)
the Blanchfield form on it
-3t^-3+23t^-2-60t^-1+82-60t+23t^2-3t^3
175
First homology
of the double branched cover of 12a_0799
Z/175
-2 2
12a_0800
2

detected by
the signature
-3+11t-20t^2+25t^3-20t^4+11t^5-3t^6
Seifert matrix of 12a_0800
1 0 0 0 0 0
0 -1 0 0 0 -1
-1 1 -3 -3 -3 1
-1 1 -2 -3 -2 1
-1 1 -2 -3 -3 1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-3t^-2+9t^-1-11+9t-3t^2
93
First homology
of the double branched cover of 12a_0800
Z/93
-4 4
12a_0801
3

detected by
the signature
-2+8t-17t^2+26t^3-29t^4+26t^5-17t^6+8t^7-2t^8
Seifert matrix of 12a_0801
1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 -1
1 -1 -2 0 0 -1 -2 -1
0 0 -1 -1 0 -1 -1 0
0 0 -1 -1 -1 -1 -1 0
1 -1 -2 0 0 -2 -2 -1
1 -1 -1 0 0 -1 -2 -1
0 0 0 0 0 0 0 -1
2
135
First homology
of the double branched cover of 12a_0801
Z/45+Z/3
-6 6
12a_0802
1

detected by
an unknotting move
-4+12t-15t^2+12t^3-4t^4
Seifert matrix of 12a_0802
1 0 0 0
0 -1 0 -1
1 -1 -4 -1
0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
47
First homology
of the double branched cover of 12a_0802
Z/47
-2 2
12a_0803
1

detected by
an unknotting move
-5+11t-5t^2
Seifert matrix of 12a_0803
1 0
-1 -5
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
t^-1-2+t
21
First homology
of the double branched cover of 12a_0803
Z/21
0 0
12a_0804
2

detected by
the signature
2-12t+32t^2-50t^3+57t^4-50t^5+32t^6-12t^7+2t^8
Seifert matrix of 12a_0804
1 0 0 0 0 0 0 0
0 -1 0 1 -1 0 -1 0
-1 0 -1 -1 1 0 1 0
1 0 0 1 0 0 0 0
0 0 0 1 -2 -1 -2 -1
0 0 0 0 0 -1 0 -1
0 0 0 1 -1 -1 -2 -1
0 0 0 0 0 0 0 -1
1 or 2
249
First homology
of the double branched cover of 12a_0804
Z/249
-4 4
12a_0805
2

detected by
the signature
1-5t+11t^2-17t^3+20t^4-21t^5+20t^6-17t^7+11t^8-5t^9+t^10
Seifert matrix of 12a_0805
1 0 0 0 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0 0 0
1 -1 -1 1 0 0 -1 1 0 0
1 -1 -1 1 1 0 -1 1 1 0
1 -1 -1 1 1 1 -1 1 1 1
0 -1 -1 0 0 0 -1 0 0 0
1 0 -1 0 0 0 -1 1 0 0
1 -1 -1 1 0 0 -1 1 1 0
1 -1 -1 1 1 0 -1 1 1 1
1
Generator of the Alexander module
(0,t,t,1-t+2t^2-2t^3+t^4-2t^5+2t^6,0,0,2t,0,0,0)
the Blanchfield form on it
129
First homology
of the double branched cover of 12a_0805
Z/129
4 4
12a_0806
2

detected by
the Lickorish test
-2+11t-27t^2+44t^3-51t^4+44t^5-27t^6+11t^7-2t^8
Seifert matrix of 12a_0806
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
1 -1 -1 1 0 0 -1 1
-1 1 1 -1 2 0 1 -1
1 -1 -1 1 -1 1 -1 1
0 -1 -1 0 0 0 -1 0
1 0 -1 0 0 0 -1 1
2
219
First homology
of the double branched cover of 12a_0806
Z/219
2 2
12a_0807
1

detected by
an unknotting move
-2+11t-28t^2+47t^3-55t^4+47t^5-28t^6+11t^7-2t^8
Seifert matrix of 12a_0807
1 0 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 0 1 0 0 0 1
0 -1 -1 0 -1 0 0 0
1 0 -1 0 -1 1 0 0
-1 1 1 1 1 -1 2 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,-1+2t,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
231
First homology
of the double branched cover of 12a_0807
Z/231
2 2
12a_0808
2

detected by
A(F_2)
-3+15t-32t^2+41t^3-32t^4+15t^5-3t^6
Seifert matrix of 12a_0808
1 0 0 0 -1 0
0 -1 0 0 0 0
0 -1 -1 0 0 0
1 -1 -1 3 -1 1
0 -1 -1 0 -1 0
1 0 -1 0 -1 1
2
141
First homology
of the double branched cover of 12a_0808
Z/141
0 2
12a_0809
2

detected by
the signature
2-11t+27t^2-39t^3+43t^4-39t^5+27t^6-11t^7+2t^8
Seifert matrix of 12a_0809
1 0 0 0 0 0 0 0
0 -1 0 1 -1 -1 -1 -1
-1 0 -1 -1 1 1 1 1
1 0 0 1 0 0 0 0
0 0 0 1 -2 -2 -2 -2
0 0 0 1 -1 -2 -1 -2
0 0 0 1 -1 -2 -2 -2
0 0 0 1 -1 -1 -1 -2
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
201
First homology
of the double branched cover of 12a_0809
Z/201
-4 4
12a_0810
2

detected by
the Nakanishi index
4-23t+57t^2-75t^3+57t^4-23t^5+4t^6
Seifert matrix of 12a_0810
1 0 0 0 0 0
0 -1 0 1 -1 1
-1 0 -1 -1 1 -1
1 0 0 1 0 0
0 0 0 1 -2 2
0 0 0 -1 1 -3
2
243
First homology
of the double branched cover of 12a_0810
Z/81+Z/3
-2 2
12a_0811
4

detected by
the signature
3-10t+19t^2-26t^3+29t^4-26t^5+19t^6-10t^7+3t^8
Seifert matrix of 12a_0811
-1 0 0 1 1 0 1 0
0 -1 0 -1 -1 0 -1 0
-1 0 -1 1 1 0 1 0
0 0 0 -2 -1 0 -2 0
0 0 0 -1 -2 0 -1 0
0 0 0 -1 0 -1 -1 0
0 0 0 -1 -1 0 -2 0
0 0 0 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,1,1,0,0,0,0,0)
the Blanchfield form on it
3t^-3-7t^-2+11t^-1-12+11t-7t^2+3t^3
145
First homology
of the double branched cover of 12a_0811
Z/145
-8 8
12a_0812
2

detected by
the signature
-5+23t-45t^2+55t^3-45t^4+23t^5-5t^6
Seifert matrix of 12a_0812
-1 0 0 1 1 1
0 1 0 0 0 0
-1 0 -1 1 1 1
0 1 0 -2 -1 -1
0 1 0 -1 -2 -1
0 1 0 0 -1 -2
1
Generator of the Alexander module
(15-115t+44t^2+416t^3+40t^4+104t^5+342t^6-60t^7+148t^8+240t^9,-57+440t-492t^2-983t^3+371t^4-779t^5-488t^6+262t^7-696t^8-280t^9,32-233t+1223t^2-988t^3-1842t^4+1156t^5-1684t^6-164t^7+460t^8-1600t^9,3-22t+35t^2+38t^3-29t^4+50t^5+6t^6-12t^7+40t^8,12-86t+608t^2-618t^3-954t^4+550t^5-944t^6-68t^7+184t^8-88
the Blanchfield form on it
x
201
First homology
of the double branched cover of 12a_0812
Z/201
-4 4
12a_0813
4

detected by
the signature
3-9t+16t^2-22t^3+25t^4-22t^5+16t^6-9t^7+3t^8
Seifert matrix of 12a_0813
-1 0 0 1 1 1 1 1
0 -1 0 -1 -1 -1 -1 -1
-1 0 -1 1 1 1 1 1
0 0 0 -2 -2 -1 -2 -2
0 0 0 -1 -2 -1 -1 -2
0 0 0 -1 -1 -2 -1 -1
0 0 0 -1 -2 -1 -2 -2
0 0 0 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(0,1,1,0,0,0,0,0)
the Blanchfield form on it
3t^-3-6t^-2+9t^-1-10+9t-6t^2+3t^3
125
First homology
of the double branched cover of 12a_0813
Z/125
-8 8
12a_0814
3

detected by
the signature
6-20t+34t^2-39t^3+34t^4-20t^5+6t^6
Seifert matrix of 12a_0814
-1 0 0 1 -1 1
0 -1 0 -1 1 -1
-1 0 -1 1 -1 1
0 0 0 -2 2 -1
0 0 0 1 -3 1
0 0 0 -1 1 -2
1 or 2
159
First homology
of the double branched cover of 12a_0814
Z/159
-6 6
12a_0815
1

detected by
an unknotting move
1-3t+7t^2-12t^3+16t^4-17t^5+16t^6-12t^7+7t^8-3t^9+t^10
Seifert matrix of 12a_0815
-1 -1 0 -1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0 0 0
0 -1 0 -1 0 0 0 0 0 0
0 -1 0 -1 1 0 0 1 0 0
0 -1 0 -1 1 1 0 1 1 0
0 -1 0 -1 1 1 1 1 1 1
0 0 0 0 0 0 0 1 0 0
0 -1 0 -1 1 0 0 1 1 0
0 -1 0 -1 1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,-t,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-2t^-3+5t^-2-6t^-1+6-6t+5t^2-2t^3+t^4
95
First homology
of the double branched cover of 12a_0815
Z/95
2 2
12a_0816
1

detected by
an unknotting move
2-7t+17t^2-30t^3+37t^4-30t^5+17t^6-7t^7+2t^8
Seifert matrix of 12a_0816
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 -1 0 -1 0 0 0 0
0 -1 0 -1 1 0 0 1
0 1 0 1 -1 2 0 -1
0 -1 0 -1 1 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,-2t,1,0)
the Blanchfield form on it
5t^-4-18t^-3+44t^-2-78t^-1+96-78t+44t^2-18t^3+5t^4
149
First homology
of the double branched cover of 12a_0816
Z/149
0 0
12a_0817
4

detected by
the signature
3-10t+19t^2-26t^3+29t^4-26t^5+19t^6-10t^7+3t^8
Seifert matrix of 12a_0817
-1 0 0 1 1 0 1 1
0 -1 0 -1 -1 0 -1 -1
-1 0 -1 1 1 0 1 1
0 0 0 -2 -2 0 -2 -1
0 0 0 -1 -2 0 -1 -1
0 0 0 -1 -1 -1 -1 0
0 0 0 -1 -2 0 -2 -1
0 0 0 -1 -1 0 -1 -2
1
Generator of the Alexander module
(-96+460t+12t^2+940t^3-396t^4,7-10t+14t^2-24t^3,-5-54t-44t^2-92t^3+66t^4,-4-68t-42t^2-108t^3+66t^4,-44+350t+48t^2+630t^3-264t^4,-52+306t+32t^2+602t^3-264t^4,-3-94t-74t^2-184t^3+132t^4,-62+6t-124t^2+130t^3)
the Blanchfield form on it
1886210t^-7-10241434t^-6+28678672t^-5-63121203t^-4+115342589t^-3-173178676t^-2+220009659t^-1-238626674+220009659t-173178676t^2+115342589t^3-63121203t^4+28678672t^5-10241434t^6+1886210t^7
145
First homology
of the double branched cover of 12a_0817
Z/145
-8 8
12a_0818
2

detected by
the Lickorish test
1-7t+23t^2-42t^3+49t^4-42t^5+23t^6-7t^7+t^8
Seifert matrix of 12a_0818
-1 0 -1 -1 0 0 0 -1
-1 -1 -1 -1 0 0 0 -1
0 0 -1 -1 -1 1 0 -1
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 -1 0 0 1 -1
0 0 0 -1 -1 1 0 -1
1 or 2
195
First homology
of the double branched cover of 12a_0818
Z/195
-2 2
12a_0819
1

detected by
an unknotting move
-1+5t-12t^2+21t^3-29t^4+33t^5-29t^6+21t^7-12t^8+5t^9-t^10
Seifert matrix of 12a_0819
1 0 0 0 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0 0 0
0 -1 -1 -1 0 0 0 -1 0 0
0 -1 0 -1 0 0 0 0 0 0
1 -1 -1 -1 1 0 -1 -1 1 0
1 -1 -1 -1 1 1 -1 -1 1 1
0 -1 -1 -1 0 0 -1 -1 0 0
0 -1 0 -1 0 0 0 -1 0 0
1 0 -1 -1 0 0 -1 -1 1 0
1 -1 -1 -1 1 0 -1 -1 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-4-5t^-3+11t^-2-17t^-1+19-17t+11t^2-5t^3+t^4
169
First homology
of the double branched cover of 12a_0819
Z/169
0 0
12a_0820
1

detected by
an unknotting move
-2+10t-23t^2+35t^3-39t^4+35t^5-23t^6+10t^7-2t^8
Seifert matrix of 12a_0820
1 0 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
0 -1 -1 -1 0 -1 0 0
0 -1 0 -1 0 0 0 0
0 -1 -1 -1 -1 -1 0 0
0 -1 0 -1 0 -1 0 0
1 0 -1 -1 -1 -1 1 0
-1 1 1 1 1 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-4+5t^-3-12t^-2+18t^-1-20+18t-12t^2+5t^3-t^4
179
First homology
of the double branched cover of 12a_0820
Z/179
-2 2
12a_0821
1

detected by
an unknotting move
-4+20t-44t^2+57t^3-44t^4+20t^5-4t^6
Seifert matrix of 12a_0821
1 0 -1 0 0 0
0 -1 0 0 0 0
0 -1 -1 1 0 0
0 1 0 -2 0 0
1 0 -1 1 1 0
-1 1 1 -1 -1 2
1 or 2
193
First homology
of the double branched cover of 12a_0821
Z/193
0 0
12a_0822
3

detected by
the signature
-2+8t-15t^2+22t^3-25t^4+22t^5-15t^6+8t^7-2t^8
Seifert matrix of 12a_0822
-1 0 0 -1 0 0 0 1
0 1 0 0 0 0 0 0
-1 0 -1 -1 0 0 0 1
0 -1 0 -1 0 0 0 1
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
0 0 0 0 0 -1 -1 -1
0 1 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-2t^-3+8t^-2-14t^-1+17-14t+8t^2-2t^3
119
First homology
of the double branched cover of 12a_0822
Z/119
-6 6
12a_0823
2

detected by
the signature
-4+17t-31t^2+37t^3-31t^4+17t^5-4t^6
Seifert matrix of 12a_0823
-1 0 0 -1 0 1
0 1 0 0 0 0
-1 0 -1 -1 0 1
0 -1 0 -1 0 1
0 0 0 0 -2 0
0 1 0 0 -1 -2
1 or 2
141
First homology
of the double branched cover of 12a_0823
Z/141
-4 4
12a_0824
1

detected by
an unknotting move
-1+3t-7t^2+13t^3-19t^4+21t^5-19t^6+13t^7-7t^8+3t^9-t^10
Seifert matrix of 12a_0824
-1 -1 0 0 -1 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0 0 0
0 0 0 1 0 0 0 1 0 0
0 -1 0 0 -1 0 0 0 0 0
0 -1 0 1 -1 1 0 1 1 0
0 -1 0 1 -1 1 1 1 1 1
0 0 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 1 1 0
0 -1 0 1 -1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+10-8t+4t^2-t^3
107
First homology
of the double branched cover of 12a_0824
Z/107
2 2
12a_0825
1

detected by
an unknotting move
2-7t+16t^2-27t^3+33t^4-27t^5+16t^6-7t^7+2t^8
Seifert matrix of 12a_0825
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 2 0 0 0 0
0 -1 0 0 -1 0 0 0
0 -1 0 -1 -1 1 0 0
0 -1 0 -1 -1 1 1 1
0 -1 0 -1 -1 1 0 1
1
Generator of the Alexander module
(0,-t,t^3,1+t+t^2,t^2,0,t^3,-t-t^3)
the Blanchfield form on it
-t^-3+2t^-2-4t^-1+5-4t+2t^2-t^3
137
First homology
of the double branched cover of 12a_0825
Z/137
0 0
12a_0826
1

detected by
an unknotting move
2-6t+11t^2-16t^3+19t^4-16t^5+11t^6-6t^7+2t^8
Seifert matrix of 12a_0826
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 1 0 1 0 0
0 -1 0 0 -1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 1 0 1 1 0
0 1 0 -1 1 -1 -1 2
1
Generator of the Alexander module
(0,0,-t+t^4,0,0,0,0,1+t-t^3)
the Blanchfield form on it
2t^-3-4t^-2+7t^-1-8+7t-4t^2+2t^3
89
First homology
of the double branched cover of 12a_0826
Z/89
0 0
12a_0827
2

detected by
the Lickorish test
4-13t+21t^2-23t^3+21t^4-13t^5+4t^6
Seifert matrix of 12a_0827
-1 -1 0 0 -1 0
0 -1 0 0 0 0
-1 -1 -1 0 -1 0
0 0 0 2 0 0
0 -1 0 0 -1 0
0 1 0 1 1 2
1
Generator of the Alexander module
(0,0,-t+t^4,0,0,1+t-t^3)
the Blanchfield form on it
4t^-2-9t^-1+12-9t+4t^2
99
First homology
of the double branched cover of 12a_0827
Z/99
-2 2
12a_0828
3

detected by
the signature
7-24t+42t^2-49t^3+42t^4-24t^5+7t^6
Seifert matrix of 12a_0828
-1 0 0 -1 1 0
0 -1 0 1 -1 0
-1 0 -1 -1 1 0
0 0 0 -3 1 -1
0 0 0 1 -2 -1
0 0 0 -1 0 -2
1 or 2
195
First homology
of the double branched cover of 12a_0828
Z/195
-6 6
12a_0829
3

detected by
the signature
-2+11t-25t^2+37t^3-41t^4+37t^5-25t^6+11t^7-2t^8
Seifert matrix of 12a_0829
-1 0 0 0 1 1 0 1
0 -1 0 0 -1 -1 0 -1
-1 0 -1 0 1 1 0 1
0 0 0 1 0 0 0 0
0 0 0 -1 -2 -2 0 -2
0 0 0 0 -1 -2 0 -1
0 0 0 -1 -1 -1 -1 -1
0 0 0 -1 -1 -2 0 -2
1
Generator of the Alexander module
(-126-244t+669t^2+2254t^3+133t^4-3596t^5-2586t^6-650t^7+3238t^8+1800t^9-468t^10-240t^11-432t^12,-127-490t+1376t^2+2969t^3-1756t^4-2774t^5-3318t^6-846t^7+4018t^8+1200t^9+204t^10-240t^11-432t^12,-17-9t+236t^2+406t^3-355t^4-715t^5-232t^6+114t^7+504t^8+24t^9,-50-202t+545t^2+1195t^3-688t^4-1111t^5-1388t^
the Blanchfield form on it
x
191
First homology
of the double branched cover of 12a_0829
Z/191
-6 6
12a_0830
1

detected by
an unknotting move
2-9t+24t^2-42t^3+51t^4-42t^5+24t^6-9t^7+2t^8
Seifert matrix of 12a_0830
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 2 0 1 0 1
0 -1 0 0 -1 0 0 0
0 -1 0 0 -1 1 0 0
0 -1 0 -1 -1 0 1 0
0 -1 0 0 -1 1 0 1
1
Generator of the Alexander module
(0,0,1,1+t-2t^2,0,1+t,t+t^2,1)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-10+8t-4t^2+t^3
205
First homology
of the double branched cover of 12a_0830
Z/205
0 0
12a_0831
1

detected by
an unknotting move
2-9t+24t^2-42t^3+51t^4-42t^5+24t^6-9t^7+2t^8
Seifert matrix of 12a_0831
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 2 0 1 0 0
0 -1 0 0 -1 0 0 0
0 -1 0 0 -1 1 0 0
0 -1 0 -1 -1 0 1 1
0 -1 0 -1 -1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-2t^-3+7t^-2-13t^-1+15-13t+7t^2-2t^3
205
First homology
of the double branched cover of 12a_0831
Z/205
0 0
12a_0832
3

detected by
the signature
-2+11t-25t^2+37t^3-41t^4+37t^5-25t^6+11t^7-2t^8
Seifert matrix of 12a_0832
-1 0 0 0 1 0 1 0
0 -1 0 0 -1 0 -1 0
-1 0 -1 0 1 0 1 0
0 0 0 1 0 0 0 0
0 0 0 -1 -2 0 -2 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 -1 0 -2 0
0 0 0 -1 -1 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-2t^-3+9t^-2-16t^-1+19-16t+9t^2-2t^3
191
First homology
of the double branched cover of 12a_0832
Z/191
-6 6
12a_0833
1

detected by
an unknotting move
-2+9t-19t^2+29t^3-33t^4+29t^5-19t^6+9t^7-2t^8
Seifert matrix of 12a_0833
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
-1 -1 -1 -1 0 0 0 1
1 0 0 1 0 0 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
0 0 0 0 0 -1 -1 -1
0 1 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-2t^-3+9t^-2-18t^-1+23-18t+9t^2-2t^3
151
First homology
of the double branched cover of 12a_0833
Z/151
-2 2
12a_0834
1

detected by
an unknotting move
-4+19t-39t^2+49t^3-39t^4+19t^5-4t^6
Seifert matrix of 12a_0834
1 0 0 0 0 0
1 1 0 1 0 0
-1 -1 -1 -1 0 1
1 0 0 1 0 0
0 0 0 0 -2 0
0 1 0 0 -1 -2
1
Generator of the Alexander module
(0,0,-4-t+12t^2-10t^3-5t^4+11t^5-4t^6,-4-t-9t^2-19t^3+82t^4-64t^5-40t^6+87t^7-36t^8,12t^2+20t^3-65t^4+24t^5+58t^6-57t^7-t^8+12t^9,15+5t-53t^2+45t^3+22t^4-51t^5+20t^6)
the Blanchfield form on it
x
173
First homology
of the double branched cover of 12a_0834
Z/173
0 2
12a_0835
1

detected by
an unknotting move
-1+3t-6t^2+9t^3-11t^4+11t^5-11t^6+9t^7-6t^8+3t^9-t^10
Seifert matrix of 12a_0835
-1 -1 0 0 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0 0 0
0 0 0 1 0 0 0 1 0 0
0 0 0 1 1 0 0 1 1 0
0 -1 0 0 0 -1 0 0 0 0
0 -1 0 1 1 -1 1 1 1 1
0 0 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 1 1 0
0 0 0 1 1 0 0 1 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-3t^-3+6t^-2-9t^-1+11-9t+6t^2-3t^3+t^4
71
First homology
of the double branched cover of 12a_0835
Z/71
2 2
12a_0836
1

detected by
an unknotting move
2-7t+15t^2-24t^3+29t^4-24t^5+15t^6-7t^7+2t^8
Seifert matrix of 12a_0836
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 0 0 1
0 0 0 -1 2 0 0 -1
0 -1 0 0 0 -1 0 0
0 -1 0 1 -1 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,2,1,-2,3-2t,2,2t,-2)
the Blanchfield form on it
2t^-3-5t^-2+10t^-1-12+10t-5t^2+2t^3
125
First homology
of the double branched cover of 12a_0836
Z/125
0 0
12a_0837
1

detected by
an unknotting move
2-8t+18t^2-28t^3+33t^4-28t^5+18t^6-8t^7+2t^8
Seifert matrix of 12a_0837
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 2 1 0 0 1
0 0 0 2 2 0 0 2
0 -1 0 0 0 -1 0 0
0 -1 0 -1 -1 -1 1 -1
0 0 0 2 1 0 0 2
1
Generator of the Alexander module
(0,0,t-t^4,0,0,0,1+t-t^3,0)
the Blanchfield form on it
2t^-3-6t^-2+12t^-1-14+12t-6t^2+2t^3
145
First homology
of the double branched cover of 12a_0837
Z/145
0 0
12a_0838
4

detected by
the signature
-1+3t-4t^2+5t^3-5t^4+5t^5-5t^6+5t^7-4t^8+3t^9-t^10
Seifert matrix of 12a_0838
-1 0 0 -1 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1 -1 -1
0 -1 0 -1 -1 -1 -1 -1 -1 -1
0 -1 0 0 -1 -1 -1 0 -1 -1
0 -1 0 0 0 -1 -1 0 0 -1
0 -1 0 0 0 0 -1 0 0 0
0 -1 0 0 -1 -1 -1 -1 -1 -1
0 -1 0 0 0 -1 -1 0 -1 -1
0 -1 0 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,1,-t,0,0,0,0,0,0,0)
the Blanchfield form on it
-t^-4+2t^-3-2t^-2+2t^-1-2+2t-2t^2+2t^3-t^4
41
First homology
of the double branched cover of 12a_0838
Z/41
-8 8
12a_0839
3

detected by
the signature
-2+7t-11t^2+14t^3-15t^4+14t^5-11t^6+7t^7-2t^8
Seifert matrix of 12a_0839
-1 0 0 -1 -1 1 -1 -1
0 1 0 0 0 0 0 0
-1 0 -1 -1 -1 1 -1 -1
0 -1 0 -1 -1 1 -1 -1
0 -1 0 0 -1 1 -1 0
0 1 0 0 0 -2 1 0
0 -1 0 0 0 0 -1 0
0 -1 0 0 -1 1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-4-4t^-3+7t^-2-9t^-1+10-9t+7t^2-4t^3+t^4
83
First homology
of the double branched cover of 12a_0839
Z/83
-6 6
12a_0840
3

detected by
the signature
-2+8t-16t^2+24t^3-27t^4+24t^5-16t^6+8t^7-2t^8
Seifert matrix of 12a_0840
-1 0 0 -1 1 1 -1 1
0 1 0 0 0 0 0 0
-1 0 -1 -1 1 1 -1 1
0 -1 0 -1 1 1 -1 1
0 1 0 0 -2 -2 1 -2
0 1 0 0 -1 -2 1 -1
0 -1 0 0 0 0 -1 0
0 1 0 0 -1 -2 1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-11t^-1+13-11t+7t^2-2t^3
127
First homology
of the double branched cover of 12a_0840
Z/127
-6 6
12a_0841
2

detected by
the signature
-4+16t-28t^2+33t^3-28t^4+16t^5-4t^6
Seifert matrix of 12a_0841
-1 0 0 -1 1 1
0 1 0 0 0 0
-1 0 -1 -1 1 1
0 -1 0 -1 1 1
0 1 0 0 -2 -1
0 1 0 0 0 -2
1
Generator of the Alexander module
(0,0,1,0,-3+2t,0)
the Blanchfield form on it
-4t^-2+10t^-1-9+10t-4t^2
129
First homology
of the double branched cover of 12a_0841
Z/129
-4 4
12a_0842
2

detected by
the Lickorish test
3-11t+20t^2-23t^3+20t^4-11t^5+3t^6
Seifert matrix of 12a_0842
-1 -1 0 -1 0 0
0 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 -1 0 -1 0 0
0 -1 0 -1 1 1
0 0 0 0 0 3
1
Generator of the Alexander module
(0,0,t-t^4,0,1+t-t^3,0)
the Blanchfield form on it
3t^-2-8t^-1+12-8t+3t^2
91
First homology
of the double branched cover of 12a_0842
Z/91
-2 2
12a_0843
2

detected by
the signature
-3+11t-18t^2+21t^3-18t^4+11t^5-3t^6
Seifert matrix of 12a_0843
-1 0 0 -1 -1 -1
0 1 0 0 0 0
-1 0 -1 -1 -1 -1
0 -1 0 -1 -1 -1
0 -1 0 0 -1 0
0 -1 0 0 -1 -3
1
Generator of the Alexander module
(0,0,0,1,0,1)
the Blanchfield form on it
-4t^-2+12t^-1-15+12t-4t^2
85
First homology
of the double branched cover of 12a_0843
Z/85
-4 4
12a_0844
1

detected by
an unknotting move
-1+8t-24t^2+43t^3-51t^4+43t^5-24t^6+8t^7-t^8
Seifert matrix of 12a_0844
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 -1 0 0 0 0
0 -1 0 1 1 -1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 1 1
0 -1 0 1 0 -1 0 1
1
Generator of the Alexander module
(0,0,-1,0,1-t,0,-1+t,-1+t)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
203
First homology
of the double branched cover of 12a_0844
Z/203
-2 2
12a_0845
2

detected by
the Lickorish test
4-14t+24t^2-27t^3+24t^4-14t^5+4t^6
Seifert matrix of 12a_0845
-1 -1 0 0 -1 0
0 -1 0 0 0 0
-1 -1 -1 0 -1 0
0 1 0 2 1 0
0 -1 0 0 -1 0
0 1 0 1 1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-3-7t^-2+11t^-1-12+11t-7t^2+2t^3
111
First homology
of the double branched cover of 12a_0845
Z/111
-2 2
12a_0846
1

detected by
an unknotting move
-1+8t-24t^2+43t^3-51t^4+43t^5-24t^6+8t^7-t^8
Seifert matrix of 12a_0846
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 -1 0 0 0 0
0 -1 0 1 1 -1 1 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 1 0
0 -1 0 1 0 -1 0 1
1
Generator of the Alexander module
(-2t-2t^2-11t^3-5t^5+73t^6+6t^7-121t^8+49t^9+42t^10-33t^11+6t^12,2+7t-2t^2-19t^3-122t^4+165t^5+114t^6-77t^7-160t^8+65t^9+90t^10-66t^11+12t^12,-2t-2t^2-11t^3-5t^5+73t^6+6t^7-121t^8+49t^9+42t^10-33t^11+6t^12,-2t-5t^2-23t^3+22t^4+47t^5+316t^6-390t^7-428t^8+318t^9+434t^10-254t^11-183t^12+159t^13-30t^14,
the Blanchfield form on it
x
203
First homology
of the double branched cover of 12a_0846
Z/203
-2 2
12a_0847
2

detected by
the signature
1-8t+24t^2-39t^3+45t^4-39t^5+24t^6-8t^7+t^8
Seifert matrix of 12a_0847
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 -1 0 0 0 0
0 -1 0 1 1 -1 0 1
0 -1 0 0 0 -1 0 0
0 -1 0 1 0 -1 1 0
0 0 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,t^2-3t^3+36t^4+14t^5-394t^6+900t^7-1152t^8+1130t^9-864t^10+446t^11-126t^12+14t^13,1+8t-8t^2-26t^3+316t^4-544t^5+600t^6-530t^7+334t^8-112t^9+14t^10,-1-11t+2t^2+177t^3-250t^4-748t^5+2490t^6-3794t^7+4200t^8-3610t^9+2188t^10-824t^11+168t^12-14t^13,0,1+7t-32t^2-33t^3+450t^4-808t^5+430t^6+290t^7-880t
the Blanchfield form on it
x
189
First homology
of the double branched cover of 12a_0847
Z/189
-4 4
12a_0848
2

detected by
the signature
2-9t+21t^2-31t^3+35t^4-31t^5+21t^6-9t^7+2t^8
Seifert matrix of 12a_0848
1 0 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
1 0 1 0 0 -1 0 0
0 0 0 1 0 0 0 0
0 0 0 1 1 0 1 0
0 -1 0 0 0 -1 0 0
0 0 0 1 0 0 1 0
-1 1 -1 1 1 1 1 2
1
Generator of the Alexander module
(0,0,0,0,t,0,0,1+t)
the Blanchfield form on it
-2t^-3+9t^-2-20t^-1+25-20t+9t^2-2t^3
161
First homology
of the double branched cover of 12a_0848
Z/161
4 4
12a_0849
1

detected by
an unknotting move
4-19t+43t^2-55t^3+43t^4-19t^5+4t^6
Seifert matrix of 12a_0849
1 0 0 -1 0 0
0 -1 0 0 0 0
1 0 1 -1 0 0
0 -1 0 -1 0 0
0 0 0 0 2 1
-1 1 -1 1 0 2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-3-10t^-2+23t^-1-30+23t-10t^2+2t^3
187
First homology
of the double branched cover of 12a_0849
Z/187
2 2
12a_0850
2

detected by
the signature
1-4t+8t^2-12t^3+13t^4-13t^5+13t^6-12t^7+8t^8-4t^9+t^10
Seifert matrix of 12a_0850
1 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 0 0 1 0 0 0 0 0 0
0 -1 0 0 -1 -1 -1 0 -1 -1
0 -1 0 0 0 -1 -1 0 0 -1
0 -1 0 0 0 0 -1 0 0 0
0 -1 0 0 -1 -1 -1 -1 -1 -1
0 -1 0 0 0 -1 -1 0 -1 -1
0 -1 0 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+8t^-2-12t^-1+13-12t+8t^2-4t^3+t^4
89
First homology
of the double branched cover of 12a_0850
Z/89
-4 4
12a_0851
1

detected by
an unknotting move
-2+9t-20t^2+32t^3-37t^4+32t^5-20t^6+9t^7-2t^8
Seifert matrix of 12a_0851
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
-1 -1 -1 -1 -1 1 -1 -1
1 0 0 1 0 0 0 0
0 -1 0 0 -1 1 -1 0
0 1 0 0 0 -2 1 0
0 -1 0 0 0 0 -1 0
0 -1 0 0 -1 1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-4-5t^-3+12t^-2-20t^-1+24-20t+12t^2-5t^3+t^4
163
First homology
of the double branched cover of 12a_0851
Z/163
-2 2
12a_0852
1

detected by
an unknotting move
-2+10t-25t^2+42t^3-49t^4+42t^5-25t^6+10t^7-2t^8
Seifert matrix of 12a_0852
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
-1 -1 -1 -1 1 1 -1 1
1 0 0 1 0 0 0 0
0 1 0 0 -2 -2 1 -2
0 1 0 0 -1 -2 1 -1
0 -1 0 0 0 0 -1 0
0 1 0 0 -1 -2 1 -2
1
Generator of the Alexander module
(0,-1,1,0,0,t,0,0)
the Blanchfield form on it
-2t^-3+8t^-2-16t^-1+21-16t+8t^2-2t^3
207
First homology
of the double branched cover of 12a_0852
Z/207
-2 2
12a_0853
1

detected by
an unknotting move
-4+19t-40t^2+51t^3-40t^4+19t^5-4t^6
Seifert matrix of 12a_0853
1 0 0 0 0 0
1 1 0 1 0 0
-1 -1 -1 -1 1 1
1 0 0 1 0 0
0 1 0 0 -2 -1
0 1 0 0 0 -2
1
Generator of the Alexander module
(0,2t,-2t-t^2,0,1-t+2t^2,-1)
the Blanchfield form on it
-4t^-2+13t^-1-16+13t-4t^2
177
First homology
of the double branched cover of 12a_0853
Z/177
0 2
12a_0854
1

detected by
an unknotting move
-3+14t-30t^2+39t^3-30t^4+14t^5-3t^6
Seifert matrix of 12a_0854
1 0 0 0 0 0
1 1 0 1 0 0
-1 -1 -1 -1 -1 -1
1 0 0 1 0 0
0 -1 0 0 -1 0
0 -1 0 0 -1 -3
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-14+11t-5t^2+t^3
133
First homology
of the double branched cover of 12a_0854
Z/133
0 0
12a_0855
2

detected by
the Lickorish test
-2+10t-23t^2+33t^3-35t^4+33t^5-23t^6+10t^7-2t^8
Seifert matrix of 12a_0855
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 -1 -1 1 -1 -1
0 -1 0 -1 -1 0 0 -1
0 -1 0 0 -1 0 0 0
-1 1 0 0 0 2 0 0
0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,-2t,2t^2,-2t^3,-2,1-2t,0,0)
the Blanchfield form on it
11t^-4-55t^-3+126t^-2-181t^-1+192-181t+126t^2-55t^3+11t^4
171
First homology
of the double branched cover of 12a_0855
Z/171
-2 2
12a_0856
1

detected by
an unknotting move
-4+22t-54t^2+73t^3-54t^4+22t^5-4t^6
Seifert matrix of 12a_0856
1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 1 -1 1
0 1 0 -2 1 0
0 -1 0 0 -1 0
-1 1 0 0 0 2
1 or 2
233
First homology
of the double branched cover of 12a_0856
Z/233
0 0
12a_0857
1

detected by
an unknotting move
-2+11t-29t^2+49t^3-57t^4+49t^5-29t^6+11t^7-2t^8
Seifert matrix of 12a_0857
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 -1 1 0 -1
0 0 0 1 0 0 1 0
0 -1 0 0 -1 0 0 0
-1 1 0 1 0 2 1 0
0 0 0 0 0 0 1 0
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,1+2t-t^2,0,2-t,0,0,0)
the Blanchfield form on it
2t^-3-5t^-2+10t^-1-11+10t-5t^2+2t^3
239
First homology
of the double branched cover of 12a_0857
Z/239
2 2
12a_0858
1

detected by
an unknotting move
-3+16t-38t^2+51t^3-38t^4+16t^5-3t^6
Seifert matrix of 12a_0858
1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 -1 -1 -1
1 -1 0 3 0 0
0 -1 0 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
1
165
First homology
of the double branched cover of 12a_0858
Z/165
0 0
12a_0859
3

detected by
the signature
1-4t+8t^2-10t^3+11t^4-11t^5+11t^6-10t^7+8t^8-4t^9+t^10
Seifert matrix of 12a_0859
1 0 0 0 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0 0 0
1 0 1 0 0 0 -1 0 0 0
1 -1 1 1 0 0 -1 1 0 0
1 -1 1 1 1 0 -1 1 1 0
1 -1 1 1 1 1 -1 1 1 1
0 -1 0 0 0 0 -1 0 0 0
1 -1 1 0 0 0 -1 1 0 0
1 -1 1 1 0 0 -1 1 1 0
1 -1 1 1 1 0 -1 1 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0,0,0)
the Blanchfield form on it
-t^-4+4t^-3-8t^-2+10t^-1-11+10t-8t^2+4t^3-t^4
79
First homology
of the double branched cover of 12a_0859
Z/79
6 6
12a_0860
2

detected by
the signature
2-9t+20t^2-28t^3+31t^4-28t^5+20t^6-9t^7+2t^8
Seifert matrix of 12a_0860
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
1 0 1 0 0 0 -1 0
1 -1 1 1 0 0 -1 1
-1 1 -1 -1 2 0 1 -1
1 -1 1 1 -1 1 -1 1
0 -1 0 0 0 0 -1 0
1 -1 1 0 0 0 -1 1
1
Generator of the Alexander module
(-2-4t,-2-4t,2+3t,0,1+2t,4t+8t^2,0,0)
the Blanchfield form on it
-386t^-3+1629t^-2-3171t^-1+3833-3171t+1629t^2-386t^3
149
First homology
of the double branched cover of 12a_0860
Z/149
4 4
12a_0861
2

detected by
the signature
2-10t+25t^2-40t^3+47t^4-40t^5+25t^6-10t^7+2t^8
Seifert matrix of 12a_0861
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
1 0 1 0 0 0 -1 0
-1 1 -1 2 1 0 1 1
-1 1 -1 2 2 0 1 2
1 -1 1 -1 -1 1 -1 -1
0 -1 0 0 0 0 -1 0
-1 1 -1 2 1 0 1 2
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-2t^-3+9t^-2-19t^-1+23-19t+9t^2-2t^3
201
First homology
of the double branched cover of 12a_0861
Z/201
4 4
12a_0862
1

detected by
an unknotting move
4-19t+42t^2-53t^3+42t^4-19t^5+4t^6
Seifert matrix of 12a_0862
1 0 0 0 -1 0
0 -1 0 0 0 0
1 0 1 0 -1 0
-1 1 -1 2 1 0
0 -1 0 0 -1 0
-1 1 -1 1 1 2
1 or 2
183
First homology
of the double branched cover of 12a_0862
Z/183
2 2
12a_0863
1

detected by
an unknotting move
3-14t+30t^2-37t^3+30t^4-14t^5+3t^6
Seifert matrix of 12a_0863
1 0 0 0 -1 0
0 -1 0 0 0 0
1 0 1 0 -1 0
1 -1 1 1 -1 1
0 -1 0 0 -1 0
1 -1 1 0 -1 3
1
Generator of the Alexander module
(0,-1,t,1,0,t)
the Blanchfield form on it
7t^-3-33t^-2+71t^-1-88+71t-33t^2+7t^3
131
First homology
of the double branched cover of 12a_0863
Z/131
2 2
12a_0864
1

detected by
an unknotting move
1-5t+12t^2-20t^3+27t^4-29t^5+27t^6-20t^7+12t^8-5t^9+t^10
Seifert matrix of 12a_0864
1 0 0 0 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 -1 0 0
1 0 -1 1 0 0 -1 -1 0 0
1 -1 -1 1 1 0 -1 -1 1 0
1 -1 -1 1 1 1 -1 -1 1 1
0 -1 -1 0 0 0 -1 -1 0 0
0 -1 0 0 0 0 0 -1 0 0
1 -1 -1 1 0 0 -1 -1 1 0
1 -1 -1 1 1 0 -1 -1 1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,0,1,0)
the Blanchfield form on it
-t^-4+5t^-3-12t^-2+19t^-1-23+19t-12t^2+5t^3-t^4
159
First homology
of the double branched cover of 12a_0864
Z/159
2 2
12a_0865
1

detected by
an unknotting move
2-11t+28t^2-46t^3+55t^4-46t^5+28t^6-11t^7+2t^8
Seifert matrix of 12a_0865
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 -1
1 0 -1 1 0 0 -1 -1
-1 1 1 -1 2 0 1 1
1 -1 -1 1 -1 1 -1 -1
0 -1 -1 0 0 0 -1 -1
0 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-4-6t^-3+16t^-2-27t^-1+32-27t+16t^2-6t^3+t^4
229
First homology
of the double branched cover of 12a_0865
Z/229
0 0
12a_0866
2

detected by
the Lickorish test
-2+12t-34t^2+62t^3-75t^4+62t^5-34t^6+12t^7-2t^8
Seifert matrix of 12a_0866
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 -1 -1 1 1 -1 -1 0
0 0 0 0 1 0 0 0
1 0 0 0 -1 2 0 1
0 -1 -1 0 0 0 -1 0
1 0 -1 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,-t-4t^2+18t^3-44t^4+63t^5-57t^6+33t^7-12t^8+2t^9,0,1+4t-17t^2+48t^3-81t^4+101t^5-96t^6+69t^7-35t^8+12t^9-2t^10,0,1+3t-17t^2+48t^3-81t^4+101t^5-96t^6+69t^7-35t^8+12t^9-2t^10)
the Blanchfield form on it
x
295
First homology
of the double branched cover of 12a_0866
Z/295
2 2
12a_0867
1

detected by
an unknotting move
1-9t+34t^2-69t^3+87t^4-69t^5+34t^6-9t^7+t^8
Seifert matrix of 12a_0867
1 0 0 0 -1 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 -1 -1 1 -1 0 0 1
0 -1 -1 0 -1 0 0 0
1 0 -1 0 -1 1 -1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,-t^2,-t-t^2,-t-t^2,1-t^2,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
313
First homology
of the double branched cover of 12a_0867
Z/313
0 0
12a_0868
2

detected by
the Lickorish test
1-10t+39t^2-84t^3+109t^4-84t^5+39t^6-10t^7+t^8
Seifert matrix of 12a_0868
1 0 0 0 0 0 0 0
1 -1 0 1 1 0 0 0
-1 0 -1 -1 -1 -1 0 -1
0 0 0 1 0 0 0 1
1 0 0 0 1 0 0 0
-1 0 0 -1 -1 -1 0 0
1 -1 0 1 0 0 -1 0
0 0 0 0 0 0 0 1
2
377
First homology
of the double branched cover of 12a_0868
Z/377
0 0
12a_0869
2

detected by
the signature
1-5t+12t^2-21t^3+27t^4-29t^5+27t^6-21t^7+12t^8-5t^9+t^10
Seifert matrix of 12a_0869
1 0 1 0 0 0 1 -1 0 0
0 -1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 0 0 0
0 -1 0 -1 0 0 0 0 0 0
1 -1 1 -1 1 0 1 -1 1 0
1 -1 1 -1 1 1 1 -1 1 1
0 0 0 0 0 0 1 0 0 0
0 -1 0 -1 0 0 0 -1 0 0
1 0 1 -1 0 0 1 -1 1 0
1 -1 1 -1 1 0 1 -1 1 1
1 or 2
161
First homology
of the double branched cover of 12a_0869
Z/161
4 4
12a_0870
1

detected by
an unknotting move
-2+10t-23t^2+37t^3-43t^4+37t^5-23t^6+10t^7-2t^8
Seifert matrix of 12a_0870
1 0 1 0 1 -1 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 1 0 0 0
0 -1 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
0 -1 0 -1 0 -1 0 0
1 0 1 -1 1 -1 1 0
-1 1 -1 1 -1 1 -1 2
1
Generator of the Alexander module
(2t^2,1-t^3,t-3t^2+4t^3+t^4+3t^5,2-t-2t^3,t,-4t,-t-t^2,1+2t+3t^2)
the Blanchfield form on it
187
First homology
of the double branched cover of 12a_0870
Z/187
2 2
12a_0871
1

detected by
an unknotting move
-2+11t-27t^2+45t^3-53t^4+45t^5-27t^6+11t^7-2t^8
Seifert matrix of 12a_0871
-1 0 0 0 0 0 0 0
0 2 0 0 0 1 1 0
-1 0 -1 0 0 0 0 0
-1 -1 -1 1 0 -1 0 0
-1 -1 -1 1 1 -1 0 1
-1 0 -1 0 0 -1 0 0
0 0 -1 0 0 0 1 0
-1 -1 -1 1 0 -1 0 1
1
Generator of the Alexander module
(0,t+t^2+2t^3-t^5,1+t^2+t^3-t^4,-1-3t^2-2t^3+2t^4,-2t^2,1-t+3t^2+2t^3-2t^4,t-t^2+2t^3+t^4-t^5,1-t)
the Blanchfield form on it
x
223
First homology
of the double branched cover of 12a_0871
Z/223
2 2
12a_0872
1

detected by
an unknotting move
-4+21t-45t^2+57t^3-45t^4+21t^5-4t^6
Seifert matrix of 12a_0872
-1 0 0 0 0 0
0 2 0 1 1 0
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
0 0 -1 0 1 0
1 1 1 1 0 2
1
Generator of the Alexander module
(2-30t-26t^2+146t^3+50t^4-260t^5+196t^6-64t^7+8t^8,-15+87t-4t^2-98t^3+90t^4-32t^5+4t^6,-3+36t+6t^2-51t^3+45t^4-16t^5+2t^6,18-71t+34t^2+41t^3-45t^4+16t^5-2t^6,-15+29t-32t^2+8t^3,-2+27t-12t^2+65t^3+14t^4-102t^5+90t^6-32t^7+4t^8)
the Blanchfield form on it
x
197
First homology
of the double branched cover of 12a_0872
Z/197
0 2
12a_0873
2

detected by
the Nakanishi index
-5+22t-42t^2+51t^3-42t^4+22t^5-5t^6
Seifert matrix of 12a_0873
1 0 0 0 0 0
1 1 1 0 0 0
1 0 1 0 0 0
1 1 1 -2 -1 -1
1 1 1 -1 -2 -1
1 1 1 0 -1 -2
2
189
First homology
of the double branched cover of 12a_0873
Z/63+Z/3
0 2
12a_0874
1

detected by
an unknotting move
-2+12t-33t^2+59t^3-71t^4+59t^5-33t^6+12t^7-2t^8
Seifert matrix of 12a_0874
-1 0 0 0 0 0 0 0
0 2 0 1 0 1 1 1
-1 0 -1 0 0 0 0 0
-1 0 -1 1 0 0 1 0
-1 -1 -1 0 1 -1 0 0
-1 0 -1 0 0 -1 0 0
0 0 -1 0 0 0 1 0
-1 0 -1 1 0 0 1 1
1
Generator of the Alexander module
(0,-3+2t,0,-2+t,0,0,0,0)
the Blanchfield form on it
2t^-3-9t^-2+18t^-1-25+18t-9t^2+2t^3
283
First homology
of the double branched cover of 12a_0874
Z/283
2 2
12a_0875
1

detected by
an unknotting move
5-29t+72t^2-95t^3+72t^4-29t^5+5t^6
Seifert matrix of 12a_0875
1 0 0 0 0 0
0 -1 1 -1 0 0
1 0 1 0 0 0
0 0 1 -2 0 -1
1 0 1 -1 -2 -1
1 0 1 -1 -1 -2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
1
307
First homology
of the double branched cover of 12a_0875
Z/307
-2 2
12a_0876
4

detected by
the signature
3-8t+13t^2-18t^3+21t^4-18t^5+13t^6-8t^7+3t^8
Seifert matrix of 12a_0876
-1 -1 -1 -1 -1 -1 -1 -1
0 -1 0 -1 -1 -1 -1 -1
0 -1 -1 -1 -1 -1 -1 -1
0 0 0 -2 -2 -1 -2 -2
0 0 0 -1 -2 -1 -1 -2
0 0 0 -1 -1 -2 -1 -1
0 0 0 -1 -2 -1 -2 -2
0 0 0 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
3t^-3-8t^-2+12t^-1-13+12t-8t^2+3t^3
105
First homology
of the double branched cover of 12a_0876
Z/105
-8 8
12a_0877
3

detected by
the signature
6-18t+27t^2-29t^3+27t^4-18t^5+6t^6
Seifert matrix of 12a_0877
-1 -1 -1 -1 1 -1
0 -1 0 -1 1 -1
0 -1 -1 -1 1 -1
0 0 0 -2 2 -1
0 0 0 1 -3 1
0 0 0 -1 1 -2
1
Generator of the Alexander module
(0,-2,0,0,3,0)
the Blanchfield form on it
-51t^-3+180t^-2-303t^-1+348-303t+180t^2-51t^3
131
First homology
of the double branched cover of 12a_0877
Z/131
-6 6
12a_0878
1

detected by
an unknotting move
-1+3t-6t^2+9t^3-12t^4+13t^5-12t^6+9t^7-6t^8+3t^9-t^10
Seifert matrix of 12a_0878
-1 -1 0 -1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0 0 0
0 -1 0 -1 0 0 0 0 0 0
-1 -1 -1 -1 1 0 0 1 0 0
-1 -1 -1 -1 1 1 0 1 1 0
-1 -1 -1 -1 1 1 1 1 1 1
0 0 0 0 0 0 0 1 0 0
-1 -1 -1 -1 1 0 0 1 1 0
-1 -1 -1 -1 1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-4-3t^-3+6t^-2-9t^-1+11-9t+6t^2-3t^3+t^4
75
First homology
of the double branched cover of 12a_0878
Z/75
2 2
12a_0879
1

detected by
an unknotting move
2-7t+15t^2-23t^3+27t^4-23t^5+15t^6-7t^7+2t^8
Seifert matrix of 12a_0879
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 -1 0 -1 0 0 0 0
-1 -1 -1 -1 1 0 0 1
1 1 1 1 -1 2 0 -1
-1 -1 -1 -1 1 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-14t^-1+16-14t+9t^2-4t^3+t^4
121
First homology
of the double branched cover of 12a_0879
Z/121
0 0
12a_0880
2

detected by
the signature
12-40t+57t^2-40t^3+12t^4
Seifert matrix of 12a_0880
-2 0 0 0
-1 -2 2 -1
1 1 -3 1
-1 -1 1 -2
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-6t^-2+22t^-1-32+22t-6t^2
161
First homology
of the double branched cover of 12a_0880
Z/161
-4 4
12a_0881
2

detected by
the signature
2-7t+13t^2-15t^3+15t^4-15t^5+13t^6-7t^7+2t^8
Seifert matrix of 12a_0881
-2 1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
1 -1 1 0 0 1 0 0
1 -1 1 1 0 1 1 0
1 -1 1 1 1 1 1 1
0 0 0 0 0 1 0 0
1 -1 1 0 0 1 1 0
1 -1 1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-13t^-1+15-13t+7t^2-2t^3
89
First homology
of the double branched cover of 12a_0881
Z/89
4 4
12a_0882
1

detected by
an unknotting move
4-16t+33t^2-41t^3+33t^4-16t^5+4t^6
Seifert matrix of 12a_0882
-2 1 0 0 0 0
0 -1 0 0 0 0
1 -1 1 0 0 1
-1 1 -1 2 0 -1
1 -1 1 -1 1 1
0 0 0 0 0 1
1 or 2
147
First homology
of the double branched cover of 12a_0882
Z/147
2 2
12a_0883
2

detected by
the Lickorish test
-4+20t-42t^2+53t^3-42t^4+20t^5-4t^6
Seifert matrix of 12a_0883
-1 0 0 0 0 0
0 2 0 1 1 -1
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
0 0 -1 0 1 0
1 0 1 0 -1 2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-2t^-3+10t^-2-21t^-1+26-21t+10t^2-2t^3
185
First homology
of the double branched cover of 12a_0883
Z/185
0 2
12a_0884
2

detected by
the Lickorish test
-1+9t-33t^2+66t^3-81t^4+66t^5-33t^6+9t^7-t^8
Seifert matrix of 12a_0884
1 0 0 0 0 0 0 0
1 -1 0 1 1 0 0 0
-1 0 -1 0 -1 0 -1 0
0 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0
1 -1 0 1 0 -1 0 0
-1 0 0 -1 -1 0 -1 0
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,-1-5t+4t^2-4t^3+t^4,-1-2t+4t^2-t^3,0,0,-2t+3t^2-4t^3+t^4,0,2t^2-3t^3+4t^4-t^5)
the Blanchfield form on it
x
299
First homology
of the double branched cover of 12a_0884
Z/299
-2 2
12a_0885
2

detected by
the Lickorish test
-1+9t-32t^2+63t^3-77t^4+63t^5-32t^6+9t^7-t^8
Seifert matrix of 12a_0885
1 0 0 0 0 0 0 0
1 -1 0 1 1 0 0 0
-1 0 -1 0 -1 -1 0 -1
0 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0
-1 0 0 -1 -1 -1 0 0
1 -1 0 1 0 0 -1 0
-1 0 0 -1 -1 -1 0 -1
1
Generator of the Alexander module
(0,-9t+17t^2-18t^3+14t^4-10t^5+5t^6-t^7,4-5t+9t^2-8t^3+6t^4-4t^5+t^6,0,9t-16t^2+10t^3-6t^4+4t^5-t^6,9-8t+2t^2-4t^3+4t^4-t^5,0,9-17t+18t^2-14t^3+10t^4-5t^5+t^6)
the Blanchfield form on it
x
287
First homology
of the double branched cover of 12a_0885
Z/287
-2 2
12a_0886
2

detected by
the Nakanishi index
-1+7t-24t^2+45t^3-53t^4+45t^5-24t^6+7t^7-t^8
Seifert matrix of 12a_0886
1 0 0 1 0 0 0 0
0 -1 -1 0 -1 1 0 -1
0 0 -1 0 -1 0 0 0
0 0 0 1 0 0 0 0
1 0 0 1 1 0 0 0
0 0 0 0 0 1 0 0
0 0 -1 0 0 0 1 -1
0 0 -1 0 -1 1 0 -1
2
207
First homology
of the double branched cover of 12a_0886
Z/69+Z/3
2 2
12a_0887
1

detected by
an unknotting move
1-9t+32t^2-63t^3+79t^4-63t^5+32t^6-9t^7+t^8
Seifert matrix of 12a_0887
1 0 1 0 0 -1 0 -1
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 -1
0 -1 0 -1 0 0 0 0
0 -1 0 -1 1 -1 0 -1
0 -1 0 -1 0 -1 0 0
1 0 1 -1 0 -1 1 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1-5t-t^2+2t^3+t^4+3t^5-t^6,-t-2t^2+3t^3+3t^4-t^5+2t^6-4t^7+t^8,7t-9t^2+3t^3+7t^4-4t^5+8t^6-9t^7+2t^8,-t+4t^2+5t^3+4t^4-3t^5-t^6-3t^7+t^8,-1-t-3t^2+7t^3+2t^4+t^5-2t^6-3t^7+t^8,-t+5t^2+t^3-2t^4-t^5-3t^6+t^7)
the Blanchfield form on it
x
289
First homology
of the double branched cover of 12a_0887
Z/289
0 0
12a_0888
1

detected by
an unknotting move
-1+9t-33t^2+67t^3-83t^4+67t^5-33t^6+9t^7-t^8
Seifert matrix of 12a_0888
1 0 0 0 0 -1 0 -1
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 -1 -1 1 -1 -1 0 -1
0 0 0 0 -1 0 0 -1
0 -1 -1 0 0 -1 0 0
1 0 -1 0 0 -1 1 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,-2t^2+5t^3-19t^4+32t^5-28t^6+12t^7-2t^8,t-15t^2+35t^3-65t^4+73t^5-61t^6+46t^7-30t^8+12t^9-2t^10,-2t+3t^2-14t^3+13t^4+4t^5-16t^6+10t^7-2t^8,2t+3t^2-35t^3+56t^4-40t^5+14t^6-2t^7,t-17t^2+32t^3-28t^4+12t^5-2t^6,1-4t+22t^2-72t^3+98t^4-70t^5+26t^6-4t^7,0)
the Blanchfield form on it
x
303
First homology
of the double branched cover of 12a_0888
Z/303
-2 2
12a_0889
1

detected by
an unknotting move
-2+10t-22t^2+32t^3-35t^4+32t^5-22t^6+10t^7-2t^8
Seifert matrix of 12a_0889
-1 0 0 0 0 0 0 -1
-1 1 -1 1 1 1 1 -1
-1 0 -1 0 0 0 0 -1
-1 0 -1 1 0 1 0 0
-1 0 -1 1 1 1 1 0
0 0 -1 0 0 1 0 0
-1 0 -1 1 0 1 1 0
0 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
2t^-3-10t^-2+21t^-1-27+21t-10t^2+2t^3
167
First homology
of the double branched cover of 12a_0889
Z/167
2 2
12a_0890
2

detected by
the Lickorish test
-4+21t-47t^2+61t^3-47t^4+21t^5-4t^6
Seifert matrix of 12a_0890
-1 0 0 0 0 -1
-1 1 -1 1 -1 -1
-1 0 -1 0 0 -1
0 0 -1 1 0 0
1 0 1 -1 2 0
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,1,0,0,-2,0)
the Blanchfield form on it
4t^-2-15t^-1+20-15t+4t^2
205
First homology
of the double branched cover of 12a_0890
Z/205
0 0
12a_0891
2

detected by
the signature
2-11t+29t^2-47t^3+55t^4-47t^5+29t^6-11t^7+2t^8
Seifert matrix of 12a_0891
-1 0 0 -1 -1 0 -1 -1
-1 1 -1 -1 0 1 0 0
-1 0 -1 -1 -1 0 -1 -1
0 0 0 -2 -2 0 -2 -2
0 0 0 -1 -2 0 -1 -2
0 0 -1 0 0 1 0 0
0 0 0 -1 -2 0 -2 -2
0 0 0 -1 -1 0 -1 -2
1
Generator of the Alexander module
(-6-2t-20t^2+15t^3,9+12t-4t^2,-2-7t-18t^2+35t^3-15t^4,4-12t+5t^2,-25+36t-15t^2,5t-15t^2+56t^3-30t^4,2,9-12t+5t^2)
the Blanchfield form on it
-2837t^-6+20279t^-5-77641t^-4+200908t^-3-383071t^-2+555940t^-1-627608+555940t-383071t^2+200908t^3-77641t^4+20279t^5-2837t^6
233
First homology
of the double branched cover of 12a_0891
Z/233
-4 4
12a_0892
1

detected by
an unknotting move
4-22t+53t^2-69t^3+53t^4-22t^5+4t^6
Seifert matrix of 12a_0892
-1 0 0 -1 1 0
-1 1 -1 -1 0 1
-1 0 -1 -1 1 0
0 0 0 -2 2 0
0 0 0 1 -3 0
0 0 -1 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,1)
the Blanchfield form on it
-2t^-1+3-2t
227
First homology
of the double branched cover of 12a_0892
Z/227
-2 2
12a_0893
1

detected by
an unknotting move
1-9t+33t^2-68t^3+87t^4-68t^5+33t^6-9t^7+t^8
Seifert matrix of 12a_0893
1 0 0 0 0 0 0 0
1 -1 0 1 1 0 0 0
-1 0 -1 -1 -1 0 -1 0
0 0 0 1 0 0 1 0
1 0 0 0 1 0 0 0
1 -1 0 1 0 -1 0 0
0 0 0 0 0 0 1 0
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-2t^-3+10t^-2-23t^-1+31-23t+10t^2-2t^3
309
First homology
of the double branched cover of 12a_0893
Z/309
0 0
12a_0894
2

detected by
the Lickorish test
2-12t+33t^2-56t^3+67t^4-56t^5+33t^6-12t^7+2t^8
Seifert matrix of 12a_0894
-1 0 0 0 -1 0 0 -1
-1 1 -1 1 -1 1 1 0
-1 0 -1 0 -1 0 0 -1
-1 0 -1 1 0 1 0 0
0 0 0 0 -2 0 0 -2
0 0 -1 0 0 1 0 0
-1 0 -1 1 0 1 1 0
0 0 0 0 -1 0 0 -2
1
Generator of the Alexander module
(12t-12t^2+6t^3+6t^4-16t^5-40t^6+56t^7-16t^8,3-9t+t^2+6t^3-28t^4+18t^5+6t^6-4t^7,15-6t-16t^2+76t^3-114t^4+64t^5-12t^6,3-11t^2+30t^3-44t^4+28t^5-6t^6,-3+2t^2-12t^3+14t^4-4t^5,9t+6t^2-28t^3+54t^4-50t^5-32t^6+56t^7-16t^8,2+t+7t^2-6t^3+16t^4-20t^5+6t^6,-3-6t+14t^2-32t^3+30t^4-8t^5)
the Blanchfield form on it
x
273
First homology
of the double branched cover of 12a_0894
Z/273
0 2
12a_0895
2

detected by
the Nakanishi index
-2+10t-27t^2+51t^3-63t^4+51t^5-27t^6+10t^7-2t^8
Seifert matrix of 12a_0895
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 0 -1 0 0 1
0 0 0 -1 0 -1 -1 -1
1 0 0 0 1 0 0 0
1 0 0 0 1 -1 0 -1
1 0 0 0 1 -1 -1 -1
1 1 0 0 1 0 0 -2
2
243
First homology
of the double branched cover of 12a_0895
Z/81+Z/3
-2 2
12a_0896
2

detected by
by the span of Levine-Tristram signatures
-2+11t-26t^2+40t^3-45t^4+40t^5-26t^6+11t^7-2t^8
Seifert matrix of 12a_0896
-1 0 0 0 0 0 0 0
0 2 0 0 0 1 0 1
-1 0 -1 -1 0 0 -1 0
-1 0 0 -1 0 0 0 0
-1 -1 -1 -1 1 -1 -1 0
-1 0 -1 -1 0 -1 -1 0
-1 0 0 -1 0 0 -1 0
0 0 -1 -1 0 0 -1 1
1
Generator of the Alexander module
?
the Blanchfield form on it
?
203
First homology
of the double branched cover of 12a_0896
Z/203
0 0
12a_0897
1

detected by
an unknotting move
-4+22t-50t^2+65t^3-50t^4+22t^5-4t^6
Seifert matrix of 12a_0897
-1 0 0 0 0 0
0 2 0 1 0 1
-1 -1 1 -1 1 0
-1 0 0 -1 1 0
1 0 0 0 -2 0
0 0 0 0 1 1
1 or 2
217
First homology
of the double branched cover of 12a_0897
Z/217
0 2
12a_0898
1

detected by
an unknotting move
-1+4t-11t^2+21t^3-30t^4+33t^5-30t^6+21t^7-11t^8+4t^9-t^10
Seifert matrix of 12a_0898
-1 -1 0 0 -1 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0 0 0
-1 0 -1 1 0 0 0 1 0 0
0 -1 0 0 -1 0 0 0 0 0
-1 -1 -1 1 -1 1 0 1 1 0
-1 -1 -1 1 -1 1 1 1 1 1
0 0 0 0 0 0 0 1 0 0
-1 0 -1 1 0 0 0 1 1 0
-1 -1 -1 1 -1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+10t^-2-17t^-1+21-17t+10t^2-4t^3+t^4
167
First homology
of the double branched cover of 12a_0898
Z/167
2 2
12a_0899
1

detected by
an unknotting move
2-8t+20t^2-35t^3+43t^4-35t^5+20t^6-8t^7+2t^8
Seifert matrix of 12a_0899
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
-1 0 -1 1 0 1 0 0
0 -1 0 0 -1 0 0 0
0 0 0 0 0 1 0 0
-1 0 -1 1 0 1 1 0
1 1 1 -1 1 -1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,-t,0,1)
the Blanchfield form on it
3t^-4-16t^-3+43t^-2-74t^-1+88-74t+43t^2-16t^3+3t^4
173
First homology
of the double branched cover of 12a_0899
Z/173
0 0
12a_0900
3

detected by
the signature
8-29t+54t^2-65t^3+54t^4-29t^5+8t^6
Seifert matrix of 12a_0900
-1 0 0 -1 1 -1
0 -1 -1 0 -1 0
0 0 -2 0 -1 -1
0 0 -1 -2 0 -1
0 0 0 1 -2 1
0 0 -1 -1 0 -2
1 or 2
247
First homology
of the double branched cover of 12a_0900
Z/247
-6 6
12a_0901 1 or 2
-1+9t-27t^2+47t^3-55t^4+47t^5-27t^6+9t^7-t^8
Seifert matrix of 12a_0901
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
0 1 1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 1 0
-1 0 0 -1 1 1 1 1
0 1 0 -1 0 0 1 0
-1 0 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,-4t-11t^2+38t^3-49t^4+23t^5+52t^6-155t^7+228t^8-243t^9+194t^10-117t^11+52t^12-15t^13+2t^14,-4t-11t^2+38t^3-49t^4+23t^5+52t^6-155t^7+228t^8-243t^9+194t^10-117t^11+52t^12-15t^13+2t^14,-2+15t-23t^2+12t^3+22t^4-77t^5+125t^6-141t^7+123t^8-80t^9+39t^10-13t^11+2t^12,3-8t+12t^2+24t^3-105t^4+184t^5-182t^6
the Blanchfield form on it
x
223
First homology
of the double branched cover of 12a_0901
Z/223
2 2
12a_0902
1

detected by
an unknotting move
-2+18t-51t^2+71t^3-51t^4+18t^5-2t^6
Seifert matrix of 12a_0902
-1 0 0 0 0 0
0 -1 0 0 0 0
0 1 1 -1 0 0
-1 0 0 -1 0 0
0 1 0 -1 1 0
1 0 0 1 -1 2
1 or 2
213
First homology
of the double branched cover of 12a_0902
Z/213
0 0
12a_0903
2

detected by
the signature
-5+26t-57t^2+73t^3-57t^4+26t^5-5t^6
Seifert matrix of 12a_0903
-1 0 -1 0 0 -1
0 1 0 0 0 0
0 0 -2 1 -1 -1
0 -1 0 -1 0 0
0 1 -1 1 -2 0
0 0 -1 1 -1 -2
1 or 2
249
First homology
of the double branched cover of 12a_0903
Z/249
-4 4
12a_0904
2

detected by
the Lickorish test
-2+10t-23t^2+36t^3-41t^4+36t^5-23t^6+10t^7-2t^8
Seifert matrix of 12a_0904
-1 0 0 0 0 0 0 -1
-1 1 -1 -1 1 -1 1 -1
-1 0 -1 -1 0 -1 0 -1
-1 0 0 -1 0 0 0 -1
-1 0 -1 -1 1 -1 1 0
-1 0 0 -1 0 -1 0 -1
0 0 -1 -1 0 -1 1 0
0 0 0 0 0 0 0 -2
2
183
First homology
of the double branched cover of 12a_0904
Z/183
-2 2
12a_0905
2

detected by
the Nakanishi index
-4+20t-43t^2+55t^3-43t^4+20t^5-4t^6
Seifert matrix of 12a_0905
-1 0 0 0 0 -1
-1 1 1 1 1 -1
-1 0 1 1 1 0
1 0 0 -2 0 1
0 0 0 1 1 0
0 0 0 0 0 -2
2
189
First homology
of the double branched cover of 12a_0905
Z/63+Z/3
0 2
12a_0906
2

detected by
the Nakanishi index
1-8t+26t^2-53t^3+69t^4-53t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0906
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 0 -1 0 -1 0
0 0 0 -1 0 -1 1 -1
1 0 0 0 1 0 0 0
1 0 0 0 1 -1 1 0
0 0 0 0 0 0 1 0
1 0 0 0 1 -1 1 -1
2
245
First homology
of the double branched cover of 12a_0906
Z/35+Z/7
0 0
12a_0907
3

detected by
the new u==2 criterion
2-11t+29t^2-45t^3+51t^4-45t^5+29t^6-11t^7+2t^8
Seifert matrix of 12a_0907
-1 0 0 0 -1 0 0 -1
-1 1 -1 -1 -1 -1 1 0
-1 0 -1 -1 -1 -1 0 -1
-1 0 0 -1 -1 0 0 -1
0 0 0 0 -2 0 0 -2
-1 0 0 -1 -1 -1 0 -1
0 0 -1 -1 0 -1 1 0
0 0 0 0 -1 0 0 -2
2
225
First homology
of the double branched cover of 12a_0907
Z/45+Z/5
-4 4
12a_0908
2

detected by
the Lickorish test
4-22t+55t^2-73t^3+55t^4-22t^5+4t^6
Seifert matrix of 12a_0908
-1 0 -1 0 0 -1
-1 1 -1 1 1 0
0 0 -2 0 0 -2
1 0 1 -2 0 1
0 0 0 1 1 0
0 0 -1 0 0 -2
1 or 2
235
First homology
of the double branched cover of 12a_0908
Z/235
-2 2
12a_0909
2

detected by
the signature
1-4t+9t^2-14t^3+16t^4-17t^5+16t^6-14t^7+9t^8-4t^9+t^10
Seifert matrix of 12a_0909
-1 -1 0 0 -1 -1 -1 -1 -1 -1
0 1 0 1 0 0 0 1 0 0
-1 0 -1 0 -1 -1 -1 0 -1 -1
0 0 0 1 0 0 0 0 0 0
0 -1 0 0 -1 -1 -1 0 -1 -1
0 -1 0 0 0 -1 -1 0 0 -1
0 -1 0 0 0 0 -1 0 0 0
0 0 0 1 0 0 0 1 0 0
0 -1 0 0 0 -1 -1 0 -1 -1
0 -1 0 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-14t^-1+15-14t+9t^2-4t^3+t^4
105
First homology
of the double branched cover of 12a_0909
Z/105
-4 4
12a_0910
1

detected by
an unknotting move
-2+9t-22t^2+36t^3-41t^4+36t^5-22t^6+9t^7-2t^8
Seifert matrix of 12a_0910
-1 -1 0 0 -1 1 -1 -1
0 1 0 1 0 0 0 1
-1 0 -1 0 -1 1 -1 0
0 0 0 1 0 0 0 0
0 -1 0 0 -1 1 -1 0
0 1 0 0 0 -2 1 0
0 -1 0 0 0 0 -1 0
0 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-4-5t^-3+13t^-2-22t^-1+26-22t+13t^2-5t^3+t^4
179
First homology
of the double branched cover of 12a_0910
Z/179
-2 2
12a_0911
1

detected by
an unknotting move
-2+9t-23t^2+39t^3-45t^4+39t^5-23t^6+9t^7-2t^8
Seifert matrix of 12a_0911
-1 -1 0 0 0 -1 1 0
0 1 0 1 0 1 0 0
-1 0 -1 0 0 0 1 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 -1
0 0 0 1 0 1 0 0
0 1 0 0 -1 0 -2 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
t^-4-5t^-3+14t^-2-25t^-1+30-25t+14t^2-5t^3+t^4
191
First homology
of the double branched cover of 12a_0911
Z/191
-2 2
12a_0912
1

detected by
an unknotting move
-3+12t-26t^2+35t^3-26t^4+12t^5-3t^6
Seifert matrix of 12a_0912
-1 -1 0 0 -1 -1
0 1 0 1 0 1
-1 0 -1 0 -1 0
0 0 0 1 0 0
0 -1 0 0 -3 0
0 0 0 1 0 1
1
Generator of the Alexander module
(-2t+t^2,0,0,-2t,1-t,t^2-2t^3)
the Blanchfield form on it
2t^-6-5t^-5-5t^-4+33t^-3-8t^-2-132t^-1+230-132t-8t^2+33t^3-5t^4-5t^5+2t^6
117
First homology
of the double branched cover of 12a_0912
Z/117
0 0
12a_0913
1

detected by
an unknotting move
1-7t+24t^2-48t^3+59t^4-48t^5+24t^6-7t^7+t^8
Seifert matrix of 12a_0913
-1 0 -1 0 0 -1 -1 0
-1 -1 -1 0 0 -1 -1 0
0 0 -1 0 -1 -1 -1 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 1 -1 -1 -1 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 -1 0 1
1 or 2
219
First homology
of the double branched cover of 12a_0913
Z/219
-2 2
12a_0914
2

detected by
the Lickorish test
5-25t+59t^2-77t^3+59t^4-25t^5+5t^6
Seifert matrix of 12a_0914
-1 0 0 0 0 0
0 2 1 1 1 0
0 0 1 0 0 0
-1 0 0 -1 0 0
0 1 1 1 2 1
1 1 0 1 1 2
1 or 2
255
First homology
of the double branched cover of 12a_0914
Z/255
2 2
12a_0915
1

detected by
an unknotting move
3-23t+65t^2-89t^3+65t^4-23t^5+3t^6
Seifert matrix of 12a_0915
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 1 -1 0
0 -1 0 -1 0 0
1 0 -1 1 -2 0
1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,-1-9t+21t^2-16t^3+4t^4,17t-44t^2+40t^3-7t^4-13t^5+9t^6-2t^7,-7t+11t^2-21t^3+32t^4-34t^5+18t^6-4t^7,1+6t-15t^2+17t^3-9t^4+2t^5,7t^2-13t^3+9t^4-2t^5)
the Blanchfield form on it
x
271
First homology
of the double branched cover of 12a_0915
Z/271
-2 2
12a_0916
1

detected by
an unknotting move
-1+4t-10t^2+18t^3-26t^4+29t^5-26t^6+18t^7-10t^8+4t^9-t^10
Seifert matrix of 12a_0916
-1 -1 0 0 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0 0 0
-1 0 -1 1 0 0 0 1 0 0
-1 0 -1 1 1 0 0 1 1 0
0 -1 0 0 0 -1 0 0 0 0
-1 -1 -1 1 1 -1 1 1 1 1
0 0 0 0 0 0 0 1 0 0
-1 0 -1 1 0 0 0 1 1 0
-1 0 -1 1 1 0 0 1 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+10t^-2-17t^-1+21-17t+10t^2-4t^3+t^4
147
First homology
of the double branched cover of 12a_0916
Z/147
2 2
12a_0917
1

detected by
an unknotting move
2-9t+23t^2-39t^3+47t^4-39t^5+23t^6-9t^7+2t^8
Seifert matrix of 12a_0917
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 1 0 0 0 1
1 0 1 -1 2 0 0 -1
0 -1 0 0 0 -1 0 0
-1 -1 -1 1 -1 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(-3t-7t^2+34t^4-59t^5+32t^6+35t^7-56t^8+26t^9-4t^10,-1-3t-2t^2+10t^3-13t^4+2t^5+13t^6-10t^7+2t^8,1+t+3t^2-t^3-3t^4+t^5+14t^6-37t^7+35t^8-14t^9+2t^10,-2t+3t^2+3t^3-11t^4+2t^5+27t^6-47t^7+37t^8-14t^9+2t^10,1+t-8t^2-3t^3+21t^4-15t^5-25t^6+60t^7-47t^8+16t^9-2t^10,-1+2t-3t^3+11t^4-12t^5-4t^6+22t^7-25t^8+
the Blanchfield form on it
x
193
First homology
of the double branched cover of 12a_0917
Z/193
0 0
12a_0918
2

detected by
the Lickorish test
-1+9t-29t^2+53t^3-63t^4+53t^5-29t^6+9t^7-t^8
Seifert matrix of 12a_0918
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
0 1 1 0 -1 0 0 0
0 1 1 1 -1 0 1 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 1 0 1
0 1 1 0 -1 0 1 0
0 1 0 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,1,-t,0,1+t,1,t)
the Blanchfield form on it
2t^-3-16t^-2+41t^-1-56+41t-16t^2+2t^3
247
First homology
of the double branched cover of 12a_0918
Z/247
2 2
12a_0919
1

detected by
an unknotting move
-2+16t-45t^2+63t^3-45t^4+16t^5-2t^6
Seifert matrix of 12a_0919
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 1 0 1
0 -1 1 0 2 0
0 1 -1 0 0 1
1
Generator of the Alexander module
(0,0,1+t,1+2t,-1-t,t)
the Blanchfield form on it
-1
189
First homology
of the double branched cover of 12a_0919
Z/189
0 0
12a_0920
2

detected by
the signature
1-4t+9t^2-16t^3+21t^4-23t^5+21t^6-16t^7+9t^8-4t^9+t^10
Seifert matrix of 12a_0920
1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 -1 -1 0 -1 -1
1 0 0 0 1 0 0 0 0 0
0 -1 0 0 0 -1 -1 0 0 -1
0 -1 0 0 0 0 -1 0 0 0
-1 -1 0 -1 -1 -1 -1 -1 -1 -1
0 -1 0 0 0 -1 -1 0 -1 -1
0 -1 0 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+8t^-2-12t^-1+13-12t+8t^2-4t^3+t^4
125
First homology
of the double branched cover of 12a_0920
Z/125
-4 4
12a_0921
3

detected by
the new u==2 criterion
-2+9t-21t^2+35t^3-41t^4+35t^5-21t^6+9t^7-2t^8
Seifert matrix of 12a_0921
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 -1 -1 1 -1 -1
-1 -1 0 -1 -1 1 -1 0
1 0 0 0 1 0 0 0
0 1 0 0 0 -2 1 0
0 -1 0 0 0 0 -1 0
-1 -1 0 -1 -1 1 -1 -1
2
175
First homology
of the double branched cover of 12a_0921
Z/35+Z/5
-2 2
12a_0922
1

detected by
an unknotting move
-2+11t-32t^2+60t^3-73t^4+60t^5-32t^6+11t^7-2t^8
Seifert matrix of 12a_0922
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 0 -1 1 -1 0
0 0 0 -1 0 -1 0 -1
1 0 0 0 1 0 0 0
1 1 0 0 1 -2 1 0
0 -1 0 0 0 0 -1 0
1 0 0 0 1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,1,1)
the Blanchfield form on it
-2t^-1+3-2t
283
First homology
of the double branched cover of 12a_0922
Z/283
-2 2
12a_0923
3

detected by
the signature
-2+9t-18t^2+25t^3-27t^4+25t^5-18t^6+9t^7-2t^8
Seifert matrix of 12a_0923
-1 0 -1 0 0 -1 0 0
0 1 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 0
0 -1 0 -1 -1 0 0 -1
0 -1 0 0 -1 0 0 0
0 0 0 1 1 -2 1 1
0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 -1
1 or 2
135
First homology
of the double branched cover of 12a_0923
Z/135
-6 6
12a_0924
2

detected by
the signature
-4+20t-43t^2+55t^3-43t^4+20t^5-4t^6
Seifert matrix of 12a_0924
-1 0 -1 0 0 -1
0 1 0 0 0 0
0 -1 -1 0 0 -1
0 1 0 -2 1 0
0 -1 0 0 -1 0
0 0 0 -1 1 -2
1
Generator of the Alexander module
(1,0,0,1,0,1)
the Blanchfield form on it
7t^-3-38t^-2+87t^-1-112+87t-38t^2+7t^3
189
First homology
of the double branched cover of 12a_0924
Z/189
-4 4
12a_0925
1

detected by
an unknotting move
2-10t+28t^2-51t^3+63t^4-51t^5+28t^6-10t^7+2t^8
Seifert matrix of 12a_0925
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 1 0 0 0 1
1 0 1 -1 2 0 1 -1
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,1+t,-3+t,0,0,0)
the Blanchfield form on it
9t^-4-45t^-3+126t^-2-230t^-1+284-230t+126t^2-45t^3+9t^4
245
First homology
of the double branched cover of 12a_0925
Z/245
0 0
12a_0926
1

detected by
an unknotting move
-2+8t-16t^2+24t^3-27t^4+24t^5-16t^6+8t^7-2t^8
Seifert matrix of 12a_0926
1 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0
1 0 1 0 0 0 0 0
0 -1 0 -1 -1 0 0 -1
0 -1 0 0 -1 0 0 0
1 1 1 1 1 -2 1 1
0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-4-4t^-3+8t^-2-12t^-1+14-12t+8t^2-4t^3+t^4
127
First homology
of the double branched cover of 12a_0926
Z/127
-2 2
12a_0927
2

detected by
the Lickorish test
-4+18t-37t^2+47t^3-37t^4+18t^5-4t^6
Seifert matrix of 12a_0927
1 0 0 0 0 0
1 1 1 0 0 0
1 0 1 0 0 0
0 1 0 -2 1 0
0 -1 0 0 -1 0
1 1 1 -1 1 -2
1
Generator of the Alexander module
(0,t+4t^2+2t^3-4t^4,1+2t-2t^2,-4t-7t^2+12t^3+2t^4-4t^5,t+2t^2-2t^3,-3-4t+15t^2-t^3-2t^4-2t^5)
the Blanchfield form on it
-2t^-2+6t^-1-7+6t-2t^2
165
First homology
of the double branched cover of 12a_0927
Z/165
0 2
12a_0928
1

detected by
an unknotting move
-1+8t-31t^2+69t^3-91t^4+69t^5-31t^6+8t^7-t^8
Seifert matrix of 12a_0928
-1 -1 0 -1 0 0 0 -1
0 1 0 0 0 0 0 0
-1 0 1 0 0 0 -1 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
-1 0 1 0 0 1 -1 -1
-1 0 0 -1 0 0 -1 -1
0 -1 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,-2t-2t^2+19t^3-2t^4-16t^5+14t^6-4t^7,1-7t+11t^2+20t^3-60t^4+25t^5+33t^6-60t^7+42t^8-18t^9+4t^10,1-6t+3t^2+32t^3-12t^4-16t^5+14t^6-4t^7,0,4t^2+4t^3-38t^4+4t^5+32t^6-28t^7+8t^8,t+4t^2-23t^3-4t^4+20t^5-14t^6+4t^7,1-2t+2t^2+9t^3-16t^4+11t^5+12t^6-20t^7+14t^8-4t^9)
the Blanchfield form on it
x
309
First homology
of the double branched cover of 12a_0928
Z/309
0 0
12a_0929
2

detected by
the Lickorish test
-2+10t-25t^2+41t^3-47t^4+41t^5-25t^6+10t^7-2t^8
Seifert matrix of 12a_0929
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 -1 -1 1 -1 -1
-1 0 0 -1 -1 1 0 -1
0 -1 0 0 -1 0 0 0
-1 1 0 0 0 2 0 0
-1 0 0 -1 -1 1 -1 -1
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-2t^-3+10t^-2-23t^-1+31-23t+10t^2-2t^3
203
First homology
of the double branched cover of 12a_0929
Z/203
-2 2
12a_0930
3

detected by
the signature
-2+9t-19t^2+28t^3-31t^4+28t^5-19t^6+9t^7-2t^8
Seifert matrix of 12a_0930
-1 0 -1 -1 0 -1 -1 0
0 1 0 0 0 0 0 0
0 -1 -1 -1 0 -1 -1 0
0 -1 0 -1 0 0 -1 0
0 -1 0 0 -1 0 0 0
0 -1 0 -1 0 -1 -1 0
0 0 0 0 1 0 -2 1
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(-t^3,0,t^2,1+t^2,0,t^2,t+t^2,0)
the Blanchfield form on it
-2t^-3+6t^-2-9t^-1+10-9t+6t^2-2t^3
147
First homology
of the double branched cover of 12a_0930
Z/147
-6 6
12a_0931
2

detected by
the signature
-4+19t-40t^2+51t^3-40t^4+19t^5-4t^6
Seifert matrix of 12a_0931
-1 0 0 1 -1 0
0 1 0 0 0 0
0 -1 -1 0 0 0
0 1 0 -2 1 0
0 0 1 0 -2 1
0 -1 -1 0 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-3t^-2+11t^-1-15+11t-3t^2
177
First homology
of the double branched cover of 12a_0931
Z/177
-4 4
12a_0932
1

detected by
an unknotting move
1-7t+24t^2-46t^3+55t^4-46t^5+24t^6-7t^7+t^8
Seifert matrix of 12a_0932
-1 0 -1 -1 0 0 -1 0
-1 -1 -1 -1 0 0 -1 0
0 0 -1 -1 -1 1 -1 0
0 0 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 -1 -1 1 -1 0
-1 0 -1 0 0 0 0 1
1
Generator of the Alexander module
(2t+29t^2+53t^3-155t^4-15t^5+46t^6-660t^7+114t^8-30t^9-424t^10-40t^11,1+12t+18t^2-49t^3+283t^4-47t^5-45t^6+204t^7+20t^8,3+10t+50t^2+243t^3-53t^4+19t^5+212t^6+20t^7,7+23t+119t^2+582t^3-127t^4+44t^5+508t^6+48t^7,7+24t-19t^2+16t^3+12t^4,-9-31t+24t^2-20t^3-16t^4,-2-11t+9t^2+87t^3+t^4-32t^5+92t^6+16t^7,-
the Blanchfield form on it
x
211
First homology
of the double branched cover of 12a_0932
Z/211
-2 2
12a_0933
1

detected by
an unknotting move
-1+8t-26t^2+49t^3-59t^4+49t^5-26t^6+8t^7-t^8
Seifert matrix of 12a_0933
1 0 1 0 1 -1 0 -1
0 -1 0 0 0 0 0 0
0 0 1 0 1 0 0 -1
1 0 1 1 1 -1 0 -1
0 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 1 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,-1,-t,t+t^2,-t,2t,t,1+t)
the Blanchfield form on it
t^-3-7t^-2+19t^-1-27+19t-7t^2+t^3
227
First homology
of the double branched cover of 12a_0933
Z/227
2 2
12a_0934
2

detected by
the Lickorish test
-2+10t-27t^2+49t^3-59t^4+49t^5-27t^6+10t^7-2t^8
Seifert matrix of 12a_0934
1 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0
1 0 1 0 0 0 0 0
1 0 1 -1 0 0 -1 0
0 -1 0 0 -1 0 0 0
1 0 1 -1 0 -1 -1 0
1 1 1 0 1 0 -2 1
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,-t-2t^2,1+t^2,1+2t-2t^2+2t^3-t^4,-t,t-2t^2+2t^3-t^4,-2+5t-7t^2+3t^3-2t^4,1+t^2+t^3)
the Blanchfield form on it
-2t^-3+8t^-2-17t^-1+23-17t+8t^2-2t^3
235
First homology
of the double branched cover of 12a_0934
Z/235
-2 2
12a_0935
1

detected by
an unknotting move
-1+8t-29t^2+59t^3-75t^4+59t^5-29t^6+8t^7-t^8
Seifert matrix of 12a_0935
-1 0 -1 0 0 0 -1 0
-1 -1 -1 0 0 0 -1 0
0 0 -1 1 -1 1 -1 0
0 0 0 1 0 1 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 0 0 1
1
Generator of the Alexander module
(0,5-12t+13t^2-6t^3+t^4,-4+4t-t^2,4-4t+t^2,0,4-4t+t^2,-4t+4t^2-t^3,0)
the Blanchfield form on it
-t^-1+2-t
269
First homology
of the double branched cover of 12a_0935
Z/269
0 0
12a_0936
1

detected by
an unknotting move
-4+20t-46t^2+61t^3-46t^4+20t^5-4t^6
Seifert matrix of 12a_0936
1 0 0 0 0 0
0 1 0 0 0 0
0 -1 -1 0 0 0
-1 1 0 2 0 0
1 0 1 -1 -2 1
0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-3-10t^-2+23t^-1-30+23t-10t^2+2t^3
201
First homology
of the double branched cover of 12a_0936
Z/201
0 0
12a_0937
3

detected by
the signature
-2+7t-11t^2+13t^3-13t^4+13t^5-11t^6+7t^7-2t^8
Seifert matrix of 12a_0937
-1 0 -1 -1 -1 -1 -1 -1
0 1 0 0 0 0 0 0
0 -1 -1 -1 -1 -1 -1 -1
0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 -1
0 -1 0 -1 -1 -1 -1 -1
0 -1 0 0 -1 0 -1 -1
0 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-11t^-1+13-11t+7t^2-2t^3
79
First homology
of the double branched cover of 12a_0937
Z/79
-6 6
12a_0938
2

detected by
the signature
-4+16t-29t^2+35t^3-29t^4+16t^5-4t^6
Seifert matrix of 12a_0938
-1 0 -1 1 -1 -1
0 1 0 0 0 0
0 -1 -1 1 -1 -1
0 1 0 -2 1 1
0 -1 0 0 -1 -1
0 0 0 0 0 -2
1 or 2
133
First homology
of the double branched cover of 12a_0938
Z/133
-4 4
12a_0939
2

detected by
the Lickorish test
-10+40t-59t^2+40t^3-10t^4
Seifert matrix of 12a_0939
-2 0 0 1
0 2 0 1
-1 0 -2 -1
0 0 -1 -2
1 or 2
159
First homology
of the double branched cover of 12a_0939
Z/159
-2 2
12a_0940
2

detected by
the Lickorish test
-2+13t-39t^2+57t^3-39t^4+13t^5-2t^6
Seifert matrix of 12a_0940
1 0 0 0 1 1
-1 -1 0 0 -1 0
0 0 -1 0 0 0
0 0 0 -2 0 0
0 0 -1 0 1 1
0 0 -1 1 0 1
1
Generator of the Alexander module
(0,5t-4t^2+t^3,0,0,1,0)
the Blanchfield form on it
-8t^-2+58t^-1-105+58t-8t^2
165
First homology
of the double branched cover of 12a_0940
Z/165
0 0
12a_0941
2

detected by
the Lickorish test
-2+8t-17t^2+26t^3-29t^4+26t^5-17t^6+8t^7-2t^8
Seifert matrix of 12a_0941
1 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0
1 0 1 0 0 0 0 0
1 0 1 -1 -1 0 -1 -1
1 0 1 0 -1 0 0 -1
1 0 1 -1 -1 -1 -1 -1
1 0 1 0 -1 0 -1 -1
1 1 1 0 0 0 0 -2
2
135
First homology
of the double branched cover of 12a_0941
Z/135
-2 2
12a_0942
1

detected by
an unknotting move
-4+18t-39t^2+51t^3-39t^4+18t^5-4t^6
Seifert matrix of 12a_0942
1 0 0 0 0 0
1 1 1 0 0 0
1 0 1 0 0 0
-1 0 -1 -2 1 1
1 0 1 0 -1 -1
1 1 1 0 0 -2
1 or 2
173
First homology
of the double branched cover of 12a_0942
Z/173
0 0
12a_0943
1

detected by
an unknotting move
-4+21t-51t^2+69t^3-51t^4+21t^5-4t^6
Seifert matrix of 12a_0943
1 0 0 0 0 0
0 1 0 0 0 0
1 -1 -1 -1 0 -1
-1 1 0 2 0 0
1 -1 -1 -1 -1 -1
1 0 0 -1 0 -2
1 or 2
221
First homology
of the double branched cover of 12a_0943
Z/221
0 0
12a_0944
1

detected by
an unknotting move
2-9t+21t^2-32t^3+37t^4-32t^5+21t^6-9t^7+2t^8
Seifert matrix of 12a_0944
-1 0 0 0 0 0 0 0
-1 -1 1 0 0 0 0 0
1 0 -2 0 0 0 0 0
0 0 0 1 0 0 1 0
0 0 -1 0 -1 0 0 0
-1 0 0 1 -1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(0,1-2t+2t^2-6t^3,-2-t-2t^2-2t^3+6t^4,2+4t^2,-4-8t^2,-2t-4t^3,2+4t^2,4t^2)
the Blanchfield form on it
3t^-7-127t^-6+579t^-5-1590t^-4+3266t^-3-5278t^-2+6955t^-1-7598+6955t-5278t^2+3266t^3-1590t^4+579t^5-127t^6+3t^7
165
First homology
of the double branched cover of 12a_0944
Z/165
0 2
12a_0945
1

detected by
an unknotting move
4-20t+46t^2-59t^3+46t^4-20t^5+4t^6
Seifert matrix of 12a_0945
-1 0 0 0 0 0
-1 -1 1 0 0 0
1 0 -2 0 0 0
0 0 0 2 0 0
0 0 -1 0 -1 0
-1 0 0 -1 -1 1
1 or 2
199
First homology
of the double branched cover of 12a_0945
Z/199
-2 2
12a_0946
3

detected by
the signature
-2+9t-19t^2+29t^3-33t^4+29t^5-19t^6+9t^7-2t^8
Seifert matrix of 12a_0946
-1 0 -1 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 -1 -1 -1 0 0 -1 0
0 0 0 -2 1 1 0 1
0 -1 0 0 -1 -1 0 -1
0 -1 0 0 0 -1 0 0
0 -1 0 -1 0 0 -1 0
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(-t,0,-2t,-t+t^3,t,0,1,0)
the Blanchfield form on it
-t^-7+3t^-6-4t^-5+13t^-4-51t^-3+120t^-2-191t^-1+222-191t+120t^2-51t^3+13t^4-4t^5+3t^6-t^7
151
First homology
of the double branched cover of 12a_0946
Z/151
-6 6
12a_0947
2

detected by
the signature
-4+18t-35t^2+43t^3-35t^4+18t^5-4t^6
Seifert matrix of 12a_0947
-1 0 -1 -1 -1 0
0 1 0 0 0 0
0 -1 -1 -1 -1 0
0 0 0 -2 0 -1
0 -1 0 -1 -1 0
0 1 0 0 0 -2
1
Generator of the Alexander module
(-2+2t-2t^2,0,0,1,0,0)
the Blanchfield form on it
-4t^-2+16t^-1-23+16t-4t^2
157
First homology
of the double branched cover of 12a_0947
Z/157
-4 4
12a_0948
1

detected by
an unknotting move
-1+9t-29t^2+54t^3-65t^4+54t^5-29t^6+9t^7-t^8
Seifert matrix of 12a_0948
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 -1 0 -1 -1 1 1
-1 0 -1 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,1,1,0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
251
First homology
of the double branched cover of 12a_0948
Z/251
-2 2
12a_0949
2

detected by
the Lickorish test
-2+10t-25t^2+42t^3-49t^4+42t^5-25t^6+10t^7-2t^8
Seifert matrix of 12a_0949
1 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0
1 0 1 0 0 0 0 0
1 1 1 -2 1 1 0 1
0 -1 0 0 -1 -1 0 -1
0 -1 0 0 0 -1 0 0
1 0 1 -1 0 0 -1 0
0 -1 0 0 0 -1 0 -1
2
207
First homology
of the double branched cover of 12a_0949
Z/207
-2 2
12a_0950
1

detected by
an unknotting move
-4+20t-45t^2+59t^3-45t^4+20t^5-4t^6
Seifert matrix of 12a_0950
1 0 0 0 0 0
1 1 1 0 0 0
1 0 1 0 0 0
1 1 1 -2 0 -1
1 0 1 -1 -1 0
0 1 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,2-2t)
the Blanchfield form on it
-10t^-4+70t^-3-223t^-2+424t^-1-522+424t-223t^2+70t^3-10t^4
197
First homology
of the double branched cover of 12a_0950
Z/197
0 0
12a_0951
2

detected by
the Lickorish test
-1+9t-32t^2+65t^3-81t^4+65t^5-32t^6+9t^7-t^8
Seifert matrix of 12a_0951
1 0 0 0 -1 0 -1 0
0 -1 0 0 0 0 0 0
1 0 1 0 -1 0 -1 0
0 -1 0 1 -1 0 0 1
0 -1 0 0 -1 0 0 0
1 -1 1 0 -1 1 -1 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 1 1
1
Generator of the Alexander module
(0,-1,0,-t,-1,0,0,1)
the Blanchfield form on it
-t^-1+1-t
295
First homology
of the double branched cover of 12a_0951
Z/295
2 2
12a_0952
3

detected by
the signature
-2+9t-17t^2+22t^3-23t^4+22t^5-17t^6+9t^7-2t^8
Seifert matrix of 12a_0952
-1 0 -1 -1 -1 0 -1 -1
0 1 0 0 0 0 0 0
0 -1 -1 -1 -1 0 -1 -1
0 -1 0 -1 -1 0 0 -1
0 0 0 0 -2 1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,-1,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
123
First homology
of the double branched cover of 12a_0952
Z/123
-6 6
12a_0953
2

detected by
the signature
-4+20t-42t^2+53t^3-42t^4+20t^5-4t^6
Seifert matrix of 12a_0953
-1 0 -1 1 -1 0
0 1 0 0 0 0
0 -1 -1 1 -1 0
0 1 0 -2 1 0
0 0 0 0 -2 1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(4-4t+2t^2+t^3,0,1,0,2-3t+t^2,0)
the Blanchfield form on it
-4t^-2+17t^-1-25+17t-4t^2
185
First homology
of the double branched cover of 12a_0953
Z/185
-4 4
12a_0954
1

detected by
an unknotting move
-2+10t-25t^2+43t^3-51t^4+43t^5-25t^6+10t^7-2t^8
Seifert matrix of 12a_0954
1 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0
1 0 1 0 0 0 0 0
1 0 1 -1 -1 0 0 -1
1 1 1 0 -2 1 0 0
0 -1 0 0 0 -1 0 0
1 0 1 -1 -1 0 -1 -1
1 0 1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,t,-t+t^2+t^3,t^2+2t^3,1-t^2+4t^3+2t^4,2t^2+t^3,-2t+t^2+t^3,3t)
the Blanchfield form on it
-15t^-6+105t^-5-256t^-4+207t^-3+342t^-2-1271t^-1+1774-1271t+342t^2+207t^3-256t^4+105t^5-15t^6
211
First homology
of the double branched cover of 12a_0954
Z/211
-2 2
12a_0955
1

detected by
an unknotting move
-4+20t-44t^2+57t^3-44t^4+20t^5-4t^6
Seifert matrix of 12a_0955
1 0 0 0 0 0
1 1 1 0 0 0
1 0 1 0 0 0
-1 0 -1 -2 1 0
1 1 1 0 -2 1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,-1,0,1)
the Blanchfield form on it
-2t^-1+3-2t
193
First homology
of the double branched cover of 12a_0955
Z/193
0 0
12a_0956
2

detected by
the signature
2-10t+26t^2-42t^3+49t^4-42t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_0956
-1 0 0 0 0 0 0 0
0 2 1 0 0 1 1 0
0 0 1 0 0 0 0 0
-1 -1 0 1 0 -1 0 0
-1 -1 0 1 1 -1 0 1
-1 0 0 0 0 -1 0 0
-1 0 1 0 0 0 1 0
-1 -1 0 1 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-2t^-3+10t^-2-24t^-1+31-24t+10t^2-2t^3
209
First homology
of the double branched cover of 12a_0956
Z/209
4 4
12a_0957
1

detected by
an unknotting move
4-20t+47t^2-61t^3+47t^4-20t^5+4t^6
Seifert matrix of 12a_0957
-1 0 0 0 0 0
0 2 1 1 1 0
0 0 1 0 0 0
-1 0 0 -1 0 0
-1 0 1 0 1 0
1 1 0 1 0 2
1
Generator of the Alexander module
(0,-1,0,1,0,1-2t)
the Blanchfield form on it
-2t^-2+6t^-1-9+6t-2t^2
203
First homology
of the double branched cover of 12a_0957
Z/203
2 2
12a_0958
2

detected by
the signature
2-10t+25t^2-39t^3+45t^4-39t^5+25t^6-10t^7+2t^8
Seifert matrix of 12a_0958
-1 0 0 0 0 0 0 0
0 2 1 1 0 1 1 1
0 0 1 0 0 0 0 0
-1 0 1 1 0 0 1 0
-1 -1 0 0 1 -1 0 0
-1 0 0 0 0 -1 0 0
-1 0 1 0 0 0 1 0
-1 0 1 1 0 0 1 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-6t^-3+17t^-2-29t^-1+34-29t+17t^2-6t^3+t^4
197
First homology
of the double branched cover of 12a_0958
Z/197
4 4
12a_0959
2

detected by
the Lickorish test
4-21t+50t^2-65t^3+50t^4-21t^5+4t^6
Seifert matrix of 12a_0959
-1 0 0 0 0 0
0 2 1 -1 0 1
0 0 1 0 0 0
1 0 -1 2 0 0
-1 -1 0 0 1 -1
-1 0 0 0 0 -1
1
Generator of the Alexander module
(0,-1,-1,0,-t,-1)
the Blanchfield form on it
-2t^-2+8t^-1-13+8t-2t^2
215
First homology
of the double branched cover of 12a_0959
Z/215
2 2
12a_0960
2

detected by
-4+25t-66t^2+91t^3-66t^4+25t^5-4t^6
Seifert matrix of 12a_0960
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 1 -1 0
0 -1 0 -1 0 0
-1 1 0 0 2 0
1 -1 -1 0 -1 -1
2
281
First homology
of the double branched cover of 12a_0960
Z/281
0 0
12a_0961
1

detected by
an unknotting move
1-9t+31t^2-60t^3+75t^4-60t^5+31t^6-9t^7+t^8
Seifert matrix of 12a_0961
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 0 -1 -1 -1 0
0 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 0 -1 -1 -1 -1 0
1 0 0 1 1 0 0 -1
1
Generator of the Alexander module
(0,0,4t-7t^2+6t^3-6t^4-2t^5+6t^6-2t^7,0,2t-t^2-3t^4+t^5-4t^6+6t^7-2t^8,2+t+2t^2-t^3-5t^4+2t^5-4t^6+6t^7-2t^8,1+2t^2-3t^3+2t^4-4t^5+2t^6,1+t+t^2-t^3-3t^4+t^5-4t^6+6t^7-2t^8)
the Blanchfield form on it
x
277
First homology
of the double branched cover of 12a_0961
Z/277
0 0
12a_0962
1

detected by
an unknotting move
-1+9t-28t^2+51t^3-61t^4+51t^5-28t^6+9t^7-t^8
Seifert matrix of 12a_0962
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 1 0 0 0 -1
-1 -1 -1 0 1 -1 0 -1
0 -1 0 0 0 -1 0 0
-1 -1 -1 1 0 -1 1 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(2t-6t^2+2t^3,0,t-3t^2+t^3,1-3t+t^2,2+3t-12t^2+4t^3,0,2-6t+2t^2,-2t^3+6t^4-2t^5)
the Blanchfield form on it
x
239
First homology
of the double branched cover of 12a_0962
Z/239
-2 2
12a_0963
1

detected by
an unknotting move
-5+24t-50t^2+63t^3-50t^4+24t^5-5t^6
Seifert matrix of 12a_0963
-1 1 1 -1 1 -1
0 2 1 0 0 0
0 1 2 0 1 0
0 0 1 -1 1 0
0 1 1 0 2 0
0 0 1 -1 1 -1
1 or 2
221
First homology
of the double branched cover of 12a_0963
Z/221
0 2
12a_0964
2

detected by
the Lickorish test
-1+9t-30t^2+55t^3-65t^4+55t^5-30t^6+9t^7-t^8
Seifert matrix of 12a_0964
1 0 1 0 0 -1 0 -1
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 -1
1 0 1 1 0 -1 0 -1
0 -1 0 0 1 -1 0 -1
0 -1 0 0 0 -1 0 0
1 -1 1 1 0 -1 1 -1
0 0 0 0 0 0 0 -1
1 or 2
255
First homology
of the double branched cover of 12a_0964
Z/255
2 2
12a_0965
1

detected by
an unknotting move
1-9t+32t^2-65t^3+83t^4-65t^5+32t^6-9t^7+t^8
Seifert matrix of 12a_0965
1 0 0 0 0 -1 0 -1
0 -1 0 0 0 0 0 0
1 0 1 0 0 -1 0 -1
0 -1 0 1 -1 -1 0 -1
0 0 0 0 -1 0 0 -1
0 -1 0 0 0 -1 0 0
1 -1 1 0 0 -1 1 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+8t^-2-22t^-1+29-22t+8t^2-t^3
297
First homology
of the double branched cover of 12a_0965
Z/297
0 0
12a_0966
1

detected by
an unknotting move
2-10t+26t^2-44t^3+53t^4-44t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_0966
-1 0 0 0 -1 0 -1 -1
-1 1 1 1 0 1 -1 0
0 0 1 0 0 0 0 0
-1 0 1 1 0 1 0 0
0 0 0 0 -2 0 -1 -2
-1 0 1 0 0 1 0 0
0 0 0 0 -2 0 -2 -2
0 0 0 0 -1 0 -1 -2
1
Generator of the Alexander module
(141-188t+373t^2-242t^3+227t^4+92t^5-125t^6+27t^7-41t^8-191t^9+26t^10-81t^11+3t^12,-85+110t-147t^2+122t^3+76t^4-38t^5+265t^6+93t^7+78t^8+197t^9-11t^10+66t^11,-5-8t+2t^2-42t^3+20t^4-55t^5-7t^6-20t^7-30t^8-t^9-11t^10,-141+186t-332t^2+213t^3-55t^4-100t^5+353t^6+84t^7+159t^8+299t^9+t^10+108t^11,-1-2t+34
the Blanchfield form on it
x
217
First homology
of the double branched cover of 12a_0966
Z/217
0 0
12a_0967
2

detected by
the signature
-5+27t-58t^2+73t^3-58t^4+27t^5-5t^6
Seifert matrix of 12a_0967
-1 0 1 -1 1 0
0 2 1 1 0 1
0 1 2 0 1 0
0 0 0 1 0 1
0 1 1 0 2 0
0 0 0 0 0 1
1 or 2
253
First homology
of the double branched cover of 12a_0967
Z/253
4 4
12a_0968
1

detected by
an unknotting move
-1+8t-23t^2+40t^3-49t^4+40t^5-23t^6+8t^7-t^8
Seifert matrix of 12a_0968
1 0 0 0 0 0 0 0
1 -1 0 0 1 1 0 1
-1 0 -1 0 -1 -1 0 -1
0 -1 0 -1 1 1 -1 1
0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 1
1 -1 0 0 1 1 -1 1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,3-11t^2-32t^3-17t^4+6t^5,17t+7t^2+21t^3+7t^4-3t^5,4-t-21t^2-34t^3-5t^4+16t^5-3t^6,-3+9t+9t^2+10t^3-3t^4,-5-3t-6t^2-11t^3+3t^4,3-11t^2-32t^3-17t^4+6t^5,-4+t)
the Blanchfield form on it
x
193
First homology
of the double branched cover of 12a_0968
Z/193
0 0
12a_0969
1

detected by
an unknotting move
2-14t+33t^2-41t^3+33t^4-14t^5+2t^6
Seifert matrix of 12a_0969
1 0 0 0 0 0
1 -1 0 0 0 -1
-1 0 -1 0 0 1
0 -1 0 -1 -1 -1
1 -1 0 0 -1 -1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
2t^-2-12t^-1+21-12t+2t^2
139
First homology
of the double branched cover of 12a_0969
Z/139
-2 2
12a_0970
2

detected by
the signature
2-8t+15t^2-18t^3+19t^4-18t^5+15t^6-8t^7+2t^8
Seifert matrix of 12a_0970
-1 0 0 0 0 0 0 -1
-1 1 1 1 1 1 1 -1
0 0 1 0 0 0 0 0
-1 0 1 1 0 1 0 0
-1 0 1 1 1 1 1 0
-1 0 1 0 0 1 0 0
-1 0 1 1 0 1 1 0
0 0 0 0 0 0 0 -2
2
105
First homology
of the double branched cover of 12a_0970
Z/105
4 4
12a_0971
1

detected by
an unknotting move
4-18t+37t^2-45t^3+37t^4-18t^5+4t^6
Seifert matrix of 12a_0971
-1 0 0 0 0 -1
-1 1 1 -1 1 -1
0 0 1 0 0 0
1 0 -1 2 0 0
-1 0 1 -1 1 0
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,t,0,1-t+2t^2,0,0)
the Blanchfield form on it
-4t^-2+16t^-1-25+16t-4t^2
163
First homology
of the double branched cover of 12a_0971
Z/163
2 2
12a_0972
2

detected by
the Lickorish test
-2+10t-24t^2+36t^3-39t^4+36t^5-24t^6+10t^7-2t^8
Seifert matrix of 12a_0972
-1 0 0 0 -1 0 0 -1
-1 1 1 1 -1 1 1 0
0 0 1 0 0 0 0 0
-1 0 1 1 0 1 0 0
0 0 0 0 -2 0 0 -2
-1 0 1 0 0 1 0 0
-1 0 1 1 0 1 1 0
0 0 0 0 -1 0 0 -2
1
Generator of the Alexander module
(0,-1+2t+3t^2-6t^3+12t^4-9t^5+2t^6,-1-t+3t^2-5t^3+7t^4-2t^5,-1+t+4t^2-5t^3+10t^4-4t^5,0,-2+3t-3t^3+10t^4-4t^5,2t+3t^2-6t^3+12t^4-9t^5+2t^6,-1-2t+2t^2-5t^3+2t^4)
the Blanchfield form on it
x
183
First homology
of the double branched cover of 12a_0972
Z/183
2 2
12a_0973
3

detected by
the signature
8-29t+53t^2-63t^3+53t^4-29t^5+8t^6
Seifert matrix of 12a_0973
-2 1 0 0 0 0
0 -2 0 -1 -1 0
0 0 -1 0 -1 0
-1 -1 0 -2 -1 0
-1 0 0 -1 -2 0
0 0 -1 0 -1 -1
2
243
First homology
of the double branched cover of 12a_0973
Z/81+Z/3
-6 6
12a_0974
2

detected by
the signature
13-44t+63t^2-44t^3+13t^4
Seifert matrix of 12a_0974
-2 1 0 0
0 -2 1 -1
1 0 -3 1
-1 -1 1 -2
1 or 2
177
First homology
of the double branched cover of 12a_0974
Z/177
-4 4
12a_0975
2

detected by
the Nakanishi index
-4+22t-52t^2+69t^3-52t^4+22t^5-4t^6
Seifert matrix of 12a_0975
-1 1 -1 1 -1 1
0 2 0 1 0 1
0 0 -1 1 -1 1
0 1 0 2 0 1
0 0 0 0 -1 1
0 1 0 1 0 2
2
225
First homology
of the double branched cover of 12a_0975
Z/45+Z/5
0 0
12a_0976
1

detected by
an unknotting move
4-25t+66t^2-89t^3+66t^4-25t^5+4t^6
Seifert matrix of 12a_0976
-1 1 -1 1 0 1
0 2 0 1 0 1
0 0 -1 0 -1 1
0 1 0 2 1 1
0 0 0 0 1 0
0 1 0 1 0 2
1
Generator of the Alexander module
(1-9t+4t^2,0,1-4t,0,0,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
279
First homology
of the double branched cover of 12a_0976
Z/279
2 2
12a_0977
3

detected by
the signature
2-10t+22t^2-34t^3+39t^4-34t^5+22t^6-10t^7+2t^8
Seifert matrix of 12a_0977
1 0 0 0 0 0 0 0
1 -1 0 0 0 0 -1 0
-1 0 -1 0 0 0 1 0
0 -1 0 -1 0 -1 -1 0
0 0 0 0 -1 0 0 -1
1 -1 0 0 0 -1 -1 0
1 0 0 0 -1 0 -2 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,-2+2t-2t^2,t,0,1+t,0)
the Blanchfield form on it
2t^-3-9t^-2+16t^-1-19+16t-9t^2+2t^3
175
First homology
of the double branched cover of 12a_0977
Z/175
-6 6
12a_0978
2

detected by
the signature
-3+15t-30t^2+37t^3-30t^4+15t^5-3t^6
Seifert matrix of 12a_0978
1 0 0 0 0 0
1 -1 0 0 1 0
-1 0 -1 0 -1 0
0 -1 0 -1 1 -1
-1 0 0 0 -3 0
1 -1 0 0 1 -1
1
Generator of the Alexander module
(0,-3t+4t^3-14t^4+2t^5+4t^6,t^2+t^3-t^4,t^2,1-2t^2+7t^3-t^4-2t^5,6t-8t^3+28t^4-4t^5-8t^6)
the Blanchfield form on it
x
133
First homology
of the double branched cover of 12a_0978
Z/133
-4 4
12a_0979
1

detected by
an unknotting move
2-10t+27t^2-46t^3+55t^4-46t^5+27t^6-10t^7+2t^8
Seifert matrix of 12a_0979
-1 -1 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 0
-1 -1 -1 1 1 -1 -1 0
0 0 0 0 1 0 0 0
1 0 1 0 -1 2 0 1
0 -1 0 0 0 0 -1 0
0 -1 0 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,-t^2,2+2t^2,0,1-t^2,0,1+t)
the Blanchfield form on it
-3t^-5+27t^-4-120t^-3+293t^-2-470t^-1+540-470t+293t^2-120t^3+27t^4-3t^5
225
First homology
of the double branched cover of 12a_0979
Z/225
0 0
12a_0980
2

detected by
the signature
2-11t+31t^2-53t^3+63t^4-53t^5+31t^6-11t^7+2t^8
Seifert matrix of 12a_0980
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
1 0 1 0 0 0 -1 0
0 -1 0 1 1 -1 -1 0
0 0 0 0 1 0 0 0
1 0 1 0 -1 2 0 1
0 -1 0 0 0 0 -1 0
1 -1 1 0 0 0 -1 1
1
Generator of the Alexander module
(t,0,t,2+t,-1-t,1,1,1)
the Blanchfield form on it
5t^-5-11t^-4-35t^-3+191t^-2-388t^-1+476-388t+191t^2-35t^3-11t^4+5t^5
257
First homology
of the double branched cover of 12a_0980
Z/257
4 4
12a_0981
1

detected by
an unknotting move
-1+4t-10t^2+17t^3-23t^4+25t^5-23t^6+17t^7-10t^8+4t^9-t^10
Seifert matrix of 12a_0981
-1 -1 0 0 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 -1 0 0
-1 0 -1 1 0 0 1 0 0 0
-1 -1 -1 1 1 0 1 -1 1 0
-1 -1 -1 1 1 1 1 -1 1 1
0 0 0 0 0 0 1 0 0 0
0 -1 0 0 0 0 0 -1 0 0
-1 -1 -1 1 0 0 1 -1 1 0
-1 -1 -1 1 1 0 1 -1 1 1
1
Generator of the Alexander module
(0,0,t-t^2+t^3-t^4,1-t^2+t^3-t^4,0,1+t-t^2+t^3-t^4,0,0,0,0)
the Blanchfield form on it
x
135
First homology
of the double branched cover of 12a_0981
Z/135
2 2
12a_0982
1

detected by
an unknotting move
2-9t+23t^2-38t^3+45t^4-38t^5+23t^6-9t^7+2t^8
Seifert matrix of 12a_0982
-1 -1 0 0 0 0 0 -1
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 -1
-1 0 -1 1 0 0 1 0
1 1 1 -1 2 0 -1 1
-1 -1 -1 1 -1 1 1 -1
0 0 0 0 0 0 1 0
0 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,-2t+t^2-t^3,-2t+t^2-t^3,1+6t-11t^2+7t^3-4t^4,0,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-14t^-1+16-14t+7t^2-2t^3
189
First homology
of the double branched cover of 12a_0982
Z/189
0 2
12a_0983
2

detected by
the signature
-5+25t-52t^2+65t^3-52t^4+25t^5-5t^6
Seifert matrix of 12a_0983
-1 0 -1 0 -1 -1
0 1 0 0 0 0
0 -1 -1 0 -1 -1
0 1 0 -2 0 -1
0 0 0 -1 -2 -1
0 0 0 -1 -1 -2
1
Generator of the Alexander module
(3t-2t^2,0,-1+t,0,-3+2t,-3+2t)
the Blanchfield form on it
-60t^-2+260t^-1-391+260t-60t^2
229
First homology
of the double branched cover of 12a_0983
Z/229
-4 4
12a_0984
3

detected by
the signature
1-4t+9t^2-13t^3+16t^4-17t^5+16t^6-13t^7+9t^8-4t^9+t^10
Seifert matrix of 12a_0984
1 0 1 0 0 0 1 -1 0 0
0 -1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 0 0 0
1 0 1 1 0 0 1 -1 0 0
1 -1 1 1 1 0 1 -1 1 0
1 -1 1 1 1 1 1 -1 1 1
0 0 0 0 0 0 1 0 0 0
0 -1 0 0 0 0 0 -1 0 0
1 -1 1 1 0 0 1 -1 1 0
1 -1 1 1 1 0 1 -1 1 1
1
Generator of the Alexander module
(0,1,0,-t,0,0,0,0,0,0)
the Blanchfield form on it
-t^-4+4t^-3-9t^-2+12t^-1-13+12t-9t^2+4t^3-t^4
103
First homology
of the double branched cover of 12a_0984
Z/103
6 6
12a_0985
2

detected by
the signature
2-9t+21t^2-30t^3+33t^4-30t^5+21t^6-9t^7+2t^8
Seifert matrix of 12a_0985
1 0 1 0 0 0 1 -1
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 1 0
1 0 1 1 0 0 1 -1
-1 1 -1 -1 2 0 -1 1
1 -1 1 1 -1 1 1 -1
0 0 0 0 0 0 1 0
0 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-4-5t^-3+12t^-2-18t^-1+20-18t+12t^2-5t^3+t^4
157
First homology
of the double branched cover of 12a_0985
Z/157
4 4
12a_0986
2

detected by
the Lickorish test
2-12t+34t^2-59t^3+71t^4-59t^5+34t^6-12t^7+2t^8
Seifert matrix of 12a_0986
-1 0 0 0 0 0 0 0
0 2 0 1 0 1 0 1
-1 0 -1 0 0 0 -1 0
0 0 -1 1 0 0 -1 0
-1 -1 -1 0 1 -1 -1 0
-1 0 -1 0 0 -1 -1 0
-1 0 0 0 0 0 -1 0
-1 0 -1 1 0 0 -1 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-7t^-3+22t^-2-40t^-1+48-40t+22t^2-7t^3+t^4
285
First homology
of the double branched cover of 12a_0986
Z/285
0 2
12a_0987
2

detected by
the Nakanishi index
2-10t+27t^2-46t^3+55t^4-46t^5+27t^6-10t^7+2t^8
Seifert matrix of 12a_0987
-1 0 0 0 0 0 0 0
0 2 1 1 0 1 1 0
0 0 1 0 0 0 0 0
-1 0 1 1 0 0 1 0
-1 -1 0 0 1 -1 0 1
-1 0 0 0 0 -1 0 0
-1 0 1 0 0 0 1 0
-1 -1 0 0 0 -1 0 1
2
225
First homology
of the double branched cover of 12a_0987
Z/75+Z/3
4 4
12a_0988
2

detected by
the signature
2-8t+17t^2-23t^3+25t^4-23t^5+17t^6-8t^7+2t^8
Seifert matrix of 12a_0988
-1 0 0 0 0 0 0 0
0 2 1 1 1 1 1 1
0 0 1 0 0 0 0 0
-1 0 1 1 0 0 1 0
-1 0 1 1 1 0 1 1
-1 0 0 0 0 -1 0 0
-1 0 1 0 0 0 1 0
-1 0 1 1 0 0 1 1
1
Generator of the Alexander module
(0,-1+t-t^2,0,0,1+t^2,0,0,0)
the Blanchfield form on it
-2t^-3+4t^-2-7t^-1+6-7t+4t^2-2t^3
125
First homology
of the double branched cover of 12a_0988
Z/125
4 4
12a_0989
2

detected by
the Lickorish test
4-18t+40t^2-51t^3+40t^4-18t^5+4t^6
Seifert matrix of 12a_0989
-1 0 0 0 0 0
0 2 1 -1 1 1
0 0 1 0 0 0
1 0 -1 2 0 0
-1 0 1 -1 1 0
-1 0 0 0 0 -1
1 or 2
175
First homology
of the double branched cover of 12a_0989
Z/175
2 2
12a_0990
2

detected by
the Nakanishi index
1-8t+26t^2-48t^3+59t^4-48t^5+26t^6-8t^7+t^8
Seifert matrix of 12a_0990
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 0 -1 -1 0 -1
0 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0
-1 -1 0 -1 -1 -1 0 0
1 0 0 1 1 0 -1 0
-1 -1 0 -1 -1 -1 0 -1
2
225
First homology
of the double branched cover of 12a_0990
Z/75+Z/3
0 0
12a_0991
2

detected by
the signature
1-8t+25t^2-44t^3+53t^4-44t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_0991
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 -1 -1 -1 0 0
0 0 0 1 0 1 0 1
1 0 0 0 1 0 0 0
0 0 0 0 0 1 0 1
1 0 0 1 1 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,-2+t+2t^2-t^3,2-4t+t^2-2t^3+t^4,0,1-t,2t-t^2-2t^3+t^4,4t-4t^2+7t^3-5t^4+t^5,-4t+2t^2+2t^3-t^4)
the Blanchfield form on it
x
209
First homology
of the double branched cover of 12a_0991
Z/209
4 4
12a_0992
2

detected by
the Lickorish test
1-9t+30t^2-57t^3+71t^4-57t^5+30t^6-9t^7+t^8
Seifert matrix of 12a_0992
1 0 0 0 0 0 0 0
1 -1 0 0 1 1 0 1
-1 0 -1 0 -1 -1 0 -1
0 -1 0 -1 0 1 -1 0
1 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
1 -1 0 0 0 1 -1 0
1 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,-7+5t-t^2-t^3,-2+2t-t^2,4t^2-4t^3+2t^4,0,-4+4t-2t^2,0,0)
the Blanchfield form on it
4287t^-3-18476t^-2+37827t^-1-48847+37827t-18476t^2+4287t^3
265
First homology
of the double branched cover of 12a_0992
Z/265
0 0
12a_0993
1

detected by
an unknotting move
2-10t+24t^2-38t^3+45t^4-38t^5+24t^6-10t^7+2t^8
Seifert matrix of 12a_0993
-1 0 0 0 0 0 0 -1
-1 1 -1 1 1 -1 1 -1
-1 0 -1 0 0 -1 0 -1
0 0 -1 1 0 -1 0 0
-1 0 -1 1 1 -1 1 0
-1 0 0 0 0 -1 0 -1
-1 0 -1 1 0 -1 1 0
0 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
-2t^-3+9t^-2-19t^-1+23-19t+9t^2-2t^3
193
First homology
of the double branched cover of 12a_0993
Z/193
0 2
12a_0994
2

detected by
the Lickorish test
-2+12t-34t^2+60t^3-71t^4+60t^5-34t^6+12t^7-2t^8
Seifert matrix of 12a_0994
-1 0 0 0 -1 0 0 -1
-1 1 -1 1 -1 -1 1 0
-1 0 -1 0 -1 -1 0 -1
0 0 -1 1 0 -1 0 0
0 0 0 0 -2 0 0 -2
-1 0 0 0 -1 -1 0 -1
-1 0 -1 1 0 -1 1 0
0 0 0 0 -1 0 0 -2
1
Generator of the Alexander module
(2-2t,0,0,-1+t,0,0,1,4-4t)
the Blanchfield form on it
-24t^-3+104t^-2-237t^-1+309-237t+104t^2-24t^3
287
First homology
of the double branched cover of 12a_0994
Z/287
-2 2
12a_0995
3

detected by
the signature
8-28t+49t^2-57t^3+49t^4-28t^5+8t^6
Seifert matrix of 12a_0995
-2 1 1 0 1 0
0 -2 -2 -1 -2 -1
0 -1 -2 -1 -1 -1
-1 -1 -1 -2 -1 -1
0 -1 -2 -1 -2 -1
-1 0 0 -1 0 -2
1 or 2
227
First homology
of the double branched cover of 12a_0995
Z/227
-6 6
12a_0996
2

detected by
the signature
14-48t+69t^2-48t^3+14t^4
Seifert matrix of 12a_0996
-2 0 -1 0
-1 -2 1 -1
0 1 -3 1
-1 -1 0 -2
1
Generator of the Alexander module
(0,2-2t,0,-1+2t)
the Blanchfield form on it
-203t^-2+703t^-1-1012+703t-203t^2
193
First homology
of the double branched cover of 12a_0996
Z/193
-4 4
12a_0997
1

detected by
an unknotting move
-2+10t-26t^2+44t^3-51t^4+44t^5-26t^6+10t^7-2t^8
Seifert matrix of 12a_0997
1 0 0 0 0 0 0 0
0 -1 0 0 1 0 1 -1
-1 0 -1 -1 -1 -1 -1 1
-1 0 0 -1 -1 0 -1 1
1 0 0 0 1 0 0 0
-1 0 0 -1 -1 -1 -1 1
1 0 0 0 1 0 1 0
0 0 0 0 1 0 1 -2
1
Generator of the Alexander module
(0,-t,-2,0,-1,0,-1,1)
the Blanchfield form on it
-6t^-3+34t^-2-85t^-1+119-85t+34t^2-6t^3
215
First homology
of the double branched cover of 12a_0997
Z/215
-2 2
12a_0998
1

detected by
an unknotting move
-2+11t-30t^2+52t^3-61t^4+52t^5-30t^6+11t^7-2t^8
Seifert matrix of 12a_0998
1 0 0 0 0 0 0 0
1 -1 0 0 1 0 1 -1
-1 0 -1 0 -1 0 -1 1
0 -1 0 -1 0 -1 0 -1
1 0 0 0 1 0 0 0
1 -1 0 0 0 -1 0 -1
1 0 0 0 1 0 1 0
1 0 0 0 1 0 1 -2
1
Generator of the Alexander module
(0,0,1,2-2t+t^2,0,0,0,-t)
the Blanchfield form on it
-2t^-3+10t^-2-23t^-1+31-23t+10t^2-2t^3
251
First homology
of the double branched cover of 12a_0998
Z/251
-2 2
12a_0999
1

detected by
an unknotting move
-1+4t-11t^2+21t^3-31t^4+35t^5-31t^6+21t^7-11t^8+4t^9-t^10
Seifert matrix of 12a_0999
-1 -1 0 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 0 -1 0
-1 0 -1 1 0 0 1 0 0 0
-1 0 -1 1 1 0 1 1 0 0
-1 -1 -1 1 1 1 1 1 -1 1
0 0 0 0 0 0 1 0 0 0
-1 0 -1 1 0 0 1 1 0 0
0 -1 0 0 0 0 0 0 -1 0
-1 -1 -1 1 1 0 1 1 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0,0,2-t+t^2)
the Blanchfield form on it
t^-4-3t^-3+7t^-2-11t^-1+14-11t+7t^2-3t^3+t^4
171
First homology
of the double branched cover of 12a_0999
Z/171
2 2
12a_1000
1

detected by
an unknotting move
2-8t+19t^2-30t^3+35t^4-30t^5+19t^6-8t^7+2t^8
Seifert matrix of 12a_1000
-1 -1 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 0
-1 -1 -1 1 1 -1 -1 1
0 0 0 0 1 0 0 0
1 0 1 0 -1 2 0 0
0 -1 0 0 0 0 -1 0
-1 -1 -1 0 1 -1 -1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-2t^-3+6t^-2-10t^-1+11-10t+6t^2-2t^3
153
First homology
of the double branched cover of 12a_1000
Z/153
0 2
12a_1001
1

detected by
an unknotting move
-4+19t-43t^2+57t^3-43t^4+19t^5-4t^6
Seifert matrix of 12a_1001
1 0 0 0 0 0
0 -1 1 0 1 -1
1 0 1 0 0 0
1 0 1 -2 1 -1
1 0 1 0 1 0
0 0 1 0 1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
2t^-3-9t^-2+20t^-1-26+20t-9t^2+2t^3
189
First homology
of the double branched cover of 12a_1001
Z/189
0 0
12a_1002
1

detected by
an unknotting move
-1+5t-13t^2+23t^3-32t^4+35t^5-32t^6+23t^7-13t^8+5t^9-t^10
Seifert matrix of 12a_1002
1 0 1 0 0 0 1 -1 0 0
0 -1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 0 0 0
0 -1 0 -1 0 0 0 0 -1 0
1 0 1 -1 1 0 1 -1 -1 0
1 -1 1 -1 1 1 1 -1 -1 1
0 0 0 0 0 0 1 0 0 0
0 -1 0 -1 0 0 0 -1 -1 0
0 -1 0 0 0 0 0 0 -1 0
1 -1 1 -1 1 0 1 -1 -1 1
1
Generator of the Alexander module
(0,1,0,0,-t,0,0,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-14t^-1+17-14t+9t^2-4t^3+t^4
183
First homology
of the double branched cover of 12a_1002
Z/183
2 2
12a_1003
2

detected by
the signature
2-10t+28t^2-48t^3+57t^4-48t^5+28t^6-10t^7+2t^8
Seifert matrix of 12a_1003
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
1 0 1 0 0 0 -1 0
0 -1 0 1 1 -1 -1 1
0 0 0 0 1 0 0 0
1 0 1 0 -1 2 0 0
0 -1 0 0 0 0 -1 0
0 -1 0 0 1 -1 -1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-2t^-3+8t^-2-18t^-1+23-18t+8t^2-2t^3
233
First homology
of the double branched cover of 12a_1003
Z/233
4 4
12a_1004
3

detected by
the signature
8-30t+57t^2-69t^3+57t^4-30t^5+8t^6
Seifert matrix of 12a_1004
-1 0 -1 0 -1 0
0 -1 0 -1 0 -1
0 0 -2 -1 -1 -1
0 0 -1 -2 0 -1
0 0 -1 -1 -2 -1
0 0 0 -1 0 -2
1
Generator of the Alexander module
(11+78t-64t^2+114t^3-174t^4+88t^5-20t^6+24t^7-24t^8,-5-16t+12t^2-14t^3+52t^4-64t^5+32t^6,9+78t-66t^2+114t^3-162t^4+72t^5-12t^6+24t^7-24t^8,9+52t-40t^2+70t^3-104t^4+48t^5-8t^6+16t^7-16t^8,4-5t-26t^2+20t^3-50t^4+96t^5-88t^6+32t^7,4+8t-4t^2+4t^3-24t^4+32t^5-16t^6)
the Blanchfield form on it
x
259
First homology
of the double branched cover of 12a_1004
Z/259
-6 6
12a_1005
1

detected by
an unknotting move
2-11t+29t^2-49t^3+59t^4-49t^5+29t^6-11t^7+2t^8
Seifert matrix of 12a_1005
-1 0 0 0 0 0 0 0
0 2 0 1 0 1 0 0
-1 0 -1 0 0 0 -1 0
0 0 -1 1 0 0 -1 0
-1 -1 -1 0 1 -1 -1 1
-1 0 -1 0 0 -1 -1 0
-1 0 0 0 0 0 -1 0
-1 -1 -1 0 0 -1 -1 1
1
Generator of the Alexander module
(0,3-17t+30t^2-40t^3+16t^4,-3+6t-13t^2+6t^3,5-9t+21t^2-10t^3,-1+4t+13t^2-28t^3+74t^4-36t^5,0,-2+28t-73t^2+133t^3-120t^4+36t^5,6t^2-33t^3+57t^4-75t^5+30t^6)
the Blanchfield form on it
x
241
First homology
of the double branched cover of 12a_1005
Z/241
0 0
12a_1006
2

detected by
the Lickorish test
2-10t+25t^2-41t^3+49t^4-41t^5+25t^6-10t^7+2t^8
Seifert matrix of 12a_1006
-1 0 0 0 0 0 0 0
0 2 0 1 1 1 0 1
-1 0 -1 0 0 0 -1 0
0 0 -1 1 0 0 -1 0
-1 0 -1 1 1 0 -1 1
-1 0 -1 0 0 -1 -1 0
-1 0 0 0 0 0 -1 0
-1 0 -1 1 0 0 -1 1
1
Generator of the Alexander module
(0,1+t,1,1,t,0,0,0)
the Blanchfield form on it
-t^-1+1-t
205
First homology
of the double branched cover of 12a_1006
Z/205
0 0
12a_1007
2

detected by
the Lickorish test
-2+9t-19t^2+27t^3-29t^4+27t^5-19t^6+9t^7-2t^8
Seifert matrix of 12a_1007
1 0 0 0 0 0 0 0
1 -1 1 1 0 1 1 -1
1 0 1 0 0 0 0 0
1 0 1 1 0 1 0 0
1 -1 0 0 -1 0 0 -1
1 0 1 0 0 1 0 0
1 0 1 1 0 1 1 0
1 0 1 1 0 1 1 -2
1
Generator of the Alexander module
(1-10t-50t^2-75t^3,1+6t+17t^2+108t^3+66t^4+9t^5+26t^6-60t^7,5t+17t^2+30t^3,-1+5t+33t^2+45t^3,1+2t-7t^2+39t^3+26t^4-60t^5,-2+18t+82t^2+175t^3-68t^4-120t^5,-1+5t+33t^2+45t^3,3-19t-78t^2-55t^3+184t^4+60t^5)
the Blanchfield form on it
x
143
First homology
of the double branched cover of 12a_1007
Z/143
2 2
12a_1008
1

detected by
an unknotting move
-4+20t-45t^2+59t^3-45t^4+20t^5-4t^6
Seifert matrix of 12a_1008
1 0 0 0 0 0
1 -1 1 -1 0 -1
1 0 1 0 0 0
-1 0 -1 2 0 0
1 -1 0 0 -1 -1
1 0 1 -1 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-3-11t^-2+26t^-1-34+26t-11t^2+2t^3
197
First homology
of the double branched cover of 12a_1008
Z/197
0 0
12a_1009
2

detected by
the signature
2-9t+19t^2-25t^3+27t^4-25t^5+19t^6-9t^7+2t^8
Seifert matrix of 12a_1009
-1 0 0 0 0 0 0 -1
-1 1 -1 -1 1 -1 -1 -1
-1 0 -1 -1 0 -1 -1 -1
-1 0 0 -1 0 0 -1 -1
0 0 -1 -1 1 -1 -1 0
-1 0 0 -1 0 -1 -1 -1
-1 0 0 0 0 0 -1 -1
0 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(-14t+24t^2+25t^3-16t^4,-3-7t^2+14t^3+7t^4-20t^5+7t^6,6-36t+38t^2+56t^3-32t^4,-6+12t-22t^2-16t^3+16t^4-2t^5,-4+3t+10t^2-5t^3,-10t+5t^2,-6+14t-23t^2-16t^3+16t^4-2t^5,16t-11t^2-42t^3+9t^4+20t^5-7t^6)
the Blanchfield form on it
x
137
First homology
of the double branched cover of 12a_1009
Z/137
-4 4
12a_1010
2

detected by
the Lickorish test
4-20t+45t^2-57t^3+45t^4-20t^5+4t^6
Seifert matrix of 12a_1010
-1 0 0 0 0 -1
-1 1 -1 1 1 -1
-1 0 -1 1 0 -1
1 0 0 -2 0 1
0 0 -1 1 1 0
0 0 0 0 0 -2
1 or 2
195
First homology
of the double branched cover of 12a_1010
Z/195
-2 2
12a_1011
1

detected by
an unknotting move
-1+4t-9t^2+15t^3-20t^4+23t^5-20t^6+15t^7-9t^8+4t^9-t^10
Seifert matrix of 12a_1011
1 0 0 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 -1 0 -1 -1 -1
1 0 0 0 1 0 0 0 0 0
1 0 0 0 1 1 0 0 1 0
-1 -1 0 -1 -1 -1 -1 -1 -1 -1
0 -1 0 0 -1 -1 0 -1 -1 -1
1 0 0 0 1 0 0 0 1 0
1 0 0 0 1 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0,0,0)
the Blanchfield form on it
-t^-4+4t^-3-8t^-2+12t^-1-13+12t-8t^2+4t^3-t^4
121
First homology
of the double branched cover of 12a_1011
Z/121
0 0
12a_1012
1

detected by
an unknotting move
-2+9t-21t^2+32t^3-35t^4+32t^5-21t^6+9t^7-2t^8
Seifert matrix of 12a_1012
1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 1 -1 -1
-1 -1 0 -1 -1 1 0 -1
1 0 0 0 1 0 0 0
-1 0 0 0 -1 2 0 0
-1 -1 0 -1 -1 1 -1 -1
0 -1 0 0 -1 1 0 -1
1
Generator of the Alexander module
(-t-t^2,1+t,t+t^2,2+t+2t^2+t^3-t^4,-1-t,1+t^2+2t^3,t+t^2,t+t^2)
the Blanchfield form on it
19t^-3-64t^-2+71t^-1-96+71t-64t^2+19t^3
163
First homology
of the double branched cover of 12a_1012
Z/163
-2 2
12a_1013
2

detected by
the Lickorish test
-1+4t-9t^2+15t^3-20t^4+21t^5-20t^6+15t^7-9t^8+4t^9-t^10
Seifert matrix of 12a_1013
1 0 1 0 0 0 1 -1 0 0
0 -1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 0 0 0
0 -1 0 -1 -1 0 0 0 -1 -1
0 -1 0 0 -1 0 0 0 0 -1
1 0 1 -1 -1 1 1 -1 -1 -1
0 0 0 0 0 0 1 0 0 0
0 -1 0 -1 -1 0 0 -1 -1 -1
0 -1 0 0 -1 0 0 0 -1 -1
0 -1 0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,t,0,-t,0,1-t^2,0,-t^2,0,0)
the Blanchfield form on it
-t^-4+3t^-3-5t^-2+7t^-1-8+7t-5t^2+3t^3-t^4
119
First homology
of the double branched cover of 12a_1013
Z/119
-2 2
12a_1014
1

detected by
an unknotting move
2-9t+21t^2-34t^3+41t^4-34t^5+21t^6-9t^7+2t^8
Seifert matrix of 12a_1014
1 0 1 0 0 0 1 -1
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 1 0
0 -1 0 -1 1 0 0 0
0 1 0 0 -2 0 0 0
1 0 1 -1 1 1 1 -1
0 0 0 0 0 0 1 0
0 -1 0 -1 1 0 0 -1
1
Generator of the Alexander module
(0,2,0,0,1,2,0,0)
the Blanchfield form on it
5t^-4-17t^-3+30t^-2-60t^-1+84-60t+30t^2-17t^3+5t^4
173
First homology
of the double branched cover of 12a_1014
Z/173
0 0
12a_1015
1

detected by
an unknotting move
-2+8t-17t^2+25t^3-27t^4+25t^5-17t^6+8t^7-2t^8
Seifert matrix of 12a_1015
1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
1 0 1 0 0 0 0 0
1 0 1 1 0 0 1 0
1 1 1 1 -2 1 1 1
0 -1 -1 -1 0 -1 -1 -1
1 0 1 0 0 0 1 0
1 0 1 1 0 0 1 1
1
Generator of the Alexander module
(0,t^2,-t^3,t^2,1-t+t^3,t+t^2-t^3,0,t^2)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
131
First homology
of the double branched cover of 12a_1015
Z/131
2 2
12a_1016
1

detected by
an unknotting move
-4+18t-40t^2+53t^3-40t^4+18t^5-4t^6
Seifert matrix of 12a_1016
1 0 0 0 0 0
0 -1 0 0 0 0
1 0 1 0 0 0
-1 0 -1 2 0 0
1 1 1 -1 -2 1
0 -1 -1 1 0 -1
1 or 2
177
First homology
of the double branched cover of 12a_1016
Z/177
0 0
12a_1017
2

detected by
the signature
2-8t+15t^2-19t^3+21t^4-19t^5+15t^6-8t^7+2t^8
Seifert matrix of 12a_1017
-1 0 0 0 0 0 0 0
0 2 0 0 1 1 0 0
-1 0 -1 -1 0 0 -1 -1
-1 0 0 -1 0 0 0 -1
0 0 -1 -1 1 0 -1 -1
-1 0 -1 -1 0 -1 -1 -1
-1 0 0 -1 0 0 -1 -1
-1 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+7t^-2-9t^-1+10-9t+7t^2-4t^3+t^4
109
First homology
of the double branched cover of 12a_1017
Z/109
-4 4
12a_1018
2

detected by
the Lickorish test
4-18t+36t^2-43t^3+36t^4-18t^5+4t^6
Seifert matrix of 12a_1018
-1 0 0 0 0 0
0 2 0 0 1 1
-1 0 -1 1 0 0
1 0 0 -2 0 0
0 0 -1 1 1 0
-1 0 -1 1 0 -1
1 or 2
159
First homology
of the double branched cover of 12a_1018
Z/159
-2 2
12a_1019
2

detected by
the Nakanishi index
1-10t+39t^2-80t^3+101t^4-80t^5+39t^6-10t^7+t^8
Seifert matrix of 12a_1019
-1 -1 0 0 -1 0 0 0
0 1 0 0 0 -1 0 0
-1 0 1 0 0 0 0 0
0 0 0 -1 0 0 0 0
0 -1 0 0 -1 0 -1 0
0 0 0 -1 0 -1 0 0
0 1 0 -1 0 -1 1 0
-1 0 1 0 -1 0 0 1
2
361
First homology
of the double branched cover of 12a_1019
Z/19+Z/19
0 0
12a_1020
2

detected by
the Lickorish test
-1+9t-34t^2+71t^3-89t^4+71t^5-34t^6+9t^7-t^8
Seifert matrix of 12a_1020
-1 -1 0 0 0 -1 0 0
0 1 0 0 0 0 -1 0
-1 0 1 -1 0 0 0 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 -1 0 0 0
0 -1 0 0 0 -1 0 -1
0 0 0 0 -1 0 -1 0
0 1 0 0 -1 0 -1 1
1 or 2
319
First homology
of the double branched cover of 12a_1020
Z/319
-2 2
12a_1021
2

detected by
the Lickorish test
-1+9t-35t^2+76t^3-97t^4+76t^5-35t^6+9t^7-t^8
Seifert matrix of 12a_1021
1 0 1 -1 0 0 0 1
-1 -1 -1 0 0 -1 0 -1
0 0 1 -1 -1 0 -1 1
0 0 0 -1 0 0 0 0
0 0 0 -1 -1 0 0 0
-1 0 -1 0 0 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 -1 -1 0 -1 1
1
Generator of the Alexander module
(2,2t^4,t^3,-2t^2,0,-1,0,-2-2t^3)
the Blanchfield form on it
637t^-3-4207t^-2+11836t^-1-15955+11836t-4207t^2+637t^3
339
First homology
of the double branched cover of 12a_1021
Z/339
-2 2
12a_1022
2

detected by
the Nakanishi index
3-21t+58t^2-79t^3+58t^4-21t^5+3t^6
Seifert matrix of 12a_1022
1 -1 1 0 0 0
0 -1 0 0 0 0
0 -1 1 0 -1 0
1 0 0 -2 0 -1
0 -1 0 0 -1 0
1 0 1 -1 0 -2
2
243
First homology
of the double branched cover of 12a_1022
Z/27+Z/9
-2 2
12a_1023
1

detected by
an unknotting move
-2+8t-16t^2+24t^3-27t^4+24t^5-16t^6+8t^7-2t^8
Seifert matrix of 12a_1023
1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
-1 -1 -1 0 0 -1 0 1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
1 0 0 0 0 1 0 0
0 0 0 0 -1 0 -1 -1
1 1 0 0 0 1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+8t^-2-15t^-1+19-15t+8t^2-2t^3
127
First homology
of the double branched cover of 12a_1023
Z/127
-2 2
12a_1024
1

detected by
an unknotting move
-4+17t-33t^2+41t^3-33t^4+17t^5-4t^6
Seifert matrix of 12a_1024
1 0 0 0 0 0
1 1 0 1 0 0
-1 -1 -1 -1 0 1
1 0 0 1 0 0
0 0 0 0 -2 0
1 1 0 1 -1 -2
1
Generator of the Alexander module
(0,0,-2,-1-t,0,1)
the Blanchfield form on it
-2t^-1+3-2t
149
First homology
of the double branched cover of 12a_1024
Z/149
0 2
12a_1025
2

detected by
the Lickorish test
-2+12t-31t^2+52t^3-61t^4+52t^5-31t^6+12t^7-2t^8
Seifert matrix of 12a_1025
-1 0 0 0 0 0 0 0
0 2 1 0 0 1 1 1
0 2 2 0 0 1 1 2
-1 0 0 -1 0 0 0 0
-1 -1 -1 -1 1 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 0 0 -1 0 0 1 0
0 2 1 0 0 1 1 2
2
255
First homology
of the double branched cover of 12a_1025
Z/255
2 2
12a_1026
2

detected by
A(F_2)
-3+17t-38t^2+49t^3-38t^4+17t^5-3t^6
Seifert matrix of 12a_1026
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 1
-1 -1 0 -1 0 0
0 -1 0 0 1 0
0 0 0 -1 -1 3
2
165
First homology
of the double branched cover of 12a_1026
Z/165
0 2
12a_1027
1

detected by
an unknotting move
-1+3t-6t^2+10t^3-14t^4+15t^5-14t^6+10t^7-6t^8+3t^9-t^10
Seifert matrix of 12a_1027
-1 -1 0 0 -1 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 1 0 0
-1 -1 0 -1 -1 0 0 0 0 0
0 -1 0 0 -1 0 0 0 0 0
-1 -1 1 -1 -1 1 0 1 1 0
-1 -1 1 -1 -1 1 1 1 1 1
0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 1 1 0
-1 -1 1 -1 -1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-4-3t^-3+5t^-2-7t^-1+9-7t+5t^2-3t^3+t^4
83
First homology
of the double branched cover of 12a_1027
Z/83
2 2
12a_1028
1

detected by
an unknotting move
2-7t+14t^2-21t^3+25t^4-21t^5+14t^6-7t^7+2t^8
Seifert matrix of 12a_1028
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
0 0 2 0 0 0 0 0
-1 -1 0 -1 -1 0 0 0
0 -1 0 0 -1 0 0 0
-1 -1 -1 -1 -1 1 0 0
-1 -1 -1 -1 -1 1 1 1
-1 -1 -1 -1 -1 1 0 1
1 or 2
113
First homology
of the double branched cover of 12a_1028
Z/113
0 0
12a_1029
1

detected by
an unknotting move
2-6t+10t^2-14t^3+17t^4-14t^5+10t^6-6t^7+2t^8
Seifert matrix of 12a_1029
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 1 0 0
-1 -1 0 -1 -1 0 0 0
0 -1 0 0 -1 0 0 0
0 0 0 0 0 1 0 0
0 0 1 0 0 1 1 0
1 1 -1 1 1 -1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-4-3t^-3+5t^-2-7t^-1+8-7t+5t^2-3t^3+t^4
81
First homology
of the double branched cover of 12a_1029
Z/81
0 0
12a_1030
1

detected by
an unknotting move
4-13t+19t^2-19t^3+19t^4-13t^5+4t^6
Seifert matrix of 12a_1030
-1 -1 0 0 -1 0
0 -1 0 0 0 0
0 0 2 0 0 0
-1 -1 0 -1 -1 0
0 -1 0 0 -1 0
1 1 1 1 1 2
1
Generator of the Alexander module
(0,0,0,1-t+2t^2-2t^3+2t^4-t^5,0,-1-t-t^4+t^5)
the Blanchfield form on it
4t^-2-13t^-1+19-13t+4t^2
91
First homology
of the double branched cover of 12a_1030
Z/91
-2 2
12a_1031
2

detected by
the signature
2-7t+13t^2-17t^3+19t^4-17t^5+13t^6-7t^7+2t^8
Seifert matrix of 12a_1031
-2 1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 1 0 0
1 -1 1 1 0 1 1 0
1 -1 1 1 1 1 1 1
0 0 0 0 0 1 0 0
0 0 1 0 0 1 1 0
1 -1 1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,1+t+t^4,0,0,t^2,0)
the Blanchfield form on it
-4t^-3+12t^-2-17t^-1+16-17t+12t^2-4t^3
97
First homology
of the double branched cover of 12a_1031
Z/97
4 4
12a_1032
1

detected by
an unknotting move
4-16t+31t^2-37t^3+31t^4-16t^5+4t^6
Seifert matrix of 12a_1032
-2 1 0 0 0 0
0 -1 0 0 0 0
0 0 2 0 0 0
1 -1 -1 1 0 0
1 -1 -1 1 1 1
1 -1 -1 1 0 1
1 or 2
139
First homology
of the double branched cover of 12a_1032
Z/139
2 2
12a_1033
1

detected by
an unknotting move
4-14t+23t^2-25t^3+23t^4-14t^5+4t^6
Seifert matrix of 12a_1033
-2 1 0 0 0 0
0 -1 0 0 0 0
0 0 1 1 0 0
0 0 0 1 0 0
0 0 1 1 1 0
-1 1 -1 -1 -1 2
1
Generator of the Alexander module
(0,0,0,0,-t,1+t)
the Blanchfield form on it
-4t^-2+14t^-1-21+14t-4t^2
107
First homology
of the double branched cover of 12a_1033
Z/107
2 2
12a_1034
1

detected by
an unknotting move
8-30t+45t^2-30t^3+8t^4
Seifert matrix of 12a_1034
-2 1 0 0
0 -1 0 0
0 0 2 0
-1 1 1 2
1 or 2
121
First homology
of the double branched cover of 12a_1034
Z/121
0 0
12a_1035
3

detected by
the signature
7-21t+32t^2-35t^3+32t^4-21t^5+7t^6
Seifert matrix of 12a_1035
-1 -1 1 -1 -1 0
0 -1 1 0 -1 0
0 0 -3 0 1 -1
0 -1 1 -1 -1 0
0 0 1 0 -2 -1
0 0 -1 0 0 -2
1 or 2
155
First homology
of the double branched cover of 12a_1035
Z/155
-6 6
12a_1036
3

detected by
the signature
-2+10t-21t^2+30t^3-33t^4+30t^5-21t^6+10t^7-2t^8
Seifert matrix of 12a_1036
-1 -1 0 -1 -1 -1 0 -1
0 -1 0 0 -1 -1 0 -1
0 0 1 0 0 0 0 0
0 -1 0 -1 -1 -1 0 -1
0 0 -1 0 -2 -2 0 -2
0 0 0 0 -1 -2 0 -1
0 0 -1 0 -1 -1 -1 -1
0 0 -1 0 -1 -2 0 -2
1
Generator of the Alexander module
(0,0,1,0,1,1,-t,1)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
159
First homology
of the double branched cover of 12a_1036
Z/159
-6 6
12a_1037
2

detected by
the signature
14-46t+65t^2-46t^3+14t^4
Seifert matrix of 12a_1037
-3 1 1 -1
0 -2 0 0
1 -1 -2 -1
-1 0 0 -2
1
Generator of the Alexander module
(-t^2,0,-t-t^2,1-2t^2)
the Blanchfield form on it
-36t^-2+120t^-1-170+120t-36t^2
185
First homology
of the double branched cover of 12a_1037
Z/185
-4 4
12a_1038
2

detected by
the signature
-4+21t-45t^2+57t^3-45t^4+21t^5-4t^6
Seifert matrix of 12a_1038
1 0 0 0 0 0
0 -2 0 0 0 0
-1 -1 -2 -2 0 -2
0 -1 -1 -2 0 -1
-1 0 -1 -1 -1 -1
-1 -1 -1 -2 0 -2
1
Generator of the Alexander module
(2-8t+4t^2+12t^3-40t^4-8t^5+20t^6-12t^7-8t^8+8t^9,10t-40t^2+8t^3+32t^4-40t^5-72t^6+140t^7+12t^8-32t^9+24t^10-16t^11,-4t^2+12t^3+8t^4-8t^5,-9+2t+42t^2-36t^3-12t^4+52t^5+92t^6-120t^7-24t^8+36t^9-16t^10+8t^11,-2+14t-24t^2-36t^3+126t^4-74t^5-32t^6+172t^7-36t^8-32t^9+56t^10-32t^11,14-28t+36t^2-28t^3+8t^4
the Blanchfield form on it
x
197
First homology
of the double branched cover of 12a_1038
Z/197
-4 4
12a_1039
1

detected by
an unknotting move
1-7t+17t^2-27t^3+33t^4-27t^5+17t^6-7t^7+t^8
Seifert matrix of 12a_1039
1 0 0 1 0 0 0 0
0 -1 0 0 0 0 -1 0
0 0 -1 0 -1 0 0 0
0 0 0 1 0 0 0 0
1 0 0 1 1 0 0 0
0 0 -1 0 0 1 -1 0
0 0 0 0 0 0 -1 0
0 -1 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-3-7t^-2+15t^-1-17+15t-7t^2+t^3
137
First homology
of the double branched cover of 12a_1039
Z/137
0 0
12a_1040
2

detected by
the Lickorish test
2-13t+27t^2-31t^3+27t^4-13t^5+2t^6
Seifert matrix of 12a_1040
1 0 0 1 0 0
0 -2 0 0 0 0
0 0 -1 0 -1 0
0 0 0 1 0 0
1 0 0 1 1 0
0 1 -1 0 0 1
1 or 2
115
First homology
of the double branched cover of 12a_1040
Z/115
2 2
12a_1041
2

detected by
the signature
2-12t+33t^2-54t^3+63t^4-54t^5+33t^6-12t^7+2t^8
Seifert matrix of 12a_1041
-1 0 0 0 -1 0 -1 0
0 -1 0 0 -1 0 -1 0
-1 0 1 -1 -1 1 0 0
-1 0 0 -1 -1 0 -1 0
0 0 0 0 -2 0 -2 0
0 0 0 -1 0 1 0 0
0 0 0 0 -1 0 -2 0
0 -1 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+4t^-1-5+4t-2t^2
265
First homology
of the double branched cover of 12a_1041
Z/265
-4 4
12a_1042
1

detected by
an unknotting move
2-11t+30t^2-52t^3+63t^4-52t^5+30t^6-11t^7+2t^8
Seifert matrix of 12a_1042
-1 0 0 0 -1 0 0 -1
-1 1 0 -1 -1 1 0 0
-1 1 1 -1 -1 1 1 0
-1 0 0 -1 -1 0 0 -1
0 0 0 0 -2 0 0 -2
0 0 0 -1 0 1 0 0
-1 1 0 -1 -1 1 1 0
0 0 0 0 -1 0 0 -2
1
Generator of the Alexander module
(0,-3+9t-15t^2+16t^3-9t^4+2t^5,0,0,0,-1+7t-7t^2+2t^3,0,0)
the Blanchfield form on it
x
253
First homology
of the double branched cover of 12a_1042
Z/253
0 0
12a_1043
1

detected by
an unknotting move
4-21t+48t^2-61t^3+48t^4-21t^5+4t^6
Seifert matrix of 12a_1043
-1 0 -1 0 0 -1
-1 -1 -1 0 0 -1
0 0 -2 0 0 -2
0 -1 0 1 0 0
1 1 1 -1 2 0
0 0 -1 0 0 -2
1 or 2
207
First homology
of the double branched cover of 12a_1043
Z/207
-2 2
12a_1044
2

detected by
the Lickorish test
3-18t+46t^2-61t^3+46t^4-18t^5+3t^6
Seifert matrix of 12a_1044
-1 1 0 0 0 0
0 -3 0 0 0 0
-1 1 1 -1 1 1
-1 1 0 -1 0 0
0 0 0 -1 1 0
0 -1 0 0 0 -1
1 or 2
195
First homology
of the double branched cover of 12a_1044
Z/195
-2 2
12a_1045
2

detected by
the signature
1-8t+22t^2-32t^3+35t^4-32t^5+22t^6-8t^7+t^8
Seifert matrix of 12a_1045
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 -1 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 -1 0 0 0 -1 0 0
0 0 0 0 -1 0 -1 -1
1 -1 0 0 0 0 0 -1
1 or 2
161
First homology
of the double branched cover of 12a_1045
Z/161
-4 4
12a_1046
1

detected by
an unknotting move
2-17t+49t^2-67t^3+49t^4-17t^5+2t^6
Seifert matrix of 12a_1046
1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 -1 0 0
0 -1 0 -1 0 0
0 0 0 0 -2 0
1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1-t,3-t,0,1)
the Blanchfield form on it
-2t^-1+5-2t
203
First homology
of the double branched cover of 12a_1046
Z/203
-2 2
12a_1047
2

detected by
the Lickorish test
-1+4t-10t^2+18t^3-25t^4+27t^5-25t^6+18t^7-10t^8+4t^9-t^10
Seifert matrix of 12a_1047
-1 -1 0 0 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 1 0 0
-1 -1 0 -1 0 -1 0 0 0 0
-1 0 1 -1 1 0 0 1 1 0
0 -1 0 0 0 -1 0 0 0 0
-1 -1 1 -1 1 -1 1 1 1 1
0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 1 1 0
-1 0 1 -1 1 0 0 1 1 1
1
Generator of the Alexander module
(0,0,0,1+t+t^3+t^4,t+t^2,1+t,2t+t^2+t^4,0,-t+t^2-t^4,0)
the Blanchfield form on it
x
143
First homology
of the double branched cover of 12a_1047
Z/143
2 2
12a_1048
1

detected by
an unknotting move
2-9t+23t^2-40t^3+49t^4-40t^5+23t^6-9t^7+2t^8
Seifert matrix of 12a_1048
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
0 0 2 0 0 0 0 0
-1 -1 0 -1 0 -1 0 0
-1 0 -1 -1 1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 -1 -1 1 -1 1 1
-1 0 -1 -1 1 0 0 1
1
Generator of the Alexander module
(-2t-3t^2-3t^3+t^4-t^5+3t^6+2t^7+2t^8+t^9,1-t+3t^2+3t^3+3t^4+t^5+3t^6-t^7+t^8-t^9,-1-2t-3t^2-2t^3-3t^4-t^5-t^6,-1-2t+t^2-4t^4-10t^5-4t^6-14t^7-5t^8-7t^9-t^10,-1-7t-12t^2-16t^3-10t^4-18t^5-18t^6-13t^7-9t^8-14t^9-2t^10-6t^11+2t^12,2t-t^4-t^5-2t^6-t^7-t^8,6t+9t^2+10t^3-t^4+6t^5-7t^6-3t^7-5t^8-2t^9,-t-2
the Blanchfield form on it
x
197
First homology
of the double branched cover of 12a_1048
Z/197
0 0
12a_1049
1

detected by
an unknotting move
-1+9t-27t^2+45t^3-51t^4+45t^5-27t^6+9t^7-t^8
Seifert matrix of 12a_1049
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
0 0 -1 0 0 0 0 0
0 0 1 1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 1 0 0 -1 1 1 1
0 0 0 0 0 0 1 0
0 1 1 0 -1 0 1 1
1 or 2
215
First homology
of the double branched cover of 12a_1049
Z/215
2 2
12a_1050
1

detected by
an unknotting move
-1+8t-29t^2+63t^3-83t^4+63t^5-29t^6+8t^7-t^8
Seifert matrix of 12a_1050
1 0 1 0 1 0 0 1
-1 -1 -1 0 -1 -1 0 -1
0 0 1 -1 0 0 -1 1
0 0 0 -1 0 0 0 0
0 0 1 -1 1 0 0 1
-1 0 -1 0 -1 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 -1 0 0 -1 1
1 or 2
285
First homology
of the double branched cover of 12a_1050
Z/285
0 0
12a_1051
2

detected by
the signature
1-4t+9t^2-15t^3+18t^4-19t^5+18t^6-15t^7+9t^8-4t^9+t^10
Seifert matrix of 12a_1051
1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 -1 -1 0 -1 -1
-1 -1 0 0 -1 -1 -1 0 0 -1
1 0 0 0 0 1 0 0 0 0
0 -1 0 0 0 0 -1 0 0 0
-1 -1 0 -1 -1 -1 -1 -1 -1 -1
-1 -1 0 0 -1 -1 -1 0 -1 -1
0 -1 0 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-15t^-1+17-15t+9t^2-4t^3+t^4
113
First homology
of the double branched cover of 12a_1051
Z/113
-4 4
12a_1052
2

detected by
the Lickorish test
-2+9t-22t^2+38t^3-45t^4+38t^5-22t^6+9t^7-2t^8
Seifert matrix of 12a_1052
1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
-1 -1 -1 1 -1 -1 -1 -1
1 1 0 -2 1 1 1 1
-1 -1 0 0 -1 -1 -1 -1
1 0 0 0 0 1 0 0
0 -1 0 0 0 0 -1 0
0 -1 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-4-5t^-3+13t^-2-23t^-1+28-23t+13t^2-5t^3+t^4
187
First homology
of the double branched cover of 12a_1052
Z/187
-2 2
12a_1053
2

detected by
A(F_3)
2-10t+27t^2-48t^3+59t^4-48t^5+27t^6-10t^7+2t^8
Seifert matrix of 12a_1053
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
0 0 2 0 1 0 0 1
-1 -1 0 -1 0 -1 0 0
-1 0 0 -1 1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 -1 -1 0 -1 1 0
-1 0 0 -1 1 0 0 1
2
233
First homology
of the double branched cover of 12a_1053
Z/233
0 0
12a_1054 1 or 2
-1+9t-28t^2+48t^3-55t^4+48t^5-28t^6+9t^7-t^8
Seifert matrix of 12a_1054
-1 0 0 0 0 0 0 0
0 1 1 0 -1 0 1 0
0 0 -1 0 0 0 0 0
0 0 1 1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 1 0 0 -1 1 1 1
0 0 1 0 -1 0 1 0
0 1 1 0 -1 0 1 1
1 or 2
227
First homology
of the double branched cover of 12a_1054
Z/227
2 2
12a_1055
1

detected by
an unknotting move
-2+17t-50t^2+71t^3-50t^4+17t^5-2t^6
Seifert matrix of 12a_1055
-1 0 0 0 0 0
0 2 -1 0 1 0
0 0 -1 0 0 0
0 0 1 1 -1 0
-1 0 0 0 -1 0
-1 -1 0 0 -1 1
1
Generator of the Alexander module
(t,-2,0,-1,0,1)
the Blanchfield form on it
t^-4-11t^-3+51t^-2-119t^-1+156-119t+51t^2-11t^3+t^4
209
First homology
of the double branched cover of 12a_1055
Z/209
0 0
12a_1056
1

detected by
an unknotting move
-2+10t-28t^2+52t^3-63t^4+52t^5-28t^6+10t^7-2t^8
Seifert matrix of 12a_1056
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
-1 -1 -1 -1 0 -1 0 1
1 0 0 1 0 0 0 0
1 0 0 1 -1 0 0 -1
-1 -1 0 -1 0 -1 0 1
1 0 0 1 -1 0 -1 -1
1 1 0 1 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,-2+2t-t^2,-1-t+t^2-t^3,0,0)
the Blanchfield form on it
-4t^-3+14t^-2-32t^-1+44-32t+14t^2-4t^3
247
First homology
of the double branched cover of 12a_1056
Z/247
-2 2
12a_1057
1

detected by
an unknotting move
-3+22t-59t^2+81t^3-59t^4+22t^5-3t^6
Seifert matrix of 12a_1057
-2 0 0 -1 0 0
1 1 -1 0 0 0
1 0 -1 1 0 0
-1 0 0 -2 0 0
1 0 -1 1 1 1
1 0 -1 0 0 1
1
Generator of the Alexander module
(2134-4268t+3374t^2-1102t^3+124t^4,256+2683t-5914t^2+4967t^3-1688t^4+195t^5,141-282t+231t^2-78t^3+9t^4,-465+930t-735t^2+240t^3-27t^4,-267-1632t+3835t^2-3144t^3+823t^4+204t^5-138t^6+18t^7,-1075+2150t-1715t^2+565t^3-64t^4)
the Blanchfield form on it
x
249
First homology
of the double branched cover of 12a_1057
Z/249
0 0
12a_1058
2

detected by
the Lickorish test
-2+18t-53t^2+75t^3-53t^4+18t^5-2t^6
Seifert matrix of 12a_1058
-1 0 0 0 0 0
0 2 -1 0 1 1
0 0 -1 0 0 0
0 0 1 1 -1 0
-1 0 0 0 -1 0
-1 0 -1 0 0 1
1 or 2
221
First homology
of the double branched cover of 12a_1058
Z/221
0 0
12a_1059
3

detected by
the signature
-2+10t-23t^2+36t^3-41t^4+36t^5-23t^6+10t^7-2t^8
Seifert matrix of 12a_1059
-1 0 0 -1 0 -1 0 0
0 1 0 0 0 0 0 0
0 0 -1 0 0 0 -1 0
0 -1 0 -1 0 -1 0 0
0 -1 0 0 -1 0 0 0
0 0 -1 0 1 -2 -1 1
0 0 0 0 0 0 -1 0
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(1-t^3+t^4+t^5,2-4t-6t^2+2t^3-4t^4,t^2+2t^3+t^4,1-2t-3t^2+t^3-2t^4,0,t,0,-t-t^2-2t^3)
the Blanchfield form on it
x
183
First homology
of the double branched cover of 12a_1059
Z/183
-6 6
12a_1060
1

detected by
an unknotting move
-2+9t-22t^2+37t^3-43t^4+37t^5-22t^6+9t^7-2t^8
Seifert matrix of 12a_1060
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
0 0 -1 0 0 0 -1 0
1 0 0 1 0 0 0 0
0 -1 0 0 -1 0 0 0
1 1 -1 1 1 -2 -1 1
0 0 0 0 0 0 -1 0
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,t,0,0,1+t,0,0)
the Blanchfield form on it
-2t^-3+8t^-2-16t^-1+21-16t+8t^2-2t^3
183
First homology
of the double branched cover of 12a_1060
Z/183
-2 2
12a_1061
1

detected by
an unknotting move
-2+11t-31t^2+56t^3-67t^4+56t^5-31t^6+11t^7-2t^8
Seifert matrix of 12a_1061
-1 -1 0 -1 0 -1 -1 0
0 1 1 0 0 1 0 0
0 0 1 0 0 0 0 0
0 -1 0 -1 0 0 -1 0
0 -1 0 0 -1 0 0 0
0 0 1 0 0 1 0 0
0 0 0 0 1 0 -2 1
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(8-23t+24t^2-2t^3-26t^4+20t^5+24t^6-32t^7+32t^8-80t^9+104t^10-48t^11,-t^2+9t^4-22t^5+26t^6-10t^7-14t^8+12t^9,-2+8t^2-20t^3+26t^4-12t^5,1-9t^2+22t^3-26t^4+10t^5+14t^6-12t^7,-2+8t^2-20t^3+26t^4-12t^5,0,2-4t+2t^2-5t^3+16t^4-31t^5+30t^6+2t^7-10t^8-14t^9+12t^10,0)
the Blanchfield form on it
x
267
First homology
of the double branched cover of 12a_1061
Z/267
-2 2
12a_1062
2

detected by
the signature
-3+15t-32t^2+41t^3-32t^4+15t^5-3t^6
Seifert matrix of 12a_1062
-1 0 1 -1 0 0
0 1 0 0 0 0
0 0 -3 0 -1 -1
0 -1 1 -1 0 0
0 -1 0 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(1+t-4t^2+10t^3-12t^4+5t^5,0,-6+65t+8t^2-129t^3+61t^4+t^5,-4+10t^2-16t^3+14t^4-5t^5,-8-t+22t^2-33t^3+28t^4-10t^5,16-32t^2+16t^3)
the Blanchfield form on it
800t^-8-6843t^-7+27705t^-6-76885t^-5+134528t^-4-51136t^-3-366593t^-2+983304t^-1-1289760+983304t-366593t^2-51136t^3+134528t^4-76885t^5+27705t^6-6843t^7+800t^8
141
First homology
of the double branched cover of 12a_1062
Z/141
-4 4
12a_1063
1

detected by
an unknotting move
-3+12t-24t^2+31t^3-24t^4+12t^5-3t^6
Seifert matrix of 12a_1063
1 0 0 0 0 0
1 1 0 1 0 0
-1 -1 -3 -1 -1 -1
1 0 0 1 0 0
0 -1 0 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1+4t-3t^2,t,t,2t)
the Blanchfield form on it
-t^-2+2t^-1-3+2t-t^2
109
First homology
of the double branched cover of 12a_1063
Z/109
0 0
12a_1064 1 or 2
-2+9t-21t^2+33t^3-37t^4+33t^5-21t^6+9t^7-2t^8
Seifert matrix of 12a_1064
-1 -1 0 -1 -1 -1 -1 -1
0 1 1 0 0 1 0 0
0 0 1 0 0 0 0 0
0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 -1
0 0 1 0 0 1 0 0
0 -1 0 0 -1 0 -1 -1
0 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+9t^-2-19t^-1+25-19t+9t^2-2t^3
167
First homology
of the double branched cover of 12a_1064
Z/167
-2 2
12a_1065
1

detected by
an unknotting move
1-8t+31t^2-67t^3+87t^4-67t^5+31t^6-8t^7+t^8
Seifert matrix of 12a_1065
1 0 0 0 1 1 0 1
-1 -1 0 0 -1 -1 0 0
0 0 -1 0 0 0 -1 0
0 0 0 -1 0 0 0 0
0 0 0 -1 1 1 -1 1
0 0 -1 -1 0 1 -1 1
0 0 0 0 0 0 -1 0
0 0 -1 -1 0 0 -1 1
1
Generator of the Alexander module
(0,-2t^2-3t^4+t^5+t^6,-t^2,-t+2t^2+t^4+t^5,3-3t^2-2t^4+t^6,1+t-t^2-t^3-3t^4-t^5,-2t+2t^2+t^4+t^5,0)
the Blanchfield form on it
x
301
First homology
of the double branched cover of 12a_1065
Z/301
0 0
12a_1066
1

detected by
an unknotting move
-2+8t-19t^2+33t^3-39t^4+33t^5-19t^6+8t^7-2t^8
Seifert matrix of 12a_1066
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
0 0 -1 0 -1 0 -1 -1
1 0 0 1 0 0 0 0
1 0 0 1 -1 0 0 -1
0 0 -1 0 -1 -1 -1 -1
1 0 0 1 -1 0 -1 -1
1 1 0 1 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+6t^-2-10t^-1+13-10t+6t^2-2t^3
163
First homology
of the double branched cover of 12a_1066
Z/163
-2 2
12a_1067
2

detected by
the Lickorish test
-1+8t-30t^2+61t^3-75t^4+61t^5-30t^6+8t^7-t^8
Seifert matrix of 12a_1067
1 0 0 0 1 0 0 1
-1 -1 0 0 -1 0 0 0
0 0 -1 0 0 0 -1 0
0 0 0 -1 0 0 0 0
0 0 -1 -1 1 0 -1 1
0 0 -1 0 0 -1 -1 0
0 0 0 0 0 0 -1 0
0 0 -1 -1 0 -1 -1 1
1
Generator of the Alexander module
(-2+4t+2t^4-2t^5,2-5t-t^3-t^4+2t^5,-t+2t^2-t^3,2t-3t^2-2t^3+t^4-2t^5+2t^6,t+t^2-5t^3+2t^4+t^5-6t^6+4t^7,0,1-2t+t^2,1+t-7t^2+6t^3-t^4-2t^5+4t^6-2t^7)
the Blanchfield form on it
x
275
First homology
of the double branched cover of 12a_1067
Z/275
-2 2
12a_1068
2

detected by
the Lickorish test
-4+16t-32t^2+41t^3-32t^4+16t^5-4t^6
Seifert matrix of 12a_1068
1 0 0 0 0 0
1 1 0 1 0 0
-1 0 -2 -1 0 0
1 0 0 1 0 0
0 0 -1 0 -1 -1
0 1 -1 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-3-8t^-2+16t^-1-20+16t-8t^2+2t^3
145
First homology
of the double branched cover of 12a_1068
Z/145
0 0
12a_1069
2

detected by
the Lickorish test
2-19t+57t^2-79t^3+57t^4-19t^5+2t^6
Seifert matrix of 12a_1069
-1 0 0 -1 0 -1
-1 1 -1 -1 0 0
0 0 -1 0 0 0
0 0 0 -2 0 -2
-1 0 -1 -1 1 -1
0 0 0 -1 0 -2
1
Generator of the Alexander module
(0,1-3t+t^2,1-3t+t^2,-1,1-2t+t^2,0)
the Blanchfield form on it
-6t^-2+21t^-1-29+21t-6t^2
235
First homology
of the double branched cover of 12a_1069
Z/235
-2 2
12a_1070
1

detected by
an unknotting move
-1+8t-29t^2+58t^3-71t^4+58t^5-29t^6+8t^7-t^8
Seifert matrix of 12a_1070
-1 0 0 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 -1
0 -1 0 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 -1 0 -1 -1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(4t-12t^2+9t^3-2t^4,-16t^2+16t^3+4t^4-32t^5+42t^6-22t^7+4t^8,16-20t+4t^2+39t^3-61t^4+33t^5-6t^6,-8+8t+2t^2-16t^3+21t^4-11t^5+2t^6,-4+12t-5t^2-10t^3+9t^4-2t^5,-11+20t-27t^2+38t^3-32t^4+13t^5-2t^6,-4+12t-9t^2+2t^3,16t^2-16t^3-4t^4+32t^5-42t^6+22t^7-4t^8)
the Blanchfield form on it
x
263
First homology
of the double branched cover of 12a_1070
Z/263
-2 2
12a_1071
1

detected by
an unknotting move
-2+10t-26t^2+46t^3-55t^4+46t^5-26t^6+10t^7-2t^8
Seifert matrix of 12a_1071
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
0 0 -1 0 -1 0 0 -1
1 0 0 1 0 0 0 0
1 1 0 1 -2 1 0 0
0 -1 0 0 0 -1 0 0
0 0 -1 0 -1 0 -1 -1
1 0 0 1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,2t+t^3+2t^4-t^5,2t+2t^2-t^3,0,4t+4t^2-2t^3,0,1+4t+3t^2-2t^3)
the Blanchfield form on it
x
223
First homology
of the double branched cover of 12a_1071
Z/223
-2 2
12a_1072
2

detected by
the signature
2-11t+30t^2-49t^3+57t^4-49t^5+30t^6-11t^7+2t^8
Seifert matrix of 12a_1072
-1 0 0 0 0 0 0 0
0 2 1 1 0 1 1 1
0 2 2 1 0 1 1 2
0 0 0 1 0 0 0 0
-1 -1 -1 0 1 -1 0 -1
-1 0 0 0 0 -1 0 0
-1 0 0 1 0 0 1 0
0 2 1 1 0 1 1 2
1
Generator of the Alexander module
(0,1,0,0,0,0,0,2)
the Blanchfield form on it
-8t^-3+42t^-2-104t^-1+137-104t+42t^2-8t^3
241
First homology
of the double branched cover of 12a_1072
Z/241
4 4
12a_1073
2

detected by
the signature
-4+22t-49t^2+63t^3-49t^4+22t^5-4t^6
Seifert matrix of 12a_1073
-1 0 1 -1 0 0
0 1 0 0 0 0
0 1 -2 0 0 0
0 -1 1 -1 0 0
0 1 -1 0 -2 1
0 -1 0 0 0 -1
1 or 2
213
First homology
of the double branched cover of 12a_1073
Z/213
-4 4
12a_1074
2

detected by
the signature
1-8t+24t^2-40t^3+47t^4-40t^5+24t^6-8t^7+t^8
Seifert matrix of 12a_1074
-1 0 0 -1 -1 0 -1 0
0 1 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 -1
0 -1 0 -1 -1 0 -1 0
0 -1 0 0 -1 0 0 -1
0 -1 0 0 0 -1 0 0
0 -1 0 0 -1 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(-3t^2+6t^3-7t^4+4t^5-t^6,6t^2-16t^4+26t^5-16t^6+4t^7,-3t^3+6t^4-4t^5+t^6,1+4t+t^2-4t^3+5t^4-9t^5+7t^6-2t^7,3t-3t^2+4t^3-6t^4+4t^5-t^6,3t^2-8t^4+13t^5-8t^6+2t^7,3t-3t^2+4t^3-6t^4+4t^5-t^6,0)
the Blanchfield form on it
x
193
First homology
of the double branched cover of 12a_1074
Z/193
-4 4
12a_1075
1

detected by
an unknotting move
-4+19t-41t^2+53t^3-41t^4+19t^5-4t^6
Seifert matrix of 12a_1075
1 0 0 0 0 0
1 1 0 1 0 0
-1 0 -2 -1 0 0
1 0 0 1 0 0
0 1 -1 0 -2 1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,3+t-12t^2+4t^3+8t^4-4t^5,1+4t-8t^3+4t^4,7-2t-29t^2+20t^3+20t^4-20t^5+4t^6,-3+4t+3t^2-8t^3+12t^4-12t^5+4t^6)
the Blanchfield form on it
x
181
First homology
of the double branched cover of 12a_1075
Z/181
0 0
12a_1076
1

detected by
an unknotting move
1-8t+29t^2-60t^3+77t^4-60t^5+29t^6-8t^7+t^8
Seifert matrix of 12a_1076
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
0 -1 -1 0 0 -1 0 -1
1 0 0 1 0 0 0 0
1 0 0 1 -1 0 0 -1
0 -1 0 0 0 -1 0 0
1 0 0 1 -1 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(4+4t-8t^2+2t^3,0,-11-10t+23t^2-6t^3,-2-2t+4t^2-t^3,-2-2t+4t^2-t^3,-4-4t+8t^2-2t^3,-2-2t+4t^2-t^3,0)
the Blanchfield form on it
166t^-3-1135t^-2+2882t^-1-3988+2882t-1135t^2+166t^3
273
First homology
of the double branched cover of 12a_1076
Z/273
0 0
12a_1077
2

detected by
the Lickorish test
3-16t+40t^2-53t^3+40t^4-16t^5+3t^6
Seifert matrix of 12a_1077
-1 0 0 0 0 0
0 1 0 0 0 0
-1 0 1 -1 0 1
-1 0 0 -1 0 0
-1 1 0 0 1 0
0 -1 0 -1 -1 3
1
Generator of the Alexander module
(0,0,0,0,1,-2+3t)
the Blanchfield form on it
-t^-2+4t^-1-7+4t-t^2
171
First homology
of the double branched cover of 12a_1077
Z/171
2 2
12a_1078
1

detected by
an unknotting move
2-11t+32t^2-58t^3+71t^4-58t^5+32t^6-11t^7+2t^8
Seifert matrix of 12a_1078
-1 0 0 0 0 0 0 0
-1 -1 1 0 0 0 0 0
1 0 -2 0 0 0 0 0
0 -1 1 1 1 0 1 0
0 0 -1 0 -1 0 0 0
-1 -1 1 1 0 1 1 1
0 0 0 0 0 0 1 0
0 -1 1 1 1 0 1 1
1
Generator of the Alexander module
(0,-2t+t^2,-1+t,0,-2+t,-2t+t^2,0,2-t)
the Blanchfield form on it
-t^-2+3t^-1-4+3t-t^2
277
First homology
of the double branched cover of 12a_1078
Z/277
0 0
12a_1079
2

detected by
the Lickorish test
-2+11t-31t^2+56t^3-67t^4+56t^5-31t^6+11t^7-2t^8
Seifert matrix of 12a_1079
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
-1 -1 -1 -1 1 -1 -1 0
1 0 0 1 0 0 0 0
1 1 0 1 -2 1 0 0
0 -1 0 0 0 -1 0 0
-1 -1 0 -1 1 -1 -1 0
1 0 0 1 -1 0 0 -1
2
267
First homology
of the double branched cover of 12a_1079
Z/267
-2 2
12a_1080
2

detected by
the signature
1-8t+24t^2-42t^3+51t^4-42t^5+24t^6-8t^7+t^8
Seifert matrix of 12a_1080
-1 0 0 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 -1 -1 0 -1 -1 0 -1
0 -1 0 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 -1 0 -1 0
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(-2t-2t^4+t^5,0,1+2t^2-t^3,2+2t^3-t^4,0,0,2+2t^3-t^4,0)
the Blanchfield form on it
x
201
First homology
of the double branched cover of 12a_1080
Z/201
-4 4
12a_1081
1

detected by
an unknotting move
1-8t+25t^2-46t^3+57t^4-46t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_1081
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
0 -1 -1 0 -1 -1 0 -1
1 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
1 0 0 1 -1 0 -1 0
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,2t-3t^2+6t^3-3t^4+2t^5,-t-t^2+4t^3-7t^4+4t^5-2t^6,-2t+t^2-t^3,1+3t-5t^2+8t^3-4t^4+2t^5,-2t+5t^2-3t^3+2t^4,-2t^2+t^3-t^4,0)
the Blanchfield form on it
x
217
First homology
of the double branched cover of 12a_1081
Z/217
0 0
12a_1082
2

detected by
the signature
-1+8t-23t^2+38t^3-45t^4+38t^5-23t^6+8t^7-t^8
Seifert matrix of 12a_1082
1 0 0 0 0 0 0 0
1 -1 0 0 0 1 0 0
-1 0 -1 -1 0 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 -1 0 0 -1 1 -1 0
0 0 0 0 0 1 0 0
1 -1 0 0 0 1 -1 0
-1 0 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+8t^-2-20t^-1+25-20t+8t^2-t^3
185
First homology
of the double branched cover of 12a_1082
Z/185
-4 4
12a_1083
2

detected by
the Lickorish test
2-9t+21t^2-33t^3+39t^4-33t^5+21t^6-9t^7+2t^8
Seifert matrix of 12a_1083
-1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 -1 0
-1 0 1 1 1 1 -1 0
0 0 0 1 0 0 0 0
-1 0 0 1 1 1 0 0
-1 0 0 1 0 1 0 0
0 0 0 0 0 0 -2 0
0 -1 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
2t^-3-8t^-2+15t^-1-17+15t-8t^2+2t^3
169
First homology
of the double branched cover of 12a_1083
Z/169
0 0
12a_1084
2

detected by
the signature
1-8t+20t^2-28t^3+31t^4-28t^5+20t^6-8t^7+t^8
Seifert matrix of 12a_1084
-1 0 0 -1 -1 0 -1 -1
0 1 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 0
0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 -1
0 0 0 0 0 1 0 0
0 -1 0 0 -1 0 -1 -1
0 -1 0 0 0 -1 0 -1
1 or 2
145
First homology
of the double branched cover of 12a_1084
Z/145
-4 4
12a_1085
1

detected by
an unknotting move
2-17t+45t^2-59t^3+45t^4-17t^5+2t^6
Seifert matrix of 12a_1085
-1 0 0 0 1 -1
0 1 0 0 0 0
0 -1 -1 -1 0 0
0 0 0 1 0 0
0 1 0 0 -2 1
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-2-13t^-1+23-13t+2t^2
187
First homology
of the double branched cover of 12a_1085
Z/187
-2 2
12a_1086
1

detected by
an unknotting move
4-20t+46t^2-59t^3+46t^4-20t^5+4t^6
Seifert matrix of 12a_1086
-1 0 0 0 0 -1
0 1 0 0 0 -1
0 0 1 0 0 0
-1 0 1 1 0 0
1 1 -1 -1 2 0
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-3-12t^-2+31t^-1-42+31t-12t^2+2t^3
199
First homology
of the double branched cover of 12a_1086
Z/199
2 2
12a_1087
2

detected by
the Lickorish test
1-8t+25t^2-48t^3+61t^4-48t^5+25t^6-8t^7+t^8
Seifert matrix of 12a_1087
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
0 -1 -1 0 0 -1 0 0
1 0 0 1 0 0 0 0
1 0 0 1 -1 0 0 -1
0 0 0 0 0 1 0 0
1 0 0 1 -1 0 -1 -1
1 0 0 1 0 -1 0 -1
1 or 2
225
First homology
of the double branched cover of 12a_1087
Z/225
0 0
12a_1088
1

detected by
an unknotting move
-1+9t-29t^2+54t^3-67t^4+54t^5-29t^6+9t^7-t^8
Seifert matrix of 12a_1088
1 0 0 0 0 0 0 0
1 -1 0 0 1 1 0 1
-1 0 -1 0 -1 -1 0 -1
0 -1 0 -1 0 1 -1 0
0 0 0 0 1 1 0 1
0 0 0 0 0 1 0 0
1 -1 0 0 1 1 -1 1
0 0 0 0 0 1 0 1
1 or 2
253
First homology
of the double branched cover of 12a_1088
Z/253
0 0
12a_1089
2

detected by
the signature
-1+8t-21t^2+31t^3-35t^4+31t^5-21t^6+8t^7-t^8
Seifert matrix of 12a_1089
1 0 0 0 0 0 0 0
1 -1 0 0 0 1 0 0
-1 0 -1 0 0 -1 0 0
0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 1 -1 0
0 0 0 0 0 1 0 0
1 -1 0 0 0 1 -1 0
0 -1 0 0 -1 0 -1 -1
1 or 2
157
First homology
of the double branched cover of 12a_1089
Z/157
-4 4
12a_1090
2

detected by
the Lickorish test
2-16t+42t^2-55t^3+42t^4-16t^5+2t^6
Seifert matrix of 12a_1090
1 0 0 0 0 0
1 -1 0 0 0 -1
-1 0 -1 -1 0 0
0 0 0 1 0 0
1 -1 0 0 -1 -1
0 0 0 -1 0 -2
1 or 2
175
First homology
of the double branched cover of 12a_1090
Z/175
-2 2
12a_1091
1

detected by
an unknotting move
2-10t+27t^2-49t^3+61t^4-49t^5+27t^6-10t^7+2t^8
Seifert matrix of 12a_1091
-1 -1 0 0 0 -1 0 -1
0 -2 0 0 0 -1 0 -2
-1 -1 1 1 1 -1 1 -1
0 0 0 1 0 0 0 0
-1 -1 0 1 1 -1 1 0
0 -2 0 0 0 -2 0 -2
-1 -1 0 1 0 -1 1 0
0 -1 0 0 0 -1 0 -2
1 or 2
237
First homology
of the double branched cover of 12a_1091
Z/237
0 0
12a_1092
2

detected by
the Nakanishi index
1-9t+29t^2-52t^3+61t^4-52t^5+29t^6-9t^7+t^8
Seifert matrix of 12a_1092
1 0 0 0 0 0 0 0
1 -1 0 0 1 1 0 0
-1 0 -1 0 -1 -1 0 0
0 -1 0 -1 0 0 -1 -1
0 0 0 0 1 1 0 0
0 0 0 0 0 1 0 0
1 -1 0 0 1 1 -1 0
0 -1 0 0 0 1 -1 -1
2
243
First homology
of the double branched cover of 12a_1092
Z/81+Z/3
-2 2
12a_1093
2

detected by
the Nakanishi index
-1+8t-25t^2+44t^3-51t^4+44t^5-25t^6+8t^7-t^8
Seifert matrix of 12a_1093
-1 0 0 -1 -1 0 -1 0
0 1 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 0
0 -1 0 -1 -1 0 -1 0
0 -1 0 0 -1 -1 0 -1
0 0 0 0 0 1 0 1
0 -1 0 0 -1 0 -1 0
0 0 0 0 0 0 0 1
2
207
First homology
of the double branched cover of 12a_1093
Z/69+Z/3
-2 2
12a_1094
1

detected by
an unknotting move
2-14t+35t^2-45t^3+35t^4-14t^5+2t^6
Seifert matrix of 12a_1094
1 0 0 0 0 0
1 -1 0 1 0 0
0 -1 -1 1 -1 0
0 0 0 1 0 0
1 -1 0 1 -1 0
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,2t^2-t^3+2t^5-t^6,t+t^2-3t^3+t^4-2t^6+t^7,-t-2t^2+t^3-2t^4-t^5+t^6,2t^2-t^3+2t^5-t^6,1+3t-t^2-4t^3+6t^4-2t^5)
the Blanchfield form on it
x
147
First homology
of the double branched cover of 12a_1094
Z/147
-2 2
12a_1095
1

detected by
an unknotting move
3-12t+22t^2-25t^3+22t^4-12t^5+3t^6
Seifert matrix of 12a_1095
-1 1 0 0 0 0
0 -3 0 0 0 0
-1 1 1 1 1 1
0 0 0 1 0 0
-1 0 0 1 1 1
-1 0 0 1 0 1
1
Generator of the Alexander module
(0,0,-t,0,0,1+t^2)
the Blanchfield form on it
-3t^-2+12t^-1-19+12t-3t^2
99
First homology
of the double branched cover of 12a_1095
Z/99
2 2
12a_1096
1

detected by
an unknotting move
-1+8t-29t^2+60t^3-75t^4+60t^5-29t^6+8t^7-t^8
Seifert matrix of 12a_1096
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
0 -1 -1 0 0 -1 0 0
1 0 0 1 0 0 0 0
1 0 0 1 -1 -1 0 -1
0 0 0 0 0 1 0 1
1 0 0 1 -1 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,-3+3t-3t^2+t^3,3t-3t^2+3t^3-t^4,1-2t+3t^2-t^3,1-2t+3t^2-t^3,-3+3t-3t^2+t^3,1-2t+3t^2-t^3,0)
the Blanchfield form on it
-t^-2+4t^-1-8+4t-t^2
271
First homology
of the double branched cover of 12a_1096
Z/271
2 2
12a_1097
2

detected by
the signature
16-54t+77t^2-54t^3+16t^4
Seifert matrix of 12a_1097
-3 1 1 -1
0 -2 1 0
1 0 -2 0
-1 0 1 -2
2
217
First homology
of the double branched cover of 12a_1097
Z/217
-4 4
12a_1098
2

detected by
the signature
-5+29t-68t^2+89t^3-68t^4+29t^5-5t^6
Seifert matrix of 12a_1098
1 0 0 0 0 0
0 -2 1 0 0 0
0 0 -2 0 -1 -1
-1 0 -1 -1 -1 -1
0 -1 -1 0 -2 -1
-1 -1 -1 0 -2 -2
1
Generator of the Alexander module
(0,-5t+25t^2+43t^3-88t^4+60t^5,5t-5t^2-23t^3+36t^4-20t^5,1+2t-5t^2+28t^4-13t^5-16t^6+20t^7,-5t^2-5t^3+13t^4-10t^5,-1-2t+5t^2+15t^3-23t^4-36t^5+72t^6-40t^7)
the Blanchfield form on it
x
293
First homology
of the double branched cover of 12a_1098
Z/293
-4 4
12a_1099
2

detected by
the signature
2-10t+27t^2-44t^3+51t^4-44t^5+27t^6-10t^7+2t^8
Seifert matrix of 12a_1099
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
0 -1 2 1 0 -1 1 1
0 0 0 1 0 0 0 0
-1 1 -1 0 1 1 -1 0
0 0 0 0 0 1 0 0
-1 0 0 0 0 0 -1 0
-1 0 0 1 0 0 0 1
1 or 2
217
First homology
of the double branched cover of 12a_1099
Z/217
4 4
12a_1100
1

detected by
an unknotting move
2-11t+31t^2-54t^3+65t^4-54t^5+31t^6-11t^7+2t^8
Seifert matrix of 12a_1100
-1 -1 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
0 0 2 0 1 0 0 1
-1 -1 0 -1 0 0 -1 0
-1 0 0 -1 1 0 0 0
-1 -1 -1 -1 0 1 -1 0
0 -1 0 0 0 0 -1 0
-1 -1 0 -1 1 0 -1 1
1
Generator of the Alexander module
(0,0,1-2t,0,1,t,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-13t^-1+15-13t+7t^2-2t^3
261
First homology
of the double branched cover of 12a_1100
Z/261
0 0
12a_1101
2

detected by
the signature
2-11t+30t^2-48t^3+55t^4-48t^5+30t^6-11t^7+2t^8
Seifert matrix of 12a_1101
1 0 0 1 0 0 -1 0
0 -1 0 0 0 0 0 0
1 0 2 1 1 0 0 1
0 0 0 1 0 0 0 0
1 0 0 1 1 0 -1 0
0 -1 -1 0 0 1 -1 0
0 -1 0 0 0 0 -1 0
1 -1 0 1 1 0 -1 1
1 or 2
237
First homology
of the double branched cover of 12a_1101
Z/237
4 4
12a_1102
2

detected by
the Lickorish test
1-8t+30t^2-68t^3+91t^4-68t^5+30t^6-8t^7+t^8
Seifert matrix of 12a_1102
-1 -1 0 0 0 -1 -1 0
0 1 0 0 -1 0 1 0
-1 0 1 -1 0 0 0 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 -1 0 0 0
0 -1 0 0 0 -1 -1 -1
0 0 0 0 0 0 1 0
0 1 0 0 -1 0 1 1
2
305
First homology
of the double branched cover of 12a_1102
Z/305
0 0
12a_1103
2

detected by
the Lickorish test
4-19t+45t^2-59t^3+45t^4-19t^5+4t^6
Seifert matrix of 12a_1103
-1 0 0 0 0 0
1 2 0 1 0 0
0 0 1 0 0 0
-1 0 0 -1 0 0
-1 0 1 0 1 0
1 1 -1 0 -1 2
1 or 2
195
First homology
of the double branched cover of 12a_1103
Z/195
2 2
12a_1104
2

detected by
the Lickorish test
-1+8t-25t^2+46t^3-55t^4+46t^5-25t^6+8t^7-t^8
Seifert matrix of 12a_1104
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 1 1 1 0 0 1
0 0 0 1 0 0 0 0
-1 0 0 1 1 0 0 1
-1 1 0 0 0 1 -1 0
-1 0 0 0 0 0 -1 0
-1 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,-2-7t,27-28t,3-14t,0)
the Blanchfield form on it
t^-1-1+t
215
First homology
of the double branched cover of 12a_1104
Z/215
2 2
12a_1105
2

detected by
the Nakanishi index
1-8t+30t^2-64t^3+83t^4-64t^5+30t^6-8t^7+t^8
Seifert matrix of 12a_1105
-1 -1 -1 0 -1 -1 0 0
0 1 0 -1 0 1 0 0
0 -1 -1 0 -1 -1 -1 0
0 0 0 -1 0 0 0 0
0 -1 0 0 -1 -1 -1 0
0 0 0 0 0 1 0 0
0 1 0 -1 0 1 1 0
-1 0 -1 0 0 0 0 1
2
289
First homology
of the double branched cover of 12a_1105
Z/17+Z/17
0 0
12a_1106
2

detected by
the Lickorish test
-3+18t-48t^2+67t^3-48t^4+18t^5-3t^6
Seifert matrix of 12a_1106
1 0 1 0 1 0
0 -1 0 0 0 0
0 -1 1 0 0 0
1 0 0 -2 1 -1
0 -1 1 0 1 0
1 0 1 -1 1 -2
1
Generator of the Alexander module
(0,1-t,0,1-2t+2t^2,-1+2t-t^2,-t+t^2)
the Blanchfield form on it
3t^-2-13t^-1+20-13t+3t^2
205
First homology
of the double branched cover of 12a_1106
Z/205
0 0
12a_1107
2

detected by
the signature
2-8t+16t^2-20t^3+21t^4-20t^5+16t^6-8t^7+2t^8
Seifert matrix of 12a_1107
-1 0 0 0 0 0 0 -1
-1 1 0 1 1 0 1 -1
-1 1 1 1 1 1 1 -1
0 0 0 1 0 0 0 0
-1 0 0 1 1 0 1 0
-1 1 0 1 1 1 1 -1
-1 0 0 1 0 0 1 0
0 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
-2t^-3+7t^-2-13t^-1+15-13t+7t^2-2t^3
113
First homology
of the double branched cover of 12a_1107
Z/113
4 4
12a_1108
2

detected by
the Lickorish test
4-17t+35t^2-43t^3+35t^4-17t^5+4t^6
Seifert matrix of 12a_1108
-1 0 0 0 0 -1
0 1 0 0 0 0
-1 1 1 0 1 0
1 -1 -1 2 -1 1
-1 1 0 0 1 0
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,1-5t^2+9t^3-16t^4+14t^5-11t^6+6t^7-2t^8+t^9,-4t+5t^2-2t^3+3t^4-4t^5+10t^6-12t^7+9t^8-5t^9+t^10,1-3t-2t^2+3t^3-t^4-3t^5+6t^6-5t^7+3t^8-t^9,-t+3t^2-4t^3+7t^4-6t^5+6t^6-4t^7+2t^8-t^9,1-t-t^3+t^4-3t^5+3t^6-2t^7+t^8)
the Blanchfield form on it
x
155
First homology
of the double branched cover of 12a_1108
Z/155
2 2
12a_1109
1

detected by
an unknotting move
-2+11t-29t^2+51t^3-61t^4+51t^5-29t^6+11t^7-2t^8
Seifert matrix of 12a_1109
-1 -1 0 -1 0 -1 0 -1
0 -1 0 -1 0 0 0 -1
0 -1 1 -1 0 -1 1 0
0 0 0 -2 0 0 0 -2
0 -1 1 -1 1 -1 1 -1
0 -1 0 -1 0 -1 0 -1
0 -1 0 0 0 -1 1 0
0 0 0 -1 0 0 0 -2
1
Generator of the Alexander module
(0,0,-t-t^2,0,-t-t^2,-t,1-t^2,0)
the Blanchfield form on it
-2t^-3+9t^-2-18t^-1+23-18t+9t^2-2t^3
247
First homology
of the double branched cover of 12a_1109
Z/247
-2 2
12a_1110
1

detected by
an unknotting move
5-27t+66t^2-87t^3+66t^4-27t^5+5t^6
Seifert matrix of 12a_1110
1 0 0 0 0 0
0 -2 1 0 0 0
0 0 -2 -1 -1 -1
0 -1 -1 -2 -1 -1
-1 -1 -1 -2 -2 -1
1 0 0 0 0 1
1
Generator of the Alexander module
(0,-1,-2,2+2t,1,-1)
the Blanchfield form on it
-39t^-3+292t^-2-797t^-1+1092-797t+292t^2-39t^3
283
First homology
of the double branched cover of 12a_1110
Z/283
-2 2
12a_1111
2

detected by
the Lickorish test
-2+11t-27t^2+41t^3-45t^4+41t^5-27t^6+11t^7-2t^8
Seifert matrix of 12a_1111
-1 0 0 0 -1 0 0 -1
-1 1 0 1 -1 0 1 0
-1 1 1 1 -1 1 1 -1
0 0 0 1 0 0 0 0
0 0 0 0 -2 0 0 -2
-1 1 0 1 -1 1 1 -1
-1 0 0 1 0 0 1 0
0 0 0 0 -1 0 0 -2
1
Generator of the Alexander module
(-7+10t-10t^2+8t^3-4t^4+t^5,-9-42t-138t^2+360t^3-378t^4+327t^5-175t^6+47t^7,5+68t-140t^2+142t^3-116t^4+59t^5-15t^6,67-130t+130t^2-104t^3+52t^4-13t^5,-1,36-70t+70t^2-56t^3+28t^4-7t^5,79-174t+101t^2+26t^3-96t^4+122t^5-74t^6+20t^7,-32+60t-60t^2+48t^3-24t^4+6t^5)
the Blanchfield form on it
x
207
First homology
of the double branched cover of 12a_1111
Z/207
2 2
12a_1112
3

detected by
the signature
8-27t+46t^2-53t^3+46t^4-27t^5+8t^6
Seifert matrix of 12a_1112
-2 -1 -1 -1 -2 -1
0 -2 1 0 0 0
-1 0 -2 -1 -1 -1
-2 -1 -1 -2 -2 -1
-1 -1 -1 -1 -2 -1
-1 -1 0 -1 -1 -2
1 or 2
215
First homology
of the double branched cover of 12a_1112
Z/215
-6 6
12a_1113
2

detected by
the signature
15-51t+73t^2-51t^3+15t^4
Seifert matrix of 12a_1113
-3 1 1 1
0 -2 1 0
1 0 -2 -1
1 -1 0 -2
1 or 2
205
First homology
of the double branched cover of 12a_1113
Z/205
-4 4
12a_1114
3

detected by
the signature
-1+4t-9t^2+12t^3-14t^4+15t^5-14t^6+12t^7-9t^8+4t^9-t^10
Seifert matrix of 12a_1114
1 0 1 1 0 0 1 1 -1 0
0 -1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 0 0 0
0 0 1 1 0 0 1 1 0 0
1 0 1 1 1 0 1 1 -1 0
1 -1 1 1 1 1 1 1 -1 1
0 0 0 0 0 0 1 0 0 0
0 0 1 0 0 0 1 1 0 0
0 -1 0 0 0 0 0 0 -1 0
1 -1 1 1 1 0 1 1 -1 1
1 or 2
95
First homology
of the double branched cover of 12a_1114
Z/95
6 6
12a_1115
2

detected by
the signature
2-9t+22t^2-32t^3+35t^4-32t^5+22t^6-9t^7+2t^8
Seifert matrix of 12a_1115
1 0 -1 1 0 0 -1 0
0 -1 0 0 0 0 0 0
0 0 2 0 0 0 0 0
0 0 -1 1 0 0 0 0
1 0 -1 1 1 0 -1 0
1 -1 -1 1 1 1 -1 1
0 -1 0 0 0 0 -1 0
1 -1 -1 1 1 0 -1 1
1 or 2
165
First homology
of the double branched cover of 12a_1115
Z/165
4 4
12a_1116
2

detected by
the signature
2-9t+23t^2-37t^3+43t^4-37t^5+23t^6-9t^7+2t^8
Seifert matrix of 12a_1116
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
0 -1 2 1 1 -1 1 1
0 0 0 1 0 0 0 0
-1 0 0 1 1 0 0 1
0 0 0 0 0 1 0 0
-1 0 0 0 0 0 -1 0
-1 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,0,1-2t,0,3-2t+t^2-2t^3,0,-t+3t^2-2t^3,0)
the Blanchfield form on it
23t^-4-104t^-3+266t^-2-429t^-1+498-429t+266t^2-104t^3+23t^4
185
First homology
of the double branched cover of 12a_1116
Z/185
4 4
12a_1117
2

detected by
the signature
-4+26t-64t^2+85t^3-64t^4+26t^5-4t^6
Seifert matrix of 12a_1117
-1 0 -1 0 0 0
0 -2 -1 0 0 -1
0 -1 -2 0 0 -1
1 1 1 1 -1 0
0 1 1 0 -1 1
0 -1 -1 0 0 -2
1
Generator of the Alexander module
(0,-1,0,1+t,t,0)
the Blanchfield form on it
-4t^-2+19t^-1-28+19t-4t^2
273
First homology
of the double branched cover of 12a_1117
Z/273
-4 4
12a_1118
2

detected by
the Lickorish test
3-12t+26t^2-33t^3+26t^4-12t^5+3t^6
Seifert matrix of 12a_1118
-1 0 0 0 0 0
0 1 0 0 0 0
-1 1 1 0 0 1
0 -1 -1 3 -1 -1
-1 0 0 0 -1 0
-1 1 0 0 0 1
1
Generator of the Alexander module
(0,0,0,-5+t+6t^2-3t^3,-2+6t-3t^2,0)
the Blanchfield form on it
-55t^-3+217t^-2-470t^-1+594-470t+217t^2-55t^3
115
First homology
of the double branched cover of 12a_1118
Z/115
2 2
12a_1119
2

detected by
the Lickorish test
2-9t+21t^2-33t^3+39t^4-33t^5+21t^6-9t^7+2t^8
Seifert matrix of 12a_1119
-1 0 0 0 0 0 0 -1
-1 1 0 -1 1 0 -1 -1
-1 1 1 -1 1 1 -1 -1
-1 0 0 -1 0 0 -1 -1
0 0 0 -1 1 0 -1 0
-1 1 0 -1 1 1 -1 -1
-1 0 0 0 0 0 -1 -1
0 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,-2+2t-2t^2+t^3,0,0,0,0,0,1)
the Blanchfield form on it
-2t^-3+9t^-2-19t^-1+23-19t+9t^2-2t^3
169
First homology
of the double branched cover of 12a_1119
Z/169
0 0
12a_1120
1

detected by
an unknotting move
-1+4t-9t^2+14t^3-18t^4+19t^5-18t^6+14t^7-9t^8+4t^9-t^10
Seifert matrix of 12a_1120
1 0 1 1 0 0 1 1 -1 0
0 -1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 0 0 0
0 0 1 1 0 0 1 1 0 0
0 -1 0 0 -1 0 0 0 0 -1
1 0 1 1 -1 1 1 1 -1 -1
0 0 0 0 0 0 1 0 0 0
0 0 1 0 0 0 1 1 0 0
0 -1 0 0 -1 0 0 0 -1 -1
0 -1 0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+2t^-1-1+2t-2t^2+t^3
111
First homology
of the double branched cover of 12a_1120
Z/111
2 2
12a_1121
1

detected by
an unknotting move
2-9t+22t^2-36t^3+43t^4-36t^5+22t^6-9t^7+2t^8
Seifert matrix of 12a_1121
1 0 -1 1 0 0 -1 0
0 -1 0 0 0 0 0 0
0 0 2 0 0 0 0 0
0 0 -1 1 0 0 0 0
0 -1 0 0 -1 0 0 -1
1 0 -1 1 -1 1 -1 -1
0 -1 0 0 -1 0 -1 -1
0 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(2t^3-t^4,2t^2-t^3,-t-2t^2-t^3+t^4-8t^5+4t^6,1+2t^2+t^3+3t^4-2t^5,t+2t^3-t^4,2t^2-3t^3-t^4+t^5,-4t^3+2t^4,-2t^3+t^4)
the Blanchfield form on it
x
181
First homology
of the double branched cover of 12a_1121
Z/181
0 0
12a_1122
2

detected by
the Lickorish test
1-8t+30t^2-63t^3+81t^4-63t^5+30t^6-8t^7+t^8
Seifert matrix of 12a_1122
1 0 -1 0 1 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
1 -1 -1 1 1 1 -1 0
0 0 0 0 1 0 0 0
1 0 -1 0 1 1 -1 0
0 0 0 0 0 0 -1 0
-1 0 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(14t-82t^2+201t^3-317t^4+319t^5-59t^6-153t^7+185t^8-81t^9+12t^10,3+7t+2t^2+6t^3+11t^4+11t^5-14t^6+3t^7,3-13t+43t^2-19t^3+5t^4+67t^5-21t^6+3t^7-7t^8+2t^9,7-36t+38t^2-65t^3+4t^4+12t^5-30t^6+21t^7-4t^8,4t-7t^2+7t^3+t^4-10t^5+6t^6-t^7,-21t^2+85t^3-191t^4+295t^5-300t^6+67t^7+143t^8-183t^9+81t^10-12t^11,1
the Blanchfield form on it
x
285
First homology
of the double branched cover of 12a_1122
Z/285
0 0
12a_1123
2

detected by
the Nakanishi index
1-9t+30t^2-56t^3+69t^4-56t^5+30t^6-9t^7+t^8
Seifert matrix of 12a_1123
1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
-1 -1 -1 -1 -1 -1 -1 0
0 -1 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
1 0 0 0 0 1 0 0
-1 -1 0 -1 -1 -1 -1 0
1 0 0 0 1 1 0 -1
2
261
First homology
of the double branched cover of 12a_1123
Z/87+Z/3
0 0
12a_1124
2

detected by
the Lickorish test
-1+13t-50t^2+77t^3-50t^4+13t^5-t^6
Seifert matrix of 12a_1124
1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 0 -1 0
1 -1 0 -1 1 0
0 0 0 0 1 0
1 -1 0 0 0 -1
2
205
First homology
of the double branched cover of 12a_1124
Z/205
0 0
12a_1125
2

detected by
the signature
-4+14t-21t^2+23t^3-21t^4+14t^5-4t^6
Seifert matrix of 12a_1125
-1 0 0 1 0 1
0 -1 -1 0 -1 -1
0 0 -1 0 0 -1
0 0 0 2 0 0
0 0 -1 0 -1 -1
0 0 0 -1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1-t+t^2,1)
the Blanchfield form on it
-4t^-2+14t^-1-19+14t-4t^2
101
First homology
of the double branched cover of 12a_1125
Z/101
-4 4
12a_1126
1

detected by
an unknotting move
-8+30t-43t^2+30t^3-8t^4
Seifert matrix of 12a_1126
-1 1 0 1
0 2 0 0
0 0 -2 0
0 -1 -1 -2
1 or 2
119
First homology
of the double branched cover of 12a_1126
Z/119
-2 2
12a_1127
1

detected by
an unknotting move
4-24t+41t^2-24t^3+4t^4
Seifert matrix of 12a_1127
-1 -1 0 0
0 2 0 0
0 0 -2 0
-1 0 -1 1
1 or 2
97
First homology
of the double branched cover of 12a_1127
Z/97
0 0
12a_1128
1

detected by
an unknotting move
-1+3t-5t^2+7t^3-9t^4+9t^5-9t^6+7t^7-5t^8+3t^9-t^10
Seifert matrix of 12a_1128
-1 -1 0 0 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 1 0 0
0 0 1 1 0 0 0 1 1 0
-1 -1 0 0 -1 -1 0 0 0 0
0 -1 0 0 0 -1 0 0 0 0
-1 -1 1 1 -1 -1 1 1 1 1
0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 1 1 0
0 0 1 1 0 0 0 1 1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0,0,0)
the Blanchfield form on it
1
59
First homology
of the double branched cover of 12a_1128
Z/59
2 2
12a_1129
1

detected by
an unknotting move
2-7t+13t^2-19t^3+23t^4-19t^5+13t^6-7t^7+2t^8
Seifert matrix of 12a_1129
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 1
0 0 -1 2 0 0 0 -1
-1 -1 0 0 -1 -1 0 0
0 -1 0 0 0 -1 0 0
-1 -1 1 -1 -1 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,t,0,1+t,0)
the Blanchfield form on it
2t^-3-7t^-2+13t^-1-15+13t-7t^2+2t^3
105
First homology
of the double branched cover of 12a_1129
Z/105
0 0
12a_1130
1

detected by
an unknotting move
2-8t+16t^2-23t^3+27t^4-23t^5+16t^6-8t^7+2t^8
Seifert matrix of 12a_1130
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
0 0 2 1 0 0 0 1
0 0 2 2 0 0 0 2
-1 -1 0 0 -1 -1 0 0
0 -1 0 0 0 -1 0 0
-1 -1 -1 -1 -1 -1 1 -1
0 0 2 1 0 0 0 2
1
Generator of the Alexander module
(0,0,0,0,t,0,1+t,0)
the Blanchfield form on it
2t^-3-8t^-2+16t^-1-19+16t-8t^2+2t^3
125
First homology
of the double branched cover of 12a_1130
Z/125
0 2
12a_1131
2

detected by
the signature
2-7t+11t^2-11t^3+11t^4-11t^5+11t^6-7t^7+2t^8
Seifert matrix of 12a_1131
-2 1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 1 0 0
0 0 1 1 0 1 1 0
1 -1 1 1 1 1 1 1
0 0 0 0 0 1 0 0
0 0 1 0 0 1 1 0
0 0 1 1 0 1 1 1
1
Generator of the Alexander module
(0,0,0,-t^2,1+t,0,0,-1-t)
the Blanchfield form on it
3t^-3-5t^-2+t^-1-4+t-5t^2+3t^3
73
First homology
of the double branched cover of 12a_1131
Z/73
4 4
12a_1132
1

detected by
an unknotting move
4-16t+29t^2-33t^3+29t^4-16t^5+4t^6
Seifert matrix of 12a_1132
-2 1 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 1
0 0 -1 2 0 -1
1 -1 1 -1 1 1
0 0 0 0 0 1
1 or 2
131
First homology
of the double branched cover of 12a_1132
Z/131
2 2
12a_1133
2

detected by
the Lickorish test
4-18t+36t^2-43t^3+36t^4-18t^5+4t^6
Seifert matrix of 12a_1133
-2 1 0 0 0 0
0 -1 0 0 0 0
0 0 2 1 0 1
0 0 2 2 0 2
1 -1 -1 -1 1 -1
0 0 2 1 0 2
1 or 2
159
First homology
of the double branched cover of 12a_1133
Z/159
2 2
12a_1134
2

detected by
the signature
1-3t+5t^2-7t^3+7t^4-7t^5+7t^6-7t^7+5t^8-3t^9+t^10
Seifert matrix of 12a_1134
1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 1 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 -1 -1 0 -1 -1
-1 -1 0 0 -1 -1 -1 0 0 -1
-1 -1 0 0 0 -1 -1 0 0 0
1 0 0 0 0 0 1 0 0 0
-1 -1 0 -1 -1 -1 -1 -1 -1 -1
-1 -1 0 0 -1 -1 -1 0 -1 -1
-1 -1 0 0 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-4-3t^-3+5t^-2-7t^-1+7-7t+5t^2-3t^3+t^4
53
First homology
of the double branched cover of 12a_1134
Z/53
-4 4
12a_1135
1

detected by
an unknotting move
-2+7t-13t^2+19t^3-21t^4+19t^5-13t^6+7t^7-2t^8
Seifert matrix of 12a_1135
1 0 0 0 0 0 0 0
1 1 0 0 0 0 1 0
-1 -1 -1 -1 1 -1 -1 -1
-1 -1 0 -1 1 -1 -1 0
1 1 0 0 -2 1 1 0
-1 -1 0 0 0 -1 -1 0
1 0 0 0 0 0 1 0
-1 -1 0 -1 1 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+8t^-2-12t^-1+14-12t+8t^2-4t^3+t^4
103
First homology
of the double branched cover of 12a_1135
Z/103
-2 2
12a_1136
2

detected by
the Lickorish test
-2+8t-18t^2+29t^3-33t^4+29t^5-18t^6+8t^7-2t^8
Seifert matrix of 12a_1136
1 0 0 0 0 0 0 0
1 1 0 0 0 0 1 0
-1 -1 -1 1 1 -1 -1 1
1 1 0 -2 -2 1 1 -2
1 1 0 -1 -2 1 1 -1
-1 -1 0 0 0 -1 -1 0
1 0 0 0 0 0 1 0
1 1 0 -1 -2 1 1 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-13t^-1+17-13t+7t^2-2t^3
147
First homology
of the double branched cover of 12a_1136
Z/147
-2 2
12a_1137
1

detected by
an unknotting move
-4+16t-31t^2+39t^3-31t^4+16t^5-4t^6
Seifert matrix of 12a_1137
1 0 0 0 0 0
1 1 0 0 1 0
-1 -1 -1 1 -1 1
1 1 0 -2 1 -1
1 0 0 0 1 0
1 1 0 0 1 -2
1
Generator of the Alexander module
(0,2,0,1,0,0)
the Blanchfield form on it
13t^-2-50t^-1+70-50t+13t^2
141
First homology
of the double branched cover of 12a_1137
Z/141
0 2
12a_1138 1 or 2
3-11t+17t^2-17t^3+17t^4-11t^5+3t^6
Seifert matrix of 12a_1138
-1 -1 0 -1 0 0
0 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 -1 0 -1 0 0
-1 -1 -1 -1 1 1
0 0 0 0 0 3
1
Generator of the Alexander module
(2+2t+4t^5,-2-6t+t^2-2t^3+2t^4-6t^5-2t^6,-16+12t-7t^2+14t^3-14t^4-18t^5+14t^6,18t^2-20t^3+12t^4-4t^5+16t^6+24t^7-24t^8+8t^9+8t^10,8-12t-16t^3+10t^4+4t^5-12t^6-4t^7-4t^8,-7+5t-3t^2+6t^3-6t^4-8t^5+6t^6)
the Blanchfield form on it
x
79
First homology
of the double branched cover of 12a_1138
Z/79
-2 2
12a_1139
1

detected by
an unknotting move
6-25t+39t^2-25t^3+6t^4
Seifert matrix of 12a_1139
-2 1 0 0
0 -1 0 0
1 -1 1 1
0 0 0 3
1 or 2
101
First homology
of the double branched cover of 12a_1139
Z/101
0 0
12a_1140
1

detected by
an unknotting move
-3+11t-21t^2+27t^3-21t^4+11t^5-3t^6
Seifert matrix of 12a_1140
1 0 0 0 0 0
1 1 0 0 1 0
-1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 0
1 0 0 0 1 0
-1 -1 0 -1 -1 -3
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-10+8t-4t^2+t^3
97
First homology
of the double branched cover of 12a_1140
Z/97
0 0
12a_1141 1 or 2
-1+8t-22t^2+34t^3-37t^4+34t^5-22t^6+8t^7-t^8
Seifert matrix of 12a_1141
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
0 0 -1 0 0 0 0 0
-1 -1 1 1 -1 -1 0 0
-1 -1 0 0 -1 -1 0 0
0 -1 0 0 0 -1 0 0
-1 -1 0 0 -1 -1 1 1
-1 -1 1 0 -1 -1 0 1
1 or 2
167
First homology
of the double branched cover of 12a_1141
Z/167
-2 2
12a_1142
2

detected by
the Nakanishi index
4-14t+21t^2-21t^3+21t^4-14t^5+4t^6
Seifert matrix of 12a_1142
-1 -1 0 0 -1 0
0 -1 0 0 0 0
1 1 2 1 1 0
-1 -1 0 -1 -1 0
0 -1 0 0 -1 0
1 1 1 1 1 2
2
99
First homology
of the double branched cover of 12a_1142
Z/33+Z/3
-2 2
12a_1143
2

detected by
the Lickorish test
-2+17t-49t^2+69t^3-49t^4+17t^5-2t^6
Seifert matrix of 12a_1143
-2 1 0 0 0 0
0 -1 0 0 0 0
0 0 -1 0 0 0
1 -1 1 1 0 0
1 -1 0 0 1 1
1 -1 1 0 0 1
1 or 2
205
First homology
of the double branched cover of 12a_1143
Z/205
0 0
12a_1144
1

detected by
an unknotting move
8-32t+49t^2-32t^3+8t^4
Seifert matrix of 12a_1144
-2 1 0 0
0 -1 0 0
-1 1 2 0
-1 1 1 2
1 or 2
129
First homology
of the double branched cover of 12a_1144
Z/129
0 0
12a_1145
1

detected by
an unknotting move
-2+6t-10t^2+14t^3-15t^4+14t^5-10t^6+6t^7-2t^8
Seifert matrix of 12a_1145
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
0 0 -1 -1 0 0 -1 -1
0 0 0 -1 0 0 0 -1
1 0 0 0 1 0 0 0
1 1 -1 -1 1 -2 -1 -1
0 0 0 -1 0 0 -1 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-4-3t^-3+5t^-2-7t^-1+8-7t+5t^2-3t^3+t^4
79
First homology
of the double branched cover of 12a_1145
Z/79
-2 2
12a_1146
1

detected by
an unknotting move
-4+14t-25t^2+31t^3-25t^4+14t^5-4t^6
Seifert matrix of 12a_1146
1 0 0 0 0 0
1 1 0 0 1 0
0 0 -1 1 0 0
0 0 0 -2 0 0
1 0 0 0 1 0
1 1 -1 1 1 -2
1 or 2
117
First homology
of the double branched cover of 12a_1146
Z/117
0 2
12a_1147
1

detected by
an unknotting move
-2+7t-15t^2+24t^3-27t^4+24t^5-15t^6+7t^7-2t^8
Seifert matrix of 12a_1147
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
0 0 -1 0 0 0 0 -1
0 0 0 -1 0 0 -1 0
1 0 0 0 1 0 0 0
0 0 0 -1 0 -1 -1 0
1 1 -1 0 1 0 -2 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-2t^-3+6t^-2-10t^-1+13-10t+6t^2-2t^3
123
First homology
of the double branched cover of 12a_1147
Z/123
-2 2
12a_1148
1

detected by
an unknotting move
-3+9t-15t^2+19t^3-15t^4+9t^5-3t^6
Seifert matrix of 12a_1148
1 0 0 0 0 0
1 1 0 0 1 0
0 0 -1 0 0 -1
-1 -1 1 -3 -1 1
1 0 0 0 1 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-6+5t-3t^2+t^3
73
First homology
of the double branched cover of 12a_1148
Z/73
0 2
12a_1149
2

detected by
the Lickorish test
-4+9t-9t^2+9t^3-4t^4
Seifert matrix of 12a_1149
1 0 0 0
1 1 1 0
1 0 1 0
1 1 1 -4
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
35
First homology
of the double branched cover of 12a_1149
Z/35
2 2
12a_1150
1

detected by
an unknotting move
1-8t+23t^2-41t^3+51t^4-41t^5+23t^6-8t^7+t^8
Seifert matrix of 12a_1150
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
0 -1 -1 0 0 -1 0 0
0 0 0 -1 0 0 0 -1
1 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 -1 0 0 -1 -1
1 0 0 0 1 -1 0 -1
1
Generator of the Alexander module
(0,1+8t-7t^2,-t+48t^2-96t^3+65t^4-14t^5,-1+t+7t^3-15t^4+7t^5,1+8t-7t^2,1+t+14t^2-30t^3+14t^4,t-t^2-7t^4+15t^5-7t^6,9t-7t^2+7t^3-15t^4+7t^5)
the Blanchfield form on it
x
197
First homology
of the double branched cover of 12a_1150
Z/197
0 0
12a_1151
2

detected by
the Lickorish test
2-14t+32t^2-39t^3+32t^4-14t^5+2t^6
Seifert matrix of 12a_1151
1 0 0 0 0 0
1 1 0 0 1 0
0 -1 -1 0 0 -1
-1 0 0 -2 -1 1
1 0 0 0 1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,-2t+t^2,t-t^2,1+4t-2t^2,0,2-t)
the Blanchfield form on it
-2t^-2+6t^-1-7+6t-2t^2
135
First homology
of the double branched cover of 12a_1151
Z/135
2 2
12a_1152
2

detected by
the Nakanishi index
1-9t+34t^2-72t^3+93t^4-72t^5+34t^6-9t^7+t^8
Seifert matrix of 12a_1152
-1 -1 0 0 0 0 -1 -1
0 1 0 0 0 -1 0 1
-1 0 1 -1 0 0 0 0
-1 0 0 -1 0 0 -1 -1
0 1 0 0 1 -1 0 1
0 0 0 0 0 -1 0 0
0 -1 0 0 -1 0 -1 -1
0 0 0 0 0 0 0 1
2
325
First homology
of the double branched cover of 12a_1152
Z/65+Z/5
0 0
12a_1153
2

detected by
the signature
1-8t+20t^2-26t^3+27t^4-26t^5+20t^6-8t^7+t^8
Seifert matrix of 12a_1153
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 -1 -1 -1 -1 0
-1 0 0 -1 -1 0 -1 0
0 -1 0 0 -1 0 0 0
-1 0 0 -1 -1 -1 -1 0
-1 0 0 0 -1 0 -1 0
1 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(4t^2-8t^3-6t^4+4t^5-2t^6,2-4t-2t^2+2t^3,-2t^4,2t^3,-2t^2,0,1-2t+2t^3+2t^4-2t^6,2t^3)
the Blanchfield form on it
x
137
First homology
of the double branched cover of 12a_1153
Z/137
-4 4
12a_1154
2

detected by
the Lickorish test
2-17t+47t^2-63t^3+47t^4-17t^5+2t^6
Seifert matrix of 12a_1154
1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 1 -1 0
1 0 0 -2 1 0
0 -1 0 0 -1 0
1 -1 0 0 0 -1
1
Generator of the Alexander module
(0,4-5t+2t^2,1-8t+10t^2-4t^3,4t-5t^2+2t^3,-4t+5t^2-2t^3,0)
the Blanchfield form on it
-t^-1+5-t
195
First homology
of the double branched cover of 12a_1154
Z/195
-2 2
12a_1155
2

detected by
the signature
-5+28t-63t^2+81t^3-63t^4+28t^5-5t^6
Seifert matrix of 12a_1155
1 0 0 0 0 0
-1 -2 -1 -1 0 -2
0 0 -2 1 0 0
0 -1 0 -2 0 -1
-1 -1 0 -1 -1 -1
-1 -1 -1 -1 0 -2
1 or 2
273
First homology
of the double branched cover of 12a_1155
Z/273
-4 4
12a_1156
2

detected by
the signature
-1+8t-25t^2+43t^3-51t^4+43t^5-25t^6+8t^7-t^8
Seifert matrix of 12a_1156
1 0 0 0 0 0 0 0
1 -1 0 1 0 0 0 0
-1 0 -1 0 0 0 -1 0
0 0 0 1 0 0 0 0
1 -1 0 1 -1 0 0 0
0 -1 0 1 -1 -1 0 0
-1 0 0 -1 0 0 -1 0
0 -1 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,-3+t,0,-2+t,0,0)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
205
First homology
of the double branched cover of 12a_1156
Z/205
-4 4
12a_1157
3

detected by
the signature
-2+5t-5t^2+5t^3-5t^4+5t^5-5t^6+5t^7-2t^8
Seifert matrix of 12a_1157
-1 -1 -1 -1 1 -1 -1 -1
0 -1 -1 -1 1 0 -1 -1
0 0 -1 -1 1 0 0 -1
0 0 0 -1 1 0 0 0
0 0 0 0 2 0 0 0
0 -1 -1 -1 1 -1 -1 -1
0 0 -1 -1 1 0 -1 -1
0 0 0 -1 1 0 0 -1
1
Generator of the Alexander module
(2t,0,0,1,0,0,0,0)
the Blanchfield form on it
-5t^-3+14t^-2-10t^-1+10-10t+14t^2-5t^3
39
First homology
of the double branched cover of 12a_1157
Z/39
-6 6
12a_1158
2

detected by
the signature
-4+12t-15t^2+15t^3-15t^4+12t^5-4t^6
Seifert matrix of 12a_1158
-1 -1 1 -1 1 -1
0 -1 1 -1 1 0
0 0 -2 1 -1 0
0 0 0 -1 1 0
0 0 0 0 2 0
0 -1 1 -1 1 -1
1 or 2
77
First homology
of the double branched cover of 12a_1158
Z/77
-4 4
12a_1159
2

detected by
the signature
-4+14t-24t^2+29t^3-24t^4+14t^5-4t^6
Seifert matrix of 12a_1159
-1 1 1 -1 1 1
0 -2 -2 1 -1 -2
0 -1 -2 1 -1 -1
0 0 0 -1 1 0
0 0 0 0 2 0
0 -1 -2 1 -1 -2
1 or 2
113
First homology
of the double branched cover of 12a_1159
Z/113
-4 4
12a_1160
1

detected by
an unknotting move
-8+28t-39t^2+28t^3-8t^4
Seifert matrix of 12a_1160
-1 1 1 1
0 -2 -1 -1
0 0 2 0
0 0 -1 -2
1
Generator of the Alexander module
(-1-t,0,-1,1)
the Blanchfield form on it
4
111
First homology
of the double branched cover of 12a_1160
Z/111
-2 2
12a_1161
2

detected by
the Lickorish test
-6+19t-25t^2+19t^3-6t^4
Seifert matrix of 12a_1161
-1 -1 1 -1
0 -1 1 0
0 0 2 0
0 -1 1 -3
1 or 2
75
First homology
of the double branched cover of 12a_1161
Z/75
-2 2
12a_1162
2

detected by
the signature
-4+11t-13t^2+13t^3-13t^4+11t^5-4t^6
Seifert matrix of 12a_1162
-1 -1 0 0 -1 -1
0 -1 0 0 0 -1
0 0 2 0 0 0
-1 -1 -1 -2 -1 -1
0 -1 0 0 -1 -1
0 0 0 0 0 -1
1 or 2
69
First homology
of the double branched cover of 12a_1162
Z/69
-4 4
12a_1163
1

detected by
an unknotting move
-8+26t-35t^2+26t^3-8t^4
Seifert matrix of 12a_1163
-1 1 0 0
0 -2 0 0
0 0 2 0
-1 1 -1 -2
1 or 2
103
First homology
of the double branched cover of 12a_1163
Z/103
-2 2
12a_1164
2

detected by
the signature
-4+13t-22t^2+27t^3-22t^4+13t^5-4t^6
Seifert matrix of 12a_1164
-1 0 0 0 0 -1
0 -1 0 0 -1 0
0 0 2 0 0 0
0 -1 0 -1 -1 0
-1 0 -1 0 -2 -1
0 0 0 0 0 -1
2
105
First homology
of the double branched cover of 12a_1164
Z/105
-4 4
12a_1165
1

detected by
an unknotting move
-6+17t-21t^2+17t^3-6t^4
Seifert matrix of 12a_1165
-1 0 0 -1
1 -3 1 1
0 0 2 0
0 0 0 -1
1 or 2
67
First homology
of the double branched cover of 12a_1165
Z/67
-2 2
12a_1166
1

detected by
an unknotting move
-8+17t-8t^2
Seifert matrix of 12a_1166
2 0
-1 -4
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
2t^-1-4+2t
33
First homology
of the double branched cover of 12a_1166
Z/33
0 0
12a_1167
2

detected by
A(F_2)
1-10t+35t^2-68t^3+85t^4-68t^5+35t^6-10t^7+t^8
Seifert matrix of 12a_1167
1 0 -1 0 0 0 0 -1
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 0
1 0 -1 1 0 -1 0 -1
0 -1 -1 0 1 -1 0 -1
0 -1 0 0 0 -1 0 0
1 -1 -1 1 0 -1 1 -1
0 0 0 0 0 0 0 -1
2
313
First homology
of the double branched cover of 12a_1167
Z/313
0 0
12a_1168
2

detected by
the Lickorish test
-1+4t-10t^2+19t^3-28t^4+31t^5-28t^6+19t^7-10t^8+4t^9-t^10
Seifert matrix of 12a_1168
-1 -1 0 -1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 0 1 0 0 0 -1 1 0 0
0 -1 0 -1 0 0 0 0 0 0
-1 -1 1 -1 1 0 -1 1 1 0
-1 -1 1 -1 1 1 -1 1 1 1
-1 -1 0 -1 0 0 -1 0 0 0
-1 0 0 0 0 0 -1 1 0 0
-1 0 1 0 0 0 -1 1 1 0
-1 -1 1 -1 1 0 -1 1 1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-14t^-1+17-14t+9t^2-4t^3+t^4
155
First homology
of the double branched cover of 12a_1168
Z/155
2 2
12a_1169
1

detected by
an unknotting move
2-8t+17t^2-26t^3+31t^4-26t^5+17t^6-8t^7+2t^8
Seifert matrix of 12a_1169
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
1 0 2 0 0 0 1 0
0 -1 0 -1 0 0 0 0
-1 -1 -1 -1 1 0 -1 0
-1 -1 -1 -1 1 1 -1 1
-1 -1 0 -1 0 0 -1 0
-1 -1 -1 -1 1 0 -1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,2)
the Blanchfield form on it
9t^-4-46t^-3+116t^-2-184t^-1+210-184t+116t^2-46t^3+9t^4
137
First homology
of the double branched cover of 12a_1169
Z/137
0 0
12a_1170
1

detected by
an unknotting move
2-8t+18t^2-30t^3+37t^4-30t^5+18t^6-8t^7+2t^8
Seifert matrix of 12a_1170
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
-1 0 1 0 -1 1 0 0
0 -1 0 -1 0 0 0 0
-1 -1 0 -1 -1 0 0 0
-1 0 0 0 -1 1 0 0
-1 0 1 0 -1 1 1 0
1 1 -1 1 1 -1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-15t^-1+18-15t+9t^2-4t^3+t^4
153
First homology
of the double branched cover of 12a_1170
Z/153
0 0
12a_1171
2

detected by
the Lickorish test
4-15t+25t^2-27t^3+25t^4-15t^5+4t^6
Seifert matrix of 12a_1171
-1 -1 0 -1 0 0
0 -1 0 0 0 0
1 0 2 0 1 0
0 -1 0 -1 0 0
-1 -1 0 -1 -1 0
1 1 1 1 1 2
1 or 2
115
First homology
of the double branched cover of 12a_1171
Z/115
-2 2
12a_1172
2

detected by
the Lickorish test
2-10t+26t^2-45t^3+55t^4-45t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_1172
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
1 0 2 0 1 0 1 1
0 -1 0 -1 0 0 0 0
0 -1 0 -1 1 0 0 0
-1 -1 -1 -1 0 1 -1 0
-1 -1 0 -1 0 0 -1 0
0 -1 0 -1 1 0 0 1
1
Generator of the Alexander module
(0,-1-2t+t^3,-2-2t-2t^3+2t^4,-2-t+t^3,1+2t-t^3,1+2t-t^3,0,1+t-t^2)
the Blanchfield form on it
2t^-3-8t^-2+16t^-1-21+16t-8t^2+2t^3
221
First homology
of the double branched cover of 12a_1172
Z/221
0 0
12a_1173
1

detected by
an unknotting move
3-21t+55t^2-73t^3+55t^4-21t^5+3t^6
Seifert matrix of 12a_1173
1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 1 -1 1
1 0 0 -2 1 -1
0 -1 0 0 -1 0
0 1 0 -1 1 -2
1
Generator of the Alexander module
(0,-t,1-t-3t^2+5t^3-2t^4,-3t+4t^2+6t^3-10t^4+4t^5,0,-t+2t^2+t^3-4t^4+2t^5)
the Blanchfield form on it
t^-2-6t^-1+11-6t+t^2
231
First homology
of the double branched cover of 12a_1173
Z/231
-2 2
12a_1174
2

detected by
the Lickorish test
2-8t+18t^2-28t^3+33t^4-28t^5+18t^6-8t^7+2t^8
Seifert matrix of 12a_1174
-1 -1 0 -1 0 0 0 -1
0 -1 0 0 0 0 0 -1
0 -1 1 -1 1 1 1 -1
0 -1 0 -1 0 0 0 -1
0 -1 0 -1 1 0 0 0
0 -1 0 -1 1 1 1 0
0 -1 0 -1 1 0 1 0
0 0 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,1+t,1,t^3,0,0,0)
the Blanchfield form on it
-2t^-3+8t^-2-16t^-1+20-16t+8t^2-2t^3
145
First homology
of the double branched cover of 12a_1174
Z/145
0 0
12a_1175
1

detected by
an unknotting move
-2+10t-26t^2+46t^3-55t^4+46t^5-26t^6+10t^7-2t^8
Seifert matrix of 12a_1175
-1 -1 0 -1 0 -1 0 -1
0 -1 0 0 0 -1 0 -1
0 -1 1 -1 1 -1 1 0
0 -1 0 -1 0 -1 0 -1
0 -1 0 -1 1 0 0 0
0 0 0 0 0 -2 0 -2
0 -1 0 -1 1 0 1 0
0 0 0 0 0 -1 0 -2
1
Generator of the Alexander module
(2t-4t^2+2t^3+2t^5-6t^6+6t^7-2t^8,0,-2t+4t^2-4t^3+6t^5-8t^6+6t^7-2t^8,2t^2-4t^3+4t^4-2t^5,2t-2t^2-2t^3+6t^4-6t^5+2t^6,2t-2t^2-2t^3+6t^4-6t^5+2t^6,0,1+4t-6t^2+4t^3-2t^4+2t^5-4t^6+2t^7)
the Blanchfield form on it
x
223
First homology
of the double branched cover of 12a_1175
Z/223
-2 2
12a_1176
1

detected by
an unknotting move
-1+4t-9t^2+15t^3-20t^4+21t^5-20t^6+15t^7-9t^8+4t^9-t^10
Seifert matrix of 12a_1176
-1 -1 0 0 -1 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 0 1 0 0 0 -1 1 0 0
-1 0 1 1 0 0 -1 1 1 0
0 -1 0 0 -1 0 0 0 0 0
-1 -1 1 1 -1 1 -1 1 1 1
-1 -1 0 0 -1 0 -1 0 0 0
-1 0 0 0 0 0 -1 1 0 0
-1 0 1 0 0 0 -1 1 1 0
-1 0 1 1 0 0 -1 1 1 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0,0,0)
the Blanchfield form on it
1
119
First homology
of the double branched cover of 12a_1176
Z/119
2 2
12a_1177
1

detected by
an unknotting move
2-9t+22t^2-38t^3+47t^4-38t^5+22t^6-9t^7+2t^8
Seifert matrix of 12a_1177
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 0 1 0 0 0 -1 1
1 0 -1 2 0 0 1 -1
0 -1 0 0 -1 0 0 0
-1 -1 1 -1 -1 1 -1 1
-1 -1 0 0 -1 0 -1 0
-1 0 0 0 0 0 -1 1
1
Generator of the Alexander module
(0,-2+5t-5t^2+2t^3,8t-22t^2+25t^3-13t^4+2t^5,-4+10t-8t^2-t^3+5t^4-2t^5,-4+8t-14t^2+18t^3-18t^4+11t^5-2t^6,1+t-3t^3+2t^4,2-t-5t^2+8t^3-4t^4,4t-26t^2+62t^3-66t^4+62t^5-58t^6+14t^7+44t^8-44t^9+8t^10)
the Blanchfield form on it
x
189
First homology
of the double branched cover of 12a_1177
Z/189
0 0
12a_1178
1

detected by
an unknotting move
2-9t+20t^2-31t^3+37t^4-31t^5+20t^6-9t^7+2t^8
Seifert matrix of 12a_1178
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
1 0 2 1 0 0 1 1
1 0 2 2 0 0 1 2
0 -1 0 0 -1 0 0 0
-1 -1 -1 -1 -1 1 -1 -1
-1 -1 0 0 -1 0 -1 0
1 0 2 1 0 0 1 2
1 or 2
161
First homology
of the double branched cover of 12a_1178
Z/161
0 0
12a_1179
2

detected by
the Lickorish test
3-12t+20t^2-21t^3+20t^4-12t^5+3t^6
Seifert matrix of 12a_1179
-1 -1 -1 0 0 0
0 -1 0 0 0 0
0 -1 -1 0 0 0
-1 -1 -1 1 -1 1
-1 -1 -1 0 -1 0
-1 0 0 0 -1 3
1
Generator of the Alexander module
(0,-4t-6t^2-24t^3-18t^4-36t^5,-2-4t-12t^2-24t^3-18t^4-36t^5,2+12t^2+18t^4,-1-2t-7t^2-12t^3-12t^4-18t^5,-2-4t-4t^2-21t^3+42t^4-36t^5+108t^6)
the Blanchfield form on it
x
91
First homology
of the double branched cover of 12a_1179
Z/91
-2 2
12a_1180
2

detected by
the Lickorish test
2-8t+19t^2-33t^3+41t^4-33t^5+19t^6-8t^7+2t^8
Seifert matrix of 12a_1180
-1 -1 0 0 -1 0 0 -1
0 -1 0 0 0 0 0 -1
0 -1 1 1 -1 1 1 -1
0 0 0 1 0 0 0 0
0 -1 0 0 -1 0 0 -1
0 -1 0 1 -1 1 1 0
0 0 0 1 0 0 1 0
0 0 0 0 0 0 0 -2
1 or 2
165
First homology
of the double branched cover of 12a_1180
Z/165
0 0
12a_1181
2

detected by
the Nakanishi index
4-16t+30t^2-35t^3+30t^4-16t^5+4t^6
Seifert matrix of 12a_1181
-1 -1 0 -1 0 -1
0 -1 0 0 0 -1
0 0 1 0 0 -1
0 -1 0 -1 0 -1
0 1 1 1 2 0
0 0 0 0 0 -2
2
135
First homology
of the double branched cover of 12a_1181
Z/45+Z/3
-2 2
12a_1182
1

detected by
an unknotting move
-2+9t-22t^2+38t^3-45t^4+38t^5-22t^6+9t^7-2t^8
Seifert matrix of 12a_1182
-1 -1 0 0 -1 -1 0 -1
0 -1 0 0 0 -1 0 -1
0 -1 1 0 -1 -1 0 0
0 -1 1 1 -1 -1 1 0
0 -1 0 0 -1 -1 0 -1
0 0 0 0 0 -2 0 -2
0 -1 1 0 -1 -1 1 0
0 0 0 0 0 -1 0 -2
1
Generator of the Alexander module
(0,0,1+t+t^2-7t^4+14t^5-10t^6+4t^7,0,1+t-t^2+4t^3-6t^4+4t^5,0,0,1+t-t^2+4t^3-6t^4+4t^5)
the Blanchfield form on it
x
187
First homology
of the double branched cover of 12a_1182
Z/187
-2 2
12a_1183
2

detected by
the Nakanishi index
-4+15t-26t^2+31t^3-26t^4+15t^5-4t^6
Seifert matrix of 12a_1183
-1 -1 -1 -1 0 -1
0 -1 0 -1 0 -1
0 -1 -1 -1 0 -1
0 0 0 -2 0 -2
0 1 1 1 2 0
0 0 0 -1 0 -2
2
121
First homology
of the double branched cover of 12a_1183
Z/11+Z/11
-4 4
12a_1184
2

detected by
the signature
-2+10t-24t^2+34t^3-37t^4+34t^5-24t^6+10t^7-2t^8
Seifert matrix of 12a_1184
-1 -1 -1 0 0 -1 0 0
0 1 1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 -1 -1 0 0 -1
0 -1 0 0 -1 0 0 0
0 0 0 1 1 -2 1 1
0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 -1
1 or 2
177
First homology
of the double branched cover of 12a_1184
Z/177
-4 4
12a_1185
2

detected by
the Lickorish test
4-22t+55t^2-73t^3+55t^4-22t^5+4t^6
Seifert matrix of 12a_1185
-1 -1 -1 0 0 -1
0 1 1 0 0 0
0 0 1 0 0 0
0 1 0 -2 1 0
0 -1 0 0 -1 0
0 0 0 -1 1 -2
1 or 2
235
First homology
of the double branched cover of 12a_1185
Z/235
-2 2
12a_1186
2

detected by
the signature
-2+11t-30t^2+50t^3-59t^4+50t^5-30t^6+11t^7-2t^8
Seifert matrix of 12a_1186
-1 -1 -1 -1 0 -1 -1 0
0 1 1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 -1 0 0 -1 0
0 -1 0 0 -1 0 0 0
0 -1 0 -1 0 -1 -1 0
0 0 0 0 1 0 -2 1
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(-8+12t+18t^2-73t^3+101t^4-81t^5+33t^6+20t^7-40t^8+19t^9-10t^10+5t^11+4t^12-2t^13,0,-9+5t+35t^2-53t^3+32t^4-15t^5-24t^6+43t^7-15t^8+8t^9-5t^10-4t^11+2t^12,9+7t-37t^2+15t^3+26t^4-40t^5+44t^6-22t^7+6t^8-3t^9-4t^10+2t^11,7-10t-29t^2+59t^3-47t^4+39t^5+6t^6-63t^7+56t^8-48t^9+25t^10-2t^11+t^12+4t^13-2t^14
the Blanchfield form on it
x
245
First homology
of the double branched cover of 12a_1186
Z/245
-4 4
12a_1187
1

detected by
an unknotting move
-2+12t-35t^2+64t^3-77t^4+64t^5-35t^6+12t^7-2t^8
Seifert matrix of 12a_1187
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 -1 0
0 0 1 0 0 0 -1 0
-1 -1 0 1 1 -1 -1 0
0 0 0 0 1 0 0 0
0 1 1 0 -1 2 0 1
-1 0 0 0 0 0 -1 0
-1 0 1 0 0 0 -1 1
1
Generator of the Alexander module
(0,1+2t,0,4t,-2,1-2t,0,0)
the Blanchfield form on it
2t^-3-9t^-2+19t^-1-25+19t-9t^2+2t^3
303
First homology
of the double branched cover of 12a_1187
Z/303
2 2
12a_1188
1

detected by
an unknotting move
1-9t+36t^2-79t^3+103t^4-79t^5+36t^6-9t^7+t^8
Seifert matrix of 12a_1188
1 0 0 0 0 0 0 0
1 -1 0 0 0 0 1 1
-1 0 -1 0 0 -1 0 -1
0 0 0 1 0 0 0 0
1 -1 0 0 -1 0 1 0
-1 0 0 -1 0 -1 -1 -1
0 0 0 1 0 0 1 0
1 0 0 0 0 0 0 1
1
Generator of the Alexander module
(2t,t,2,2t^2,1,1,0,0)
the Blanchfield form on it
-62t^-3+364t^-2-883t^-1+1167-883t+364t^2-62t^3
353
First homology
of the double branched cover of 12a_1188
Z/353
0 0
12a_1189
2

detected by
the Lickorish test
4-24t+63t^2-85t^3+63t^4-24t^5+4t^6
Seifert matrix of 12a_1189
1 0 0 0 0 0
0 -1 0 1 -1 0
-1 0 -1 -1 0 1
1 0 0 1 0 0
-1 0 0 0 -2 1
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,-1+2t,-2+3t-2t^2,0,-2t+4t^2,0)
the Blanchfield form on it
2t^-2-9t^-1+16-9t+2t^2
267
First homology
of the double branched cover of 12a_1189
Z/267
-2 2
12a_1190
1

detected by
an unknotting move
-1+9t-31t^2+61t^3-75t^4+61t^5-31t^6+9t^7-t^8
Seifert matrix of 12a_1190
1 0 0 0 0 0 0 0
1 -1 0 0 0 0 1 1
-1 0 -1 -1 0 -1 0 -1
-1 0 0 -1 0 0 -1 -1
1 -1 0 0 -1 0 1 0
-1 0 0 -1 0 -1 0 -1
0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 1
1
Generator of the Alexander module
(-t,-2t,-6+7t-6t^2,-3+2t-3t^2+t^3,t,-3+3t-3t^2+t^3,1,3-3t+3t^2-t^3)
the Blanchfield form on it
252t^-3-1053t^-2+2215t^-1-2751+2215t-1053t^2+252t^3
279
First homology
of the double branched cover of 12a_1190
Z/279
-2 2
12a_1191
2

detected by
the signature
-1+5t-12t^2+20t^3-25t^4+27t^5-25t^6+20t^7-12t^8+5t^9-t^10
Seifert matrix of 12a_1191
1 0 -1 0 0 0 1 0 0 0
0 -1 0 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 -1 0 0
1 0 -1 1 0 0 1 -1 0 0
1 -1 -1 1 1 0 1 -1 1 0
1 -1 -1 1 1 1 1 -1 1 1
0 0 0 0 0 0 1 0 0 0
0 -1 0 0 0 0 0 -1 0 0
1 -1 -1 1 0 0 1 -1 1 0
1 -1 -1 1 1 0 1 -1 1 1
1
Generator of the Alexander module
(0,1,0,-t,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-5t^-3+12t^-2-19t^-1+21-19t+12t^2-5t^3+t^4
153
First homology
of the double branched cover of 12a_1191
Z/153
4 4
12a_1192
1

detected by
an unknotting move
-2+11t-28t^2+46t^3-53t^4+46t^5-28t^6+11t^7-2t^8
Seifert matrix of 12a_1192
1 0 -1 0 0 0 1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 -1
1 0 -1 1 0 0 1 -1
-1 1 1 -1 2 0 -1 1
1 -1 -1 1 -1 1 1 -1
0 0 0 0 0 0 1 0
0 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-4+6t^-3-16t^-2+27t^-1-32+27t-16t^2+6t^3-t^4
227
First homology
of the double branched cover of 12a_1192
Z/227
2 2
12a_1193
2

detected by
the Lickorish test
-2+13t-38t^2+68t^3-81t^4+68t^5-38t^6+13t^7-2t^8
Seifert matrix of 12a_1193
1 0 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
1 0 2 0 1 0 0 1
0 -1 0 -1 0 0 -1 0
1 0 0 -1 1 0 -1 0
0 -1 -1 -1 0 1 -1 0
0 -1 0 0 0 0 -1 0
1 -1 0 -1 1 0 -1 1
1
Generator of the Alexander module
(0,3,6-6t^2,-3t,1,-5+3t^2,3,0)
the Blanchfield form on it
2t^-3-9t^-2+17t^-1-22+17t-9t^2+2t^3
323
First homology
of the double branched cover of 12a_1193
Z/323
2 2
12a_1194
3

detected by
the new u==2 criterion
-2+10t-23t^2+34t^3-37t^4+34t^5-23t^6+10t^7-2t^8
Seifert matrix of 12a_1194
-1 0 0 0 0 0 0 -1
-1 1 1 1 0 -1 1 -1
0 0 1 0 0 -1 0 0
-1 0 1 1 0 -1 1 0
-1 1 1 1 1 -1 1 -1
-1 0 0 0 0 -1 0 -1
-1 0 1 0 0 -1 1 0
0 0 0 0 0 0 0 -2
2
175
First homology
of the double branched cover of 12a_1194
Z/35+Z/5
2 2
12a_1195
1

detected by
an unknotting move
-1+9t-29t^2+51t^3-59t^4+51t^5-29t^6+9t^7-t^8
Seifert matrix of 12a_1195
1 0 0 0 0 0 0 0
1 -1 0 0 0 1 0 1
-1 0 -1 0 0 -1 0 -1
0 -1 0 -1 -1 1 -1 0
1 -1 0 0 -1 1 0 0
0 0 0 0 0 1 0 0
0 -1 0 0 -1 1 -1 0
1 0 0 0 0 0 0 1
1 or 2
239
First homology
of the double branched cover of 12a_1195
Z/239
-2 2
12a_1196
1

detected by
an unknotting move
2-13t+36t^2-61t^3+73t^4-61t^5+36t^6-13t^7+2t^8
Seifert matrix of 12a_1196
-1 0 0 -1 0 0 0 -1
-1 1 1 -1 0 -1 1 0
0 0 1 0 0 -1 0 0
0 0 0 -2 0 0 0 -2
-1 1 1 -1 1 -1 1 -1
-1 0 0 -1 0 -1 0 -1
-1 0 1 0 0 -1 1 0
0 0 0 -1 0 0 0 -2
1
Generator of the Alexander module
(0,5-t+7t^2-4t^3+5t^4+50t^5-87t^6+16t^7+19t^8-6t^9,-2-3t+6t^2-13t^3+9t^4+33t^5-30t^6-7t^7+6t^8,-3t+t^2-5t^3+2t^4+28t^6+t^7-6t^8,2-7t+14t^2-9t^3+29t^4+8t^5-65t^6+26t^7+13t^8-6t^9,3-4t+10t^2-9t^3+13t^4-26t^5-4t^6+6t^7,3-5t+9t^2-7t^3+6t^4+33t^5-58t^6-8t^7+12t^8,-t-3t^2-4t^3-15t^4+29t^5+4t^6-6t^7)
the Blanchfield form on it
x
297
First homology
of the double branched cover of 12a_1196
Z/297
0 2
12a_1197
1

detected by
an unknotting move
2-11t+29t^2-48t^3+57t^4-48t^5+29t^6-11t^7+2t^8
Seifert matrix of 12a_1197
1 0 0 0 0 0 0 0
1 -1 0 0 1 1 1 -1
-1 0 -1 0 -1 -1 -1 1
1 -1 0 -1 0 0 0 -1
1 0 0 0 1 1 0 0
1 0 0 0 0 1 0 0
1 0 0 0 1 1 1 0
1 0 0 0 1 1 1 -2
1
Generator of the Alexander module
(0,5-8t+4t^2,-3t+6t^2-4t^3,2-2t,0,0,0,10t-16t^2+8t^3)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-9+8t-4t^2+t^3
237
First homology
of the double branched cover of 12a_1197
Z/237
0 2
12a_1198
1

detected by
an unknotting move
4-22t+52t^2-67t^3+52t^4-22t^5+4t^6
Seifert matrix of 12a_1198
1 0 0 0 0 0
1 -1 0 0 -1 -1
-1 0 -1 0 1 1
1 -1 0 -1 0 -1
-1 0 0 0 2 0
1 0 0 0 -1 -2
1
Generator of the Alexander module
(0,0,2t-2t^2,2-2t,0,5-8t+4t^2)
the Blanchfield form on it
2t^-2-8t^-1+13-8t+2t^2
223
First homology
of the double branched cover of 12a_1198
Z/223
-2 2
12a_1199
1

detected by
an unknotting move
-1+5t-13t^2+23t^3-32t^4+37t^5-32t^6+23t^7-13t^8+5t^9-t^10
Seifert matrix of 12a_1199
1 0 -1 0 0 0 1 0 0 0
0 -1 0 0 0 0 0 0 0 0
0 -1 -1 -1 0 0 0 -1 -1 0
0 -1 0 -1 0 0 0 0 -1 0
1 0 -1 -1 1 0 1 -1 -1 0
1 -1 -1 -1 1 1 1 -1 -1 1
0 0 0 0 0 0 1 0 0 0
0 -1 0 -1 0 0 0 -1 -1 0
0 -1 0 0 0 0 0 0 -1 0
1 -1 -1 -1 1 0 1 -1 -1 1
1
Generator of the Alexander module
(0,0,1-t,0,1,1-t,0,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-14t^-1+15-14t+9t^2-4t^3+t^4
185
First homology
of the double branched cover of 12a_1199
Z/185
0 0
12a_1200
2

detected by
the Lickorish test
-2+10t-25t^2+39t^3-43t^4+39t^5-25t^6+10t^7-2t^8
Seifert matrix of 12a_1200
1 0 -1 0 0 0 1 0
0 -1 0 0 0 0 0 0
0 -1 -1 1 0 0 0 0
0 1 0 -2 0 0 0 0
1 0 -1 1 1 0 1 0
1 -1 -1 1 1 1 1 1
0 0 0 0 0 0 1 0
1 -1 -1 1 1 0 1 1
1
Generator of the Alexander module
(0,-t^2+t^3,1,0,-t+t^3-t^4,t^2-t^3,0,t^3-t^4)
the Blanchfield form on it
4t^-3-22t^-2+54t^-1-73+54t-22t^2+4t^3
195
First homology
of the double branched cover of 12a_1200
Z/195
2 2
12a_1201
1

detected by
an unknotting move
2-10t+26t^2-43t^3+51t^4-43t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_1201
1 0 0 0 0 0 0 0
0 -1 0 1 0 1 1 -1
-1 0 -1 -1 -1 -1 -1 1
1 0 0 1 0 1 0 0
-1 0 0 -1 -1 -1 -1 1
1 0 0 0 0 1 0 0
1 0 0 1 0 1 1 0
0 0 0 1 0 1 1 -2
1
Generator of the Alexander module
(0,2t-2t^3,6t^4,-2t+2t^2-2t^3,1+4t^2-10t^3+12t^4-2t^5+2t^6,-2t-2t^3,-2t^3,-2t^4)
the Blanchfield form on it
x
213
First homology
of the double branched cover of 12a_1201
Z/213
0 2
12a_1202
2

detected by
the Nakanishi index
9-42t+67t^2-42t^3+9t^4
Seifert matrix of 12a_1202
2 0 1 0
-1 -2 0 -1
1 0 2 0
-1 -1 -1 -2
2
169
First homology
of the double branched cover of 12a_1202
Z/13+Z/13
0 0
12a_1203
2

detected by
the Lickorish test
1-4t+10t^2-18t^3+25t^4-27t^5+25t^6-18t^7+10t^8-4t^9+t^10
Seifert matrix of 12a_1203
-1 -1 0 -1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
0 0 1 0 0 0 1 0 0 0
0 -1 0 -1 0 0 0 0 0 0
-1 -1 1 -1 1 0 1 -1 1 0
-1 -1 1 -1 1 1 1 -1 1 1
0 0 0 0 0 0 1 0 0 0
-1 -1 0 -1 0 0 0 -1 0 0
-1 0 1 0 0 0 1 -1 1 0
-1 -1 1 -1 1 0 1 -1 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-4+4t^-3-9t^-2+14t^-1-17+14t-9t^2+4t^3-t^4
143
First homology
of the double branched cover of 12a_1203
Z/143
2 2
12a_1204
1

detected by
an unknotting move
2-8t+18t^2-29t^3+35t^4-29t^5+18t^6-8t^7+2t^8
Seifert matrix of 12a_1204
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 1 0 0 0
0 -1 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
-1 -1 0 -1 0 -1 0 0
-1 0 1 0 1 -1 1 0
1 1 -1 1 -1 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-15t^-1+18-15t+9t^2-4t^3+t^4
149
First homology
of the double branched cover of 12a_1204
Z/149
0 0
12a_1205
2

detected by
4-15t+26t^2-29t^3+26t^4-15t^5+4t^6
Seifert matrix of 12a_1205
-1 -1 0 -1 0 0
0 -1 0 0 0 0
1 0 2 0 1 -1
0 -1 0 -1 0 0
-1 -1 0 -1 -1 0
0 1 0 1 0 2
2
119
First homology
of the double branched cover of 12a_1205
Z/119
-2 2
12a_1206
2

detected by
the Nakanishi index
-4+24t-57t^2+75t^3-57t^4+24t^5-4t^6
Seifert matrix of 12a_1206
-1 0 0 -1 0 -1
-1 1 -1 -1 0 0
0 0 -1 0 -1 0
0 0 0 -2 0 -2
1 0 0 1 -2 1
0 0 0 -1 0 -2
2
245
First homology
of the double branched cover of 12a_1206
Z/35+Z/7
-4 4
12a_1207
2

detected by
the signature
-2+11t-28t^2+42t^3-47t^4+42t^5-28t^6+11t^7-2t^8
Seifert matrix of 12a_1207
-1 -1 -1 -1 -1 0 -1 -1
0 1 1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 -1 -1 0 0 -1
0 0 0 0 -2 1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(-t,0,0,0,1-t,-2+t,0,0)
the Blanchfield form on it
-2t^-3+7t^-2-11t^-1+12-11t+7t^2-2t^3
213
First homology
of the double branched cover of 12a_1207
Z/213
-4 4
12a_1208
2

detected by
the Lickorish test
4-23t+58t^2-77t^3+58t^4-23t^5+4t^6
Seifert matrix of 12a_1208
-1 -1 -1 1 -1 0
0 1 1 0 0 0
0 0 1 0 0 0
0 1 0 -2 1 0
0 0 0 0 -2 1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-3+12t^-2-31t^-1+42-31t+12t^2-2t^3
247
First homology
of the double branched cover of 12a_1208
Z/247
-2 2
12a_1209
1

detected by
an unknotting move
1-5t+12t^2-22t^3+32t^4-37t^5+32t^6-22t^7+12t^8-5t^9+t^10
Seifert matrix of 12a_1209
-1 0 -1 0 -1 0 0 -1 0 0
0 1 0 0 0 0 0 -1 0 0
0 0 -1 0 0 0 0 0 0 0
-1 0 -1 -1 -1 0 0 -1 0 0
0 0 -1 0 -1 0 0 0 0 0
0 1 -1 0 -1 1 0 -1 1 0
0 1 -1 0 -1 1 1 -1 1 1
0 0 -1 0 -1 0 0 -1 0 0
0 1 0 0 -1 0 0 -1 1 0
0 1 -1 0 -1 1 0 -1 1 1
1
Generator of the Alexander module
(0,-t^3+t^4-2t^5+t^6,-4-2t^2+t^3+t^4-2t^5+t^6,-2-t^2+t^4-2t^5+t^6,1-t+2t^2-t^4+2t^5-t^6,0,-2-2t^2+t^3-2t^5+3t^6-t^7,-1-t^2+2t^5-t^6,-t^2+t^3-2t^4+t^5,-2+t-3t^2-2t^3+2t^4-3t^5+t^7)
the Blanchfield form on it
x
181
First homology
of the double branched cover of 12a_1209
Z/181
0 0
12a_1210
2

detected by
the signature
-1+5t-12t^2+21t^3-28t^4+31t^5-28t^6+21t^7-12t^8+5t^9-t^10
Seifert matrix of 12a_1210
1 0 0 0 0 0 0 -1 0 0
1 1 0 1 0 0 0 -1 0 0
0 0 -1 0 0 0 0 0 0 0
1 0 0 1 0 0 0 -1 0 0
0 0 -1 0 -1 0 0 0 0 0
1 1 -1 1 -1 1 0 -1 1 0
1 1 -1 1 -1 1 1 -1 1 1
0 0 -1 0 -1 0 0 -1 0 0
1 1 0 1 -1 0 0 -1 1 0
1 1 -1 1 -1 1 0 -1 1 1
1
Generator of the Alexander module
(0,0,0,-t,1,2+t^2-t^3-t^4,0,-t,0,0)
the Blanchfield form on it
x
165
First homology
of the double branched cover of 12a_1210
Z/165
4 4
12a_1211
2

detected by
the Lickorish test
1-6t+17t^2-33t^3+48t^4-55t^5+48t^6-33t^7+17t^8-6t^9+t^10
Seifert matrix of 12a_1211
1 0 0 0 0 0 0 -1 0 0
0 -1 -1 0 0 -1 0 0 0 0
0 0 -1 0 0 0 0 0 0 0
0 -1 -1 -1 0 -1 0 0 0 0
1 -1 0 -1 1 0 0 -1 1 0
0 0 -1 0 0 -1 0 0 0 0
1 -1 -1 -1 1 -1 1 -1 1 1
0 -1 -1 -1 0 -1 0 -1 0 0
1 0 0 -1 0 0 0 -1 1 0
1 -1 0 -1 1 0 0 -1 1 1
1
Generator of the Alexander module
(0,0,0,0,2t-t^2,0,-1,1,-t+2t^2-t^3,0)
the Blanchfield form on it
-t^-4+5t^-3-12t^-2+20t^-1-22+20t-12t^2+5t^3-t^4
265
First homology
of the double branched cover of 12a_1211
Z/265
0 0
12a_1212
1

detected by
an unknotting move
-1+6t-16t^2+29t^3-41t^4+45t^5-41t^6+29t^7-16t^8+6t^9-t^10
Seifert matrix of 12a_1212
1 0 0 0 0 0 0 0 0 0
0 -1 -1 0 0 -1 -1 0 -1 -1
1 0 1 0 1 0 0 0 1 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 0 0
0 0 -1 0 0 -1 -1 0 0 -1
0 0 -1 0 0 0 -1 0 0 0
0 -1 -1 0 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 1 0
0 0 -1 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,3-5t+5t^2-2t^3,1+5t-5t^2+2t^3,-6t-2t^2+7t^3-2t^4,-1-2t+3t^2-2t^3,4-3t^2+8t^3-7t^4+2t^5,3-2t,3-5t+2t^2,3-2t+6t^2-7t^3+2t^4,3-2t-t^2-2t^3+3t^4-2t^5)
the Blanchfield form on it
x
231
First homology
of the double branched cover of 12a_1212
Z/231
-2 2
12a_1213
1

detected by
an unknotting move
2-12t+31t^2-51t^3+61t^4-51t^5+31t^6-12t^7+2t^8
Seifert matrix of 12a_1213
1 0 0 0 0 0 0 0
0 -1 -1 0 0 0 -1 1
1 0 1 0 1 0 1 0
-1 -1 -1 -1 -1 -1 -1 1
1 0 0 0 1 0 0 0
0 -1 -1 0 -1 -1 -1 1
1 0 0 0 1 0 1 0
0 0 1 0 0 0 0 -2
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
253
First homology
of the double branched cover of 12a_1213
Z/253
0 2
12a_1214
4

detected by
the signature
1-3t+4t^2-5t^3+6t^4-7t^5+6t^6-5t^7+4t^8-3t^9+t^10
Seifert matrix of 12a_1214
-1 -1 0 0 -1 -1 -1 -1 -1 -1
0 -1 0 0 0 -1 -1 -1 -1 -1
0 0 1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 -1 -1 -1 -1 -1
0 -1 0 0 -1 -1 -1 -1 -1 -1
0 0 -1 0 0 -1 -1 -1 -1 -1
0 0 -1 0 0 0 -1 -1 0 -1
0 0 -1 0 0 0 0 -1 0 0
0 0 -1 0 0 0 -1 -1 -1 -1
0 0 -1 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-4-3t^-3+4t^-2-5t^-1+5-5t+4t^2-3t^3+t^4
45
First homology
of the double branched cover of 12a_1214
Z/45
-8 8
12a_1215
2

detected by
the signature
1-4t+9t^2-15t^3+19t^4-21t^5+19t^6-15t^7+9t^8-4t^9+t^10
Seifert matrix of 12a_1215
-1 0 0 0 -1 0 -1 -1 -1 -1
0 1 0 0 0 0 0 0 0 0
0 1 1 0 0 1 0 0 0 0
-1 0 0 -1 -1 0 -1 -1 -1 -1
0 -1 -1 0 -1 -1 -1 -1 -1 -1
0 1 0 0 0 1 0 0 0 0
0 0 -1 0 0 0 -1 -1 0 -1
0 0 -1 0 0 0 0 -1 0 0
0 0 -1 0 0 0 -1 -1 -1 -1
0 0 -1 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-14t^-1+15-14t+9t^2-4t^3+t^4
117
First homology
of the double branched cover of 12a_1215
Z/117
-4 4
12a_1216
2

detected by
the Lickorish test
-2+11t-25t^2+35t^3-37t^4+35t^5-25t^6+11t^7-2t^8
Seifert matrix of 12a_1216
1 0 0 0 -1 0 0 0
0 -1 0 0 0 -1 0 0
1 0 1 0 -1 1 1 0
1 0 1 1 -1 1 1 1
0 0 0 0 -1 1 0 0
0 0 0 0 0 -2 0 0
1 1 0 0 -1 1 1 0
1 0 1 0 -1 1 1 1
1
Generator of the Alexander module
(0,0,-t^2-t^3,0,-2,1,0,0)
the Blanchfield form on it
-2t^-2+7t^-1-11+7t-2t^2
183
First homology
of the double branched cover of 12a_1216
Z/183
2 2
12a_1217
1

detected by
an unknotting move
-4+23t-55t^2+73t^3-55t^4+23t^5-4t^6
Seifert matrix of 12a_1217
1 0 -1 0 0 0
0 -1 0 -1 0 0
0 0 -1 1 0 0
0 0 0 -2 0 0
1 1 -1 1 1 0
-1 0 1 -1 -1 2
1
Generator of the Alexander module
(0,t+7t^2+2t^3-9t^4+4t^5+3t^6-4t^7+t^8,-2t+4t^2+6t^3-8t^4-5t^5+8t^6-2t^7,-1+2t^2-2t^3-3t^4+4t^5-t^6,-3t^3+4t^4-t^5-7t^6+8t^7-2t^8,1+2t+t^2+2t^5-3t^7+t^8)
the Blanchfield form on it
x
237
First homology
of the double branched cover of 12a_1217
Z/237
0 0
12a_1218
1

detected by
an unknotting move
-1+4t-8t^2+13t^3-18t^4+21t^5-18t^6+13t^7-8t^8+4t^9-t^10
Seifert matrix of 12a_1218
1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0
1 1 1 0 1 1 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 0 0
1 1 0 0 1 1 0 0 0 0
0 0 -1 0 0 0 -1 -1 0 -1
0 0 -1 0 0 0 0 -1 0 0
0 0 -1 0 0 0 -1 -1 -1 -1
0 0 -1 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-2-2t^-1+3-2t+t^2
109
First homology
of the double branched cover of 12a_1218
Z/109
0 0
12a_1219
1

detected by
an unknotting move
1-4t+9t^2-15t^3+21t^4-23t^5+21t^6-15t^7+9t^8-4t^9+t^10
Seifert matrix of 12a_1219
-1 0 -1 0 0 0 0 -1 0 0
0 1 0 0 0 0 0 -1 0 0
0 0 -1 0 0 0 0 0 0 0
-1 0 -1 -1 0 0 0 -1 0 0
0 1 0 0 1 0 0 -1 0 0
0 1 -1 0 1 1 0 -1 1 0
0 1 -1 0 1 1 1 -1 1 1
0 0 -1 0 0 0 0 -1 0 0
0 1 -1 0 1 0 0 -1 1 0
0 1 -1 0 1 1 0 -1 1 1
1
Generator of the Alexander module
(0,1+t-t^2+t^3,0,t-t^2+t^3,0,0,0,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-4t^-1+4-4t+3t^2-t^3
123
First homology
of the double branched cover of 12a_1219
Z/123
2 2
12a_1220
3

detected by
the signature
1-4t+8t^2-11t^3+14t^4-15t^5+14t^6-11t^7+8t^8-4t^9+t^10
Seifert matrix of 12a_1220
1 0 0 0 0 0 0 -1 0 0
1 1 0 1 0 0 0 -1 0 0
0 0 -1 0 0 0 0 0 0 0
1 0 0 1 0 0 0 -1 0 0
1 1 0 1 1 0 0 -1 0 0
1 1 -1 1 1 1 0 -1 1 0
1 1 -1 1 1 1 1 -1 1 1
0 0 -1 0 0 0 0 -1 0 0
1 1 -1 1 1 0 0 -1 1 0
1 1 -1 1 1 1 0 -1 1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,0,1,0)
the Blanchfield form on it
-t^-4+4t^-3-8t^-2+10t^-1-11+10t-8t^2+4t^3-t^4
91
First homology
of the double branched cover of 12a_1220
Z/91
6 6
12a_1221
2

detected by
the Lickorish test
-1+5t-13t^2+24t^3-35t^4+39t^5-35t^6+24t^7-13t^8+5t^9-t^10
Seifert matrix of 12a_1221
-1 0 -1 0 -1 0 0 -1 -1 0
0 1 0 0 0 0 0 -1 0 0
0 0 -1 0 0 0 0 0 0 0
-1 0 -1 -1 -1 0 0 -1 -1 0
0 0 -1 0 -1 0 0 0 -1 0
0 1 0 0 -1 1 0 -1 -1 0
0 1 -1 0 -1 1 1 -1 -1 1
0 0 -1 0 -1 0 0 -1 -1 0
0 0 -1 0 0 0 0 0 -1 0
0 1 -1 0 -1 1 0 -1 -1 1
1
Generator of the Alexander module
(0,0,0,t^2,0,0,t+t^2,1+t,0,0)
the Blanchfield form on it
-t^-4+5t^-3-12t^-2+19t^-1-23+19t-12t^2+5t^3-t^4
195
First homology
of the double branched cover of 12a_1221
Z/195
-2 2
12a_1222
2

detected by
the Lickorish test
-1+5t-13t^2+25t^3-37t^4+43t^5-37t^6+25t^7-13t^8+5t^9-t^10
Seifert matrix of 12a_1222
1 0 0 0 0 0 0 0 0 0
0 -1 -1 0 0 -1 -1 0 -1 -1
0 0 -1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 0 0
0 0 -1 0 0 -1 -1 0 -1 -1
1 0 0 0 1 0 1 0 1 0
0 -1 -1 0 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 1 0
1 0 0 0 1 0 1 0 1 1
1
Generator of the Alexander module
(0,-1+2t,-1+t,2t-t^2,2,-1+t-2t^2+t^3,-1,2t-t^2,0,-1)
the Blanchfield form on it
t^-3-3t^-2+6t^-1-7+6t-3t^2+t^3
205
First homology
of the double branched cover of 12a_1222
Z/205
0 0
12a_1223
2

detected by
the signature
1-4t+10t^2-18t^3+23t^4-25t^5+23t^6-18t^7+10t^8-4t^9+t^10
Seifert matrix of 12a_1223
-1 0 0 0 -1 -1 0 -1 -1 -1
0 1 0 0 0 0 0 0 0 0
0 1 1 0 0 0 1 0 0 0
-1 0 0 -1 -1 -1 0 -1 -1 -1
0 -1 -1 0 -1 -1 -1 -1 -1 -1
0 -1 -1 0 0 -1 -1 -1 0 -1
0 1 0 0 0 0 1 0 0 0
0 0 -1 0 0 0 0 -1 0 0
0 -1 -1 0 0 -1 -1 -1 -1 -1
0 0 -1 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,1+t,-2t+t^4,t^2+t^3-t^4-t^6,t+t^2,t+t^2-t^3,1,0,0,0)
the Blanchfield form on it
137
First homology
of the double branched cover of 12a_1223
Z/137
-4 4
12a_1224
2

detected by
the Lickorish test
-2+8t-18t^2+29t^3-33t^4+29t^5-18t^6+8t^7-2t^8
Seifert matrix of 12a_1224
-1 0 0 0 0 -1 1 -1
0 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0
-1 0 0 -1 0 -1 1 -1
0 1 0 0 1 0 0 0
0 0 -1 0 0 -1 0 0
0 1 1 0 1 1 -2 1
0 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(-t^3+t^4,-1,-1,-1+t+t^2,-3-t^3,-t,3-3t-2t^2,-t)
the Blanchfield form on it
-5t^-7+11t^-6-16t^-5+55t^-4-165t^-3+353t^-2-548t^-1+632-548t+353t^2-165t^3+55t^4-16t^5+11t^6-5t^7
147
First homology
of the double branched cover of 12a_1224
Z/147
-2 2
12a_1225
2

detected by
the Nakanishi index
-1+5t-14t^2+28t^3-41t^4+47t^5-41t^6+28t^7-14t^8+5t^9-t^10
Seifert matrix of 12a_1225
1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0
1 1 1 0 1 0 1 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 0 0
0 -1 -1 0 0 -1 -1 -1 0 -1
1 1 0 0 1 0 1 0 0 0
0 0 -1 0 0 0 0 -1 0 0
0 -1 -1 0 0 -1 -1 -1 -1 -1
0 0 -1 0 0 0 0 -1 0 -1
2
225
First homology
of the double branched cover of 12a_1225
Z/75+Z/3
0 0
12a_1226
2

detected by
the Lickorish test
-1+4t-10t^2+18t^3-26t^4+29t^5-26t^6+18t^7-10t^8+4t^9-t^10
Seifert matrix of 12a_1226
-1 0 -1 0 0 0 0 0 -1 0
0 1 0 0 1 0 0 1 -1 0
0 0 -1 0 0 0 0 0 0 0
-1 0 -1 -1 0 0 0 0 -1 0
0 0 0 0 1 0 0 1 0 0
0 1 0 0 1 1 0 1 -1 0
0 1 -1 0 1 1 1 1 -1 1
0 0 0 0 0 0 0 1 0 0
0 0 -1 0 0 0 0 0 -1 0
0 1 -1 0 1 1 0 1 -1 1
1
Generator of the Alexander module
(0,-t-t^2+t^4+t^5,t+t^2-t^4-t^5,t-2t^3-2t^4+2t^6+t^7,-1-t+t^4,-t-t^2+t^4+t^5,1-2t^2-2t^3+2t^5+t^6,-2-2t+2t^4,1+t-t^3-t^4,t+t^2-t^4-t^5)
the Blanchfield form on it
x
147
First homology
of the double branched cover of 12a_1226
Z/147
2 2
12a_1227
1

detected by
an unknotting move
-1+5t-13t^2+24t^3-34t^4+37t^5-34t^6+24t^7-13t^8+5t^9-t^10
Seifert matrix of 12a_1227
1 0 0 0 0 0 0 -1 0 0
1 1 0 -1 1 0 0 -1 -1 0
0 0 -1 0 0 0 0 0 0 0
0 0 -1 -1 0 0 0 0 -1 0
1 0 0 -1 1 0 0 -1 -1 0
1 1 0 -1 1 1 0 -1 -1 0
1 1 -1 -1 1 1 1 -1 -1 1
0 0 -1 -1 0 0 0 -1 -1 0
0 0 -1 0 0 0 0 0 -1 0
1 1 -1 -1 1 1 0 -1 -1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-4-5t^-3+12t^-2-19t^-1+23-19t+12t^2-5t^3+t^4
191
First homology
of the double branched cover of 12a_1227
Z/191
2 2
12a_1228
1

detected by
an unknotting move
2-10t+24t^2-39t^3+47t^4-39t^5+24t^6-10t^7+2t^8
Seifert matrix of 12a_1228
1 0 0 0 0 -1 0 0
-1 2 0 1 0 1 1 0
0 0 -1 0 0 0 0 0
0 0 -1 -1 0 0 -1 0
1 -1 -1 -1 1 -1 -1 1
0 0 -1 -1 0 -1 -1 0
0 0 -1 0 0 0 -1 0
1 -1 -1 -1 0 -1 -1 1
1
Generator of the Alexander module
(0,1,0,0,0,-1+t,0,t-t^2)
the Blanchfield form on it
-2t^-3+8t^-2-14t^-1+15-14t+8t^2-2t^3
197
First homology
of the double branched cover of 12a_1228
Z/197
0 0
12a_1229
2

detected by
the Lickorish test
-1+5t-14t^2+27t^3-40t^4+47t^5-40t^6+27t^7-14t^8+5t^9-t^10
Seifert matrix of 12a_1229
1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0
0 0 -1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 0 0
0 -1 -1 0 0 -1 -1 0 -1 -1
1 1 0 0 1 0 1 0 0 0
0 -1 -1 0 0 -1 -1 -1 -1 -1
0 0 -1 0 0 0 -1 0 -1 -1
1 1 0 0 1 0 1 0 0 1
2
221
First homology
of the double branched cover of 12a_1229
Z/221
0 0
12a_1230
2

detected by
the Lickorish test
-1+5t-14t^2+27t^3-39t^4+43t^5-39t^6+27t^7-14t^8+5t^9-t^10
Seifert matrix of 12a_1230
1 0 0 0 0 0 0 -1 0 0
1 1 0 -1 1 0 0 -1 -1 0
0 0 -1 0 0 0 0 0 0 0
0 0 -1 -1 0 -1 0 0 -1 -1
1 0 0 -1 1 0 0 -1 -1 0
0 0 -1 0 0 -1 0 0 0 -1
1 1 0 -1 1 -1 1 -1 -1 -1
0 0 -1 -1 0 -1 0 -1 -1 -1
0 0 -1 0 0 -1 0 0 -1 -1
0 0 -1 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,-1,1,2t,0,0,0)
the Blanchfield form on it
2t^-4-11t^-3+25t^-2-34t^-1+39-34t+25t^2-11t^3+2t^4
215
First homology
of the double branched cover of 12a_1230
Z/215
-2 2
12a_1231
1

detected by
an unknotting move
-1+5t-13t^2+24t^3-34t^4+39t^5-34t^6+24t^7-13t^8+5t^9-t^10
Seifert matrix of 12a_1231
1 0 0 0 0 0 0 0 0 0
0 -1 -1 0 0 0 -1 0 0 -1
0 0 -1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 0 0
1 0 0 0 1 1 0 0 1 0
0 0 -1 0 0 0 -1 0 0 -1
0 -1 -1 0 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 1 0
1 0 0 0 1 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,-1-t^2+t^3,0,2+t^2-t^3,0,0,0)
the Blanchfield form on it
t^-1-2+t
193
First homology
of the double branched cover of 12a_1231
Z/193
0 0
12a_1232
2

detected by
the Lickorish test
-2+10t-24t^2+37t^3-41t^4+37t^5-24t^6+10t^7-2t^8
Seifert matrix of 12a_1232
1 0 0 0 0 0 0 0
0 -1 -1 0 -1 0 0 -1
0 0 -1 0 0 0 0 0
-1 -1 -1 -1 -1 -1 1 -1
0 0 -1 0 -1 0 0 -1
0 -1 -1 0 -1 -1 1 -1
-1 0 0 0 0 0 2 0
1 0 0 0 0 0 -1 1
1
Generator of the Alexander module
(0,-2t+t^2-t^3,1-2t+t^2-t^3,-6t+5t^2-4t^3+t^4,-3t+t^2-t^3,1-2t+t^2-t^3,-2+t-t^2,2-t+t^2)
the Blanchfield form on it
-2t^-3+8t^-2-16t^-1+21-16t+8t^2-2t^3
187
First homology
of the double branched cover of 12a_1232
Z/187
-2 2
12a_1233
2

detected by
the signature
1-3t+6t^2-10t^3+12t^4-13t^5+12t^6-10t^7+6t^8-3t^9+t^10
Seifert matrix of 12a_1233
-1 0 0 0 -1 -1 -1 0 -1 -1
0 1 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 1 0 0
-1 0 0 -1 -1 -1 -1 0 -1 -1
0 -1 -1 0 -1 -1 -1 -1 -1 -1
0 -1 -1 0 0 -1 -1 -1 0 -1
0 -1 -1 0 0 0 -1 -1 0 0
0 1 0 0 0 0 0 1 0 0
0 -1 -1 0 0 -1 -1 -1 -1 -1
0 -1 -1 0 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-4-3t^-3+6t^-2-10t^-1+11-10t+6t^2-3t^3+t^4
77
First homology
of the double branched cover of 12a_1233
Z/77
-4 4
12a_1234 1 or 2
-2+7t-15t^2+25t^3-29t^4+25t^5-15t^6+7t^7-2t^8
Seifert matrix of 12a_1234
-1 0 0 0 -1 1 -1 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1
-1 0 0 -1 -1 1 -1 0
0 -1 -1 0 -1 1 -1 -1
0 1 1 0 0 -2 1 1
0 -1 -1 0 0 0 -1 -1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1-t,0,-3+2t,0,0)
the Blanchfield form on it
-4t^-3+9t^-2-15t^-1+23-15t+9t^2-4t^3
127
First homology
of the double branched cover of 12a_1234
Z/127
-2 2
12a_1235
1

detected by
an unknotting move
-1+4t-9t^2+16t^3-23t^4+27t^5-23t^6+16t^7-9t^8+4t^9-t^10
Seifert matrix of 12a_1235
1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0
1 1 1 0 1 0 0 1 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 0 0
0 -1 -1 0 0 -1 -1 -1 0 -1
0 -1 -1 0 0 0 -1 -1 0 0
1 1 0 0 1 0 0 1 0 0
0 -1 -1 0 0 -1 -1 -1 -1 -1
0 -1 -1 0 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,-2+t-t^2+t^3,-1-t^2+t^3,-1+2t+t^2-t^4,0,-1+t-t^3,-2+2t^2-t^3,-1-t^2+t^3,2t-t^2+t^3-t^4,-1+t-t^3)
the Blanchfield form on it
x
133
First homology
of the double branched cover of 12a_1235
Z/133
0 0
12a_1236 1 or 2
-2+9t-21t^2+33t^3-37t^4+33t^5-21t^6+9t^7-2t^8
Seifert matrix of 12a_1236
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
1 1 1 0 1 0 0 1
-1 -1 -1 -1 -1 1 -1 -1
1 0 0 0 1 0 0 0
0 1 1 0 0 -2 1 1
0 -1 -1 0 0 0 -1 -1
1 1 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,3-4t+2t^2,-2+2t,2-t-2t^2,-3t+2t^2,0)
the Blanchfield form on it
-2t^-3+7t^-2-11t^-1+13-11t+7t^2-2t^3
167
First homology
of the double branched cover of 12a_1236
Z/167
2 2
12a_1237
2

detected by
the Lickorish test
2-11t+28t^2-45t^3+53t^4-45t^5+28t^6-11t^7+2t^8
Seifert matrix of 12a_1237
1 0 0 0 0 -1 0 0
-1 2 0 1 1 1 1 1
0 0 -1 0 0 0 0 0
0 0 -1 -1 0 0 -1 0
0 0 -1 0 1 0 0 1
0 0 -1 -1 0 -1 -1 0
0 0 -1 0 0 0 -1 0
0 0 -1 0 0 0 0 1
1
Generator of the Alexander module
(0,1-2t,0,0,0,1,1,0)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
225
First homology
of the double branched cover of 12a_1237
Z/225
0 2
12a_1238
1

detected by
an unknotting move
-1+4t-9t^2+16t^3-23t^4+25t^5-23t^6+16t^7-9t^8+4t^9-t^10
Seifert matrix of 12a_1238
1 0 0 0 0 0 0 -1 0 0
1 1 0 -1 -1 1 0 -1 -1 -1
0 0 -1 0 0 0 0 0 0 0
0 0 -1 -1 -1 0 0 0 -1 -1
0 0 -1 0 -1 0 0 0 0 -1
1 0 0 -1 -1 1 0 -1 -1 -1
1 1 0 -1 -1 1 1 -1 -1 -1
0 0 -1 -1 -1 0 0 -1 -1 -1
0 0 -1 0 -1 0 0 0 -1 -1
0 0 -1 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1+t-2t^2+t^3,0,t,1-t^2,0)
the Blanchfield form on it
-t^-2+3t^-1-4+3t-t^2
131
First homology
of the double branched cover of 12a_1238
Z/131
-2 2
12a_1239
1

detected by
an unknotting move
-2+9t-21t^2+35t^3-43t^4+35t^5-21t^6+9t^7-2t^8
Seifert matrix of 12a_1239
1 0 0 0 0 0 0 -1
1 1 0 -1 1 1 0 -1
0 0 -1 0 0 0 0 0
0 0 -1 -1 1 0 0 0
0 0 1 0 -2 0 0 0
1 0 0 -1 1 1 0 -1
1 1 0 -1 1 1 1 -1
0 0 -1 -1 1 0 0 -1
1
Generator of the Alexander module
(0,2-3t-t^2+7t^3-13t^4+15t^5-13t^6+6t^7-t^8,-11+21t-2t^2-21t^3+23t^4-13t^5+3t^6,-2+9t-6t^2-5t^3+9t^4-5t^5+t^6,9-16t-4t^2+23t^3-23t^4+13t^5-3t^6,2+3t-2t^2-16t^3+20t^4-4t^5-5t^6+4t^7-t^8,2t-5t^2+6t^3-2t^4,19t-31t^2+7t^3+26t^4-28t^5+14t^6-3t^7)
the Blanchfield form on it
x
177
First homology
of the double branched cover of 12a_1239
Z/177
0 0
12a_1240
2

detected by
the signature
2-8t+14t^2-16t^3+17t^4-16t^5+14t^6-8t^7+2t^8
Seifert matrix of 12a_1240
1 0 0 0 0 -1 0 0
-1 2 0 1 1 1 1 1
0 0 -1 0 0 0 0 0
0 0 -1 -1 -1 0 -1 -1
0 0 -1 0 -1 0 0 -1
0 0 -1 -1 -1 -1 -1 -1
0 0 -1 0 -1 0 -1 -1
0 0 -1 0 0 0 0 -1
1 or 2
97
First homology
of the double branched cover of 12a_1240
Z/97
-4 4
12a_1241
2

detected by
the Lickorish test
4-18t+35t^2-41t^3+35t^4-18t^5+4t^6
Seifert matrix of 12a_1241
1 0 0 0 0 -1
-1 2 0 1 -1 1
0 0 -1 0 0 0
0 0 -1 -1 1 0
0 0 1 0 -2 0
0 0 -1 -1 1 -1
1 or 2
155
First homology
of the double branched cover of 12a_1241
Z/155
-2 2
12a_1242
3

detected by
the signature
2-5t+6t^2-7t^3+7t^4-7t^5+6t^6-5t^7+2t^8
Seifert matrix of 12a_1242
-1 0 -1 -1 -1 0 -1 -1
-1 -1 -1 -1 -1 0 -1 -1
0 0 -1 -1 -1 1 -1 -1
0 0 0 -1 -1 1 0 -1
0 0 0 0 -1 1 0 0
0 0 0 0 0 2 0 0
0 0 0 -1 -1 1 -1 -1
0 0 0 0 -1 1 0 -1
1
Generator of the Alexander module
(0,-t+t^2-t^3-t^4+t^5+t^7-t^8,0,t^2+t^3-t^4-t^6+t^7,-1+3t^2-2t^5+t^7,-t-t^2+t^3+t^5-t^6,t+t^2-t^3-t^5+t^6,t+t^2-t^3-t^5+t^6)
the Blanchfield form on it
x
47
First homology
of the double branched cover of 12a_1242
Z/47
-6 6
12a_1243
2

detected by
the signature
-4+12t-17t^2+19t^3-17t^4+12t^5-4t^6
Seifert matrix of 12a_1243
-1 0 -1 1 -1 0
-1 -1 -1 1 -1 0
0 0 -1 1 -1 1
0 0 0 -2 1 -1
0 0 0 0 -1 1
0 0 0 0 0 2
1 or 2
85
First homology
of the double branched cover of 12a_1243
Z/85
-4 4
12a_1244
2

detected by
the Lickorish test
-2+8t-16t^2+22t^3-23t^4+22t^5-16t^6+8t^7-2t^8
Seifert matrix of 12a_1244
1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 1 -1 -1
1 0 1 0 0 0 0 0
0 0 0 -1 -1 1 0 -1
0 0 0 0 -1 1 0 0
-1 0 -1 0 0 2 0 0
0 0 0 -1 -1 1 -1 -1
0 0 0 0 -1 1 0 -1
1
Generator of the Alexander module
(0,3t,-1,-1-t^3,-1,2+t,-1+t,-1)
the Blanchfield form on it
-t^-1+1-t
119
First homology
of the double branched cover of 12a_1244
Z/119
-2 2
12a_1245
1

detected by
an unknotting move
-4+18t-39t^2+51t^3-39t^4+18t^5-4t^6
Seifert matrix of 12a_1245
1 0 0 0 0 0
-1 -1 -1 1 -1 1
1 0 1 0 0 0
0 0 0 -2 1 -1
0 0 0 0 -1 1
-1 0 -1 0 0 2
1 or 2
173
First homology
of the double branched cover of 12a_1245
Z/173
0 0
12a_1246
1

detected by
an unknotting move
1-4t+10t^2-18t^3+25t^4-27t^5+25t^6-18t^7+10t^8-4t^9+t^10
Seifert matrix of 12a_1246
-1 -1 -1 0 0 -1 0 -1 0 0
0 -1 -1 0 0 -1 0 0 0 0
0 0 -1 0 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 -1 0 0
0 -1 0 0 1 0 0 -1 1 0
0 0 -1 0 0 -1 0 0 0 0
0 -1 -1 0 1 -1 1 -1 1 1
0 -1 -1 0 0 -1 0 -1 0 0
0 -1 0 0 0 0 0 -1 1 0
0 -1 0 0 1 0 0 -1 1 1
1
Generator of the Alexander module
(0,4+4t-t^2+3t^3-2t^4-3t^5+3t^6-2t^7,2t-t^2-t^3+t^4-3t^5+2t^6,1-t-t^2-2t^4-t^6-t^8+2t^9,4t+4t^2-3t^3+4t^4-t^5-4t^6+6t^7-4t^8,2+t+t^3-2t^4,-2+t+t^2-3t^3+2t^4-2t^5-t^6+2t^7,2+t-2t^2+2t^3-t^4-t^5+3t^6-2t^7,-2-3t+t^2-2t^3+3t^5-3t^6+2t^7,2t+t^2-2t^3+2t^4-t^5-t^6+3t^7-2t^8)
the Blanchfield form on it
x
143
First homology
of the double branched cover of 12a_1246
Z/143
-2 2
12a_1247
2

detected by
the signature
2-8t+16t^2-21t^3+23t^4-21t^5+16t^6-8t^7+2t^8
Seifert matrix of 12a_1247
-1 -1 -1 0 0 -1 0 -1
0 -1 -1 0 0 -1 0 0
0 0 -1 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 -1
0 1 0 0 2 0 0 1
0 0 -1 0 0 -1 0 0
0 -1 -1 0 -1 -1 1 -1
0 -1 -1 0 0 -1 0 -1
1 or 2
117
First homology
of the double branched cover of 12a_1247
Z/117
-4 4
12a_1248
2

detected by
the Lickorish test
-1+6t-17t^2+32t^3-46t^4+51t^5-46t^6+32t^7-17t^8+6t^9-t^10
Seifert matrix of 12a_1248
1 0 0 0 0 0 -1 0 0 0
1 1 0 -1 0 0 -1 1 0 0
0 0 -1 0 0 0 0 0 0 0
0 0 -1 -1 0 0 0 0 -1 0
1 1 0 -1 1 0 -1 1 -1 0
1 1 -1 -1 1 1 -1 1 -1 1
0 0 -1 -1 0 0 -1 0 -1 0
1 0 0 -1 0 0 -1 1 0 0
0 0 -1 0 0 0 0 0 -1 0
1 1 -1 -1 1 0 -1 1 -1 1
1
Generator of the Alexander module
(0,6+4t+2t^2+20t^3-14t^4+14t^5-10t^6+2t^7,0,12t-22t^2+8t^3+10t^4-48t^5+62t^6-52t^7+36t^8-14t^9+2t^10,6t-11t^2+4t^3+5t^4-24t^5+31t^6-26t^7+18t^8-7t^9+t^10,-6+2t-t^2-8t^3+17t^4-14t^5+12t^6-6t^7+t^8,0,1-9t+22t^2-39t^3+33t^4-3t^5-38t^6+67t^7-69t^8+50t^9-26t^10+8t^11-t^12,0,-3-2t-t^2-10t^3+7t^4-7t^5+5t^6
the Blanchfield form on it
x
255
First homology
of the double branched cover of 12a_1248
Z/255
2 2
12a_1249
1

detected by
an unknotting move
1-6t+17t^2-32t^3+46t^4-53t^5+46t^6-32t^7+17t^8-6t^9+t^10
Seifert matrix of 12a_1249
1 0 0 0 0 0 0 0 0 0
0 -1 -1 0 0 -1 -1 0 0 -1
1 0 1 0 1 1 0 0 1 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 0 0
1 0 0 0 1 1 0 0 1 0
0 0 -1 0 0 0 -1 0 0 0
0 -1 -1 0 -1 -1 -1 -1 -1 -1
1 0 0 0 1 0 0 0 1 0
0 0 -1 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,-2+9t-18t^2+28t^3-33t^4+28t^5-19t^6+8t^7-2t^8,0,3-6t+11t^2-11t^3+11t^4-6t^5+2t^6,3t-9t^2+20t^3-28t^4+33t^5-28t^6+19t^7-8t^8+2t^9,0,0,0,0,0)
the Blanchfield form on it
x
257
First homology
of the double branched cover of 12a_1249
Z/257
0 0
12a_1250
1

detected by
an unknotting move
1-5t+14t^2-27t^3+39t^4-45t^5+39t^6-27t^7+14t^8-5t^9+t^10
Seifert matrix of 12a_1250
-1 -1 -1 0 0 -1 -1 -1 -1 -1
0 1 0 0 1 0 0 0 1 0
0 1 1 0 1 0 1 0 1 0
-1 0 0 -1 0 -1 0 -1 0 -1
0 0 0 0 1 0 0 0 0 0
0 -1 -1 0 0 -1 -1 -1 0 -1
0 1 0 0 1 0 1 0 1 0
0 0 -1 0 0 0 0 -1 0 0
0 0 0 0 1 0 0 0 1 0
0 0 -1 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-15t^-1+17-15t+9t^2-4t^3+t^4
217
First homology
of the double branched cover of 12a_1250
Z/217
0 0
12a_1251
2

detected by
-4+25t-62t^2+83t^3-62t^4+25t^5-4t^6
Seifert matrix of 12a_1251
-1 0 0 0 -1 0
0 2 0 1 0 1
0 -1 1 -1 1 0
0 0 0 -1 1 0
0 0 0 0 -2 0
1 0 0 0 1 1
2
265
First homology
of the double branched cover of 12a_1251
Z/265
0 0
12a_1252
2

detected by
the Lickorish test
-2+10t-27t^2+48t^3-57t^4+48t^5-27t^6+10t^7-2t^8
Seifert matrix of 12a_1252
-1 0 0 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0
0 -1 -1 -1 -1 0 -1 0
0 1 0 0 1 0 0 0
0 0 -1 0 0 -1 0 0
0 0 0 0 0 1 -2 1
0 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(3t-5t^2-t^3+12t^4-12t^5+6t^6,0,1,2+3t-11t^2-5t^3+24t^4-27t^5-12t^6+24t^7-18t^8,-12t+22t^2+2t^3-48t^4+48t^5-24t^6,-1,-3-t+9t^2-10t^3-12t^4+18t^5-12t^6,0)
the Blanchfield form on it
x
231
First homology
of the double branched cover of 12a_1252
Z/231
-2 2
12a_1253
1

detected by
an unknotting move
-1+5t-14t^2+26t^3-37t^4+41t^5-37t^6+26t^7-14t^8+5t^9-t^10
Seifert matrix of 12a_1253
-1 0 -1 0 0 0 0 0 -1 0
-1 1 0 -1 1 0 0 1 -1 0
0 0 -1 0 0 0 0 0 0 0
-1 0 -1 -1 0 0 0 0 -1 0
-1 0 0 -1 1 0 0 1 0 0
-1 1 0 -1 1 1 0 1 -1 0
-1 1 -1 -1 1 1 1 1 -1 1
0 0 0 0 0 0 0 1 0 0
0 0 -1 0 0 0 0 0 -1 0
-1 1 -1 -1 1 1 0 1 -1 1
1
Generator of the Alexander module
(0,-8t+3t^2+3t^4+5t^5,-1+t^4,1-3t+3t^2+2t^4+t^5,5t-2t^2-2t^4-3t^5,2t+t^3-t^5,2t-t^2+t^3-t^4-t^5,-1-t^2,t+t^3,2t-t^2+t^3-t^4-t^5)
the Blanchfield form on it
x
207
First homology
of the double branched cover of 12a_1253
Z/207
2 2
12a_1254
1

detected by
an unknotting move
-1+4t-10t^2+18t^3-25t^4+29t^5-25t^6+18t^7-10t^8+4t^9-t^10
Seifert matrix of 12a_1254
1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0
0 0 -1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 0 -1 -1 -1 0 -1 -1
1 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 1 0 0 0
-1 -1 -1 0 -1 -1 -1 -1 -1 -1
0 0 -1 0 0 0 -1 0 -1 -1
1 1 0 0 0 1 1 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0,1,0)
the Blanchfield form on it
t^-4-3t^-3+6t^-2-10t^-1+11-10t+6t^2-3t^3+t^4
145
First homology
of the double branched cover of 12a_1254
Z/145
0 0
12a_1255
2

detected by
the signature
-1+5t-13t^2+23t^3-30t^4+33t^5-30t^6+23t^7-13t^8+5t^9-t^10
Seifert matrix of 12a_1255
1 0 0 0 0 0 0 0 0 0
0 -1 -1 0 0 0 -1 0 0 -1
0 0 -1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 0 -1 -1 -1 0 -1 -1
1 0 0 0 0 1 0 0 0 0
0 0 -1 0 0 0 -1 0 0 -1
-1 -1 -1 0 -1 -1 -1 -1 -1 -1
0 -1 -1 0 0 -1 -1 0 -1 -1
1 0 0 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,-1-t^2,0,0,0,0,1)
the Blanchfield form on it
-t^-4+5t^-3-12t^-2+19t^-1-21+19t-12t^2+5t^3-t^4
177
First homology
of the double branched cover of 12a_1255
Z/177
-4 4
12a_1256
1

detected by
an unknotting move
-2+8t-18t^2+27t^3-29t^4+27t^5-18t^6+8t^7-2t^8
Seifert matrix of 12a_1256
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
0 0 -1 0 0 0 0 0
1 0 0 1 0 0 0 0
1 1 0 1 1 0 0 0
1 1 1 1 1 -2 1 1
0 0 -1 0 -1 0 -1 -1
1 1 0 1 1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-4-4t^-3+9t^-2-13t^-1+14-13t+9t^2-4t^3+t^4
139
First homology
of the double branched cover of 12a_1256
Z/139
2 2
12a_1257
2

detected by
the Lickorish test
-2+10t-25t^2+41t^3-47t^4+41t^5-25t^6+10t^7-2t^8
Seifert matrix of 12a_1257
1 0 0 0 0 0 0 0
0 -1 -1 0 -1 0 0 -1
0 0 -1 0 0 0 0 0
1 0 0 1 0 0 0 0
0 0 -1 0 -1 0 0 -1
1 1 1 1 1 -2 1 1
0 -1 -1 -1 -1 0 -1 -1
1 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,-2,0,0,0,5-6t+4t^2-2t^3,0,0)
the Blanchfield form on it
-67t^-5+426t^-4-1360t^-3+2848t^-2-4281t^-1+4890-4281t+2848t^2-1360t^3+426t^4-67t^5
203
First homology
of the double branched cover of 12a_1257
Z/203
-2 2
12a_1258
1

detected by
an unknotting move
1-4t+10t^2-19t^3+28t^4-33t^5+28t^6-19t^7+10t^8-4t^9+t^10
Seifert matrix of 12a_1258
-1 -1 -1 0 0 -1 -1 -1 -1 -1
0 1 0 0 1 0 0 0 1 0
0 1 1 0 1 0 0 1 1 0
-1 0 0 -1 0 -1 -1 0 0 -1
0 0 0 0 1 0 0 0 0 0
0 -1 -1 0 0 -1 -1 -1 0 -1
0 -1 -1 0 0 0 -1 -1 0 0
0 1 0 0 1 0 0 1 1 0
0 0 0 0 1 0 0 0 1 0
0 -1 -1 0 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,-t^2-t^4+2t^5+t^7,-2-t^2+3t^3+t^4-2t^6-t^7-t^8,0,0,-1-t-t^2+t^3+2t^4+t^5+t^6,-2-2t-t^2+2t^3+5t^4+2t^6-t^7,0,0)
the Blanchfield form on it
x
157
First homology
of the double branched cover of 12a_1258
Z/157
0 0
12a_1259
1

detected by
an unknotting move
-2+8t-18t^2+28t^3-31t^4+28t^5-18t^6+8t^7-2t^8
Seifert matrix of 12a_1259
-1 -1 -1 0 0 -1 -1 1
0 1 0 0 1 0 1 0
0 1 1 0 1 1 1 0
-1 0 0 -1 0 0 0 1
0 0 0 0 1 0 0 0
0 1 0 0 1 1 1 0
0 0 0 0 1 0 1 0
0 1 1 0 0 1 0 -2
1
Generator of the Alexander module
(-59+86t-244t^2+431t^3+62t^4-1649t^5+3383t^6-2460t^7+1960t^8-3926t^9+3152t^10-780t^11,-2t^2+50t^3+6t^4-162t^5+334t^6-268t^7+192t^8-444t^9+400t^10-104t^11,32-48t+141t^2-248t^3-72t^4+1031t^5-2039t^6+1504t^7-1244t^8+2402t^9-1904t^10+468t^11,19-31t+95t^2-166t^3-131t^4+873t^5-1595t^6+1234t^7-1084t^8+1930
the Blanchfield form on it
x
143
First homology
of the double branched cover of 12a_1259
Z/143
2 2
12a_1260
2

detected by
the Nakanishi index
-1+4t-10t^2+19t^3-27t^4+31t^5-27t^6+19t^7-10t^8+4t^9-t^10
Seifert matrix of 12a_1260
1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0
1 1 1 0 0 1 0 1 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 0 -1 -1 -1 -1 0 -1
1 0 0 0 0 1 0 0 0 0
0 -1 -1 0 0 0 -1 -1 0 0
1 1 0 0 0 1 0 1 0 0
-1 -1 -1 0 -1 -1 -1 -1 -1 -1
0 -1 -1 0 0 0 -1 -1 0 -1
2
153
First homology
of the double branched cover of 12a_1260
Z/51+Z/3
0 0
12a_1261
1

detected by
an unknotting move
-2+9t-23t^2+40t^3-47t^4+40t^5-23t^6+9t^7-2t^8
Seifert matrix of 12a_1261
-1 0 0 -1 0 0 -1 0
0 1 0 0 0 0 0 0
0 1 1 0 0 1 0 0
0 -1 -1 -1 0 -1 -1 0
0 -1 -1 0 -1 -1 0 0
0 1 0 0 0 1 0 0
0 0 0 0 1 0 -2 1
0 -1 -1 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,-2t^2-t^4+t^5+t^6-2t^7+t^8,-2t^2-2t^4+2t^5,1+4t+t^2+2t^3-4t^4,0,t+t^3-t^4,-2-2t^2+2t^3,1+t^2-t^3-t^4+t^5-t^6+2t^7-t^8)
the Blanchfield form on it
x
195
First homology
of the double branched cover of 12a_1261
Z/195
-2 2
12a_1262
2

detected by
the Lickorish test
-2+8t-18t^2+29t^3-33t^4+29t^5-18t^6+8t^7-2t^8
Seifert matrix of 12a_1262
1 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0
1 1 1 1 0 1 0 0
1 0 0 1 0 0 0 0
0 -1 -1 0 -1 -1 0 0
1 1 0 1 0 1 0 0
1 1 1 1 1 1 -2 1
0 -1 -1 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,2+2t+t^2,0,0,0,0,1+t,-t)
the Blanchfield form on it
16t^-3-65t^-2+126t^-1-166+126t-65t^2+16t^3
147
First homology
of the double branched cover of 12a_1262
Z/147
2 2
12a_1263
1

detected by
an unknotting move
4-21t+49t^2-63t^3+49t^4-21t^5+4t^6
Seifert matrix of 12a_1263
2 0 0 1 1 0
0 -1 0 0 0 -1
-1 -1 1 0 0 -1
0 -1 0 1 1 0
0 -1 0 0 1 0
0 0 0 0 0 -2
1 or 2
211
First homology
of the double branched cover of 12a_1263
Z/211
2 2
12a_1264
1

detected by
an unknotting move
2-8t+17t^2-24t^3+25t^4-24t^5+17t^6-8t^7+2t^8
Seifert matrix of 12a_1264
-1 0 0 -1 -1 1 -1 -1
-1 -1 0 -1 -1 0 0 -1
0 0 1 0 0 0 0 0
0 0 0 -1 -1 1 0 -1
0 0 0 0 -1 1 0 0
0 0 -1 0 0 2 -1 0
0 0 1 0 0 0 1 0
0 0 0 0 -1 1 0 -1
1 or 2
127
First homology
of the double branched cover of 12a_1264
Z/127
-2 2
12a_1265
2

detected by
the Lickorish test
-4+17t-37t^2+49t^3-37t^4+17t^5-4t^6
Seifert matrix of 12a_1265
-1 0 0 1 -1 1
-1 -1 0 0 0 1
0 0 1 0 0 0
0 0 -1 2 -1 0
0 0 1 0 1 0
0 0 0 -1 0 -2
1 or 2
165
First homology
of the double branched cover of 12a_1265
Z/165
0 0
12a_1266
2

detected by
the signature
-4+15t-28t^2+35t^3-28t^4+15t^5-4t^6
Seifert matrix of 12a_1266
-1 -1 0 0 -1 0
0 -1 0 1 -1 0
0 0 -1 1 0 0
0 0 0 2 0 0
0 0 1 0 -2 1
0 0 -1 1 0 -1
1 or 2
129
First homology
of the double branched cover of 12a_1266
Z/129
-4 4
12a_1267
2

detected by
the Lickorish test
-4+16t-32t^2+41t^3-32t^4+16t^5-4t^6
Seifert matrix of 12a_1267
1 0 0 0 0 0
1 1 0 0 0 0
0 0 -1 1 0 0
-1 -1 0 2 0 0
1 1 1 -1 -2 1
0 0 -1 1 0 -1
1 or 2
145
First homology
of the double branched cover of 12a_1267
Z/145
0 0
12a_1268
1

detected by
an unknotting move
2-10t+26t^2-45t^3+55t^4-45t^5+26t^6-10t^7+2t^8
Seifert matrix of 12a_1268
-1 -1 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
0 0 2 1 0 1 0 1
0 0 0 1 0 0 0 0
-1 -1 -1 0 1 -1 -1 0
-1 -1 0 0 0 -1 -1 0
0 -1 0 0 0 0 -1 0
-1 -1 0 1 0 0 -1 1
1
Generator of the Alexander module
(0,0,-3+2t-2t^2,0,0,0,0,-1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
221
First homology
of the double branched cover of 12a_1268
Z/221
0 0
12a_1269
2

detected by
-4+17t-38t^2+51t^3-38t^4+17t^5-4t^6
Seifert matrix of 12a_1269
-1 1 -1 0 0 1
0 2 0 0 -1 0
0 -1 1 0 1 0
-1 0 0 -1 0 1
0 0 0 0 1 0
0 0 1 0 0 -2
2
169
First homology
of the double branched cover of 12a_1269
Z/169
0 0
12a_1270
2

detected by
the Lickorish test
2-11t+30t^2-53t^3+63t^4-53t^5+30t^6-11t^7+2t^8
Seifert matrix of 12a_1270
1 0 0 0 0 0 0 0
1 -1 0 0 0 0 -1 0
1 0 1 1 0 0 0 0
1 0 0 1 0 0 0 0
0 0 -1 0 -1 0 0 0
1 -1 0 0 0 -1 -1 0
1 0 1 1 1 0 -2 1
0 0 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
2t^-3-8t^-2+16t^-1-21+16t-8t^2+2t^3
255
First homology
of the double branched cover of 12a_1270
Z/255
-2 2
12a_1271
1

detected by
an unknotting move
4-20t+44t^2-55t^3+44t^4-20t^5+4t^6
Seifert matrix of 12a_1271
2 1 0 1 0 1
0 1 0 0 0 0
-1 0 1 -1 1 0
0 0 0 -1 1 0
0 0 0 0 -2 0
0 1 0 0 1 1
1 or 2
191
First homology
of the double branched cover of 12a_1271
Z/191
2 2
12a_1272
1

detected by
an unknotting move
2-10t+25t^2-40t^3+47t^4-40t^5+25t^6-10t^7+2t^8
Seifert matrix of 12a_1272
-2 0 1 0 0 0 0 1
1 1 0 1 1 0 1 0
0 0 -1 0 0 0 0 0
0 0 0 1 0 0 1 0
-1 0 0 0 -1 0 0 0
1 1 0 1 0 1 1 -1
0 0 0 0 0 0 1 0
0 0 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,2t^2-5t^3-2t^5-4t^6,-2-3t-4t^2-2t^3-4t^4,-2t+t^2+2t^3-2t^4+4t^5,2t+3t^2+4t^3+2t^4+4t^5,1-2t-t^2-t^3-6t^4+2t^5-4t^6,2t+3t^2+4t^3+2t^4+4t^5,2t+3t^2+4t^3+2t^4+4t^5)
the Blanchfield form on it
x
201
First homology
of the double branched cover of 12a_1272
Z/201
0 2
12a_1273
1

detected by
an unknotting move
-1+3t-5t^2+7t^3-9t^4+11t^5-9t^6+7t^7-5t^8+3t^9-t^10
Seifert matrix of 12a_1273
1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 1 0 0 0
1 1 1 0 0 0 1 1 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 0 -1 -1 -1 -1 0 -1
-1 -1 -1 0 0 -1 -1 -1 0 0
1 0 0 0 0 0 1 0 0 0
1 1 0 0 0 0 1 1 0 0
-1 -1 -1 0 -1 -1 -1 -1 -1 -1
-1 -1 -1 0 0 -1 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-4+3t^-3-5t^-2+7t^-1-7+7t-5t^2+3t^3-t^4
61
First homology
of the double branched cover of 12a_1273
Z/61
0 0
12a_1274
1

detected by
an unknotting move
-2+7t-13t^2+17t^3-17t^4+17t^5-13t^6+7t^7-2t^8
Seifert matrix of 12a_1274
1 0 0 0 0 0 0 0
1 1 0 0 0 0 1 0
1 1 1 0 0 0 1 1
-1 -1 -1 -1 1 -1 -1 -1
1 1 1 0 -2 1 1 1
-1 -1 -1 0 0 -1 -1 -1
1 0 0 0 0 0 1 0
1 1 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-4-4t^-3+8t^-2-10t^-1+10-10t+8t^2-4t^3+t^4
95
First homology
of the double branched cover of 12a_1274
Z/95
2 2
12a_1275
1

detected by
an unknotting move
-4+16t-33t^2+43t^3-33t^4+16t^5-4t^6
Seifert matrix of 12a_1275
1 0 0 0 0 0
-1 2 0 0 0 0
1 -1 1 0 0 0
-1 1 -1 -1 1 -1
1 -1 1 0 -2 1
-1 1 -1 0 0 -1
1 or 2
149
First homology
of the double branched cover of 12a_1275
Z/149
0 0
12a_1276
1

detected by
an unknotting move
-2+6t-10t^2+13t^3-13t^4+13t^5-10t^6+6t^7-2t^8
Seifert matrix of 12a_1276
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
1 1 1 0 1 1 0 0
0 0 0 -1 0 0 0 -1
1 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0
1 1 1 -1 1 1 -2 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,-t^4,0,1+t,0)
the Blanchfield form on it
2t^-3-6t^-2+10t^-1-13+10t-6t^2+2t^3
75
First homology
of the double branched cover of 12a_1276
Z/75
2 2
12a_1277
1

detected by
an unknotting move
-4+14t-26t^2+33t^3-26t^4+14t^5-4t^6
Seifert matrix of 12a_1277
1 0 0 0 0 0
-1 2 0 0 0 0
1 -1 1 0 0 0
0 0 0 -1 0 -1
1 -1 1 -1 -2 -1
0 0 0 0 0 -1
1 or 2
121
First homology
of the double branched cover of 12a_1277
Z/121
0 0
12a_1278
2

detected by
the signature
-3+7t-7t^2+7t^3-7t^4+7t^5-3t^6
Seifert matrix of 12a_1278
1 0 0 0 0 0
1 1 0 0 1 0
1 1 1 0 1 1
-1 -1 -1 -3 -1 -1
1 0 0 0 1 0
1 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1+t+2t^3,-2t+2t^2-2t^3+3t^4-2t^5+2t^6,0)
the Blanchfield form on it
41
First homology
of the double branched cover of 12a_1278
Z/41
4 4
12a_1279
1

detected by
an unknotting move
-6+17t-21t^2+17t^3-6t^4
Seifert matrix of 12a_1279
1 0 0 0
-1 2 0 0
1 -1 1 0
-1 1 -1 -3
1
Generator of the Alexander module
(0,3-2t,0,1)
the Blanchfield form on it
15t^-1-32+15t
67
First homology
of the double branched cover of 12a_1279
Z/67
2 2
12a_1280
2

detected by
A(F_3)
1-9t+28t^2-51t^3+63t^4-51t^5+28t^6-9t^7+t^8
Seifert matrix of 12a_1280
-1 0 0 0 -1 0 0 -1
0 1 0 0 0 0 0 0
0 1 1 0 0 1 0 0
0 0 -1 -1 0 0 -1 0
0 -1 -1 0 -1 -1 0 -1
0 1 0 0 0 1 0 0
0 0 0 0 0 0 1 0
0 0 -1 0 0 0 -1 -1
2
241
First homology
of the double branched cover of 12a_1280
Z/241
0 0
12a_1281
1

detected by
an unknotting move
-4+13t-23t^2+29t^3-23t^4+13t^5-4t^6
Seifert matrix of 12a_1281
1 0 0 1 0 0
0 -1 0 0 0 -1
1 0 2 1 0 0
0 0 0 1 0 0
0 -1 -1 0 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-3-7t^-2+13t^-1-16+13t-7t^2+2t^3
109
First homology
of the double branched cover of 12a_1281
Z/109
0 0
12a_1282
1

detected by
an unknotting move
-6+16t-19t^2+16t^3-6t^4
Seifert matrix of 12a_1282
1 0 0 1
0 -3 1 0
1 0 2 1
0 0 0 1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
2t^-2-5t^-1+6-5t+2t^2
63
First homology
of the double branched cover of 12a_1282
Z/63
2 2
12a_1283
2

detected by
the Nakanishi index
1-3t+6t^2-10t^3+13t^4-15t^5+13t^6-10t^7+6t^8-3t^9+t^10
Seifert matrix of 12a_1283
1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 1 0 0
1 1 1 0 0 0 1 1 0 0
0 -1 -1 -1 -1 -1 -1 0 -1 -1
0 -1 -1 0 -1 -1 -1 0 0 -1
0 -1 -1 0 0 -1 -1 0 0 0
1 1 0 0 0 0 1 1 0 0
1 0 0 0 0 0 0 1 0 0
0 -1 -1 0 -1 -1 -1 0 -1 -1
0 -1 -1 0 0 -1 -1 0 0 -1
2
81
First homology
of the double branched cover of 12a_1283
Z/27+Z/3
0 0
12a_1284
1

detected by
an unknotting move
-2+7t-15t^2+24t^3-27t^4+24t^5-15t^6+7t^7-2t^8
Seifert matrix of 12a_1284
1 0 0 0 0 0 0 0
1 1 0 0 0 0 0 1
1 1 1 0 0 0 1 1
0 -1 -1 -1 1 -1 -1 0
0 1 1 0 -2 1 1 0
0 -1 -1 0 0 -1 -1 0
1 1 0 0 0 0 1 1
1 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,-2t-2t^2-4t^3-2t^4-t^5,-t-t^2-2t^3-t^4,t+2t^2+5t^3+4t^4+2t^5,1+5t-t^2+t^3-5t^4-5t^5-t^6-2t^7,-t-2t^2+t^4+2t^5,-t-2t^2-t^3+3t^5+2t^6+2t^7,t+3t^2+t^3-6t^5-4t^6-4t^7)
the Blanchfield form on it
x
123
First homology
of the double branched cover of 12a_1284
Z/123
2 2
12a_1285
1

detected by
an unknotting move
-2+6t-11t^2+16t^3-17t^4+16t^5-11t^6+6t^7-2t^8
Seifert matrix of 12a_1285
1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
1 1 1 0 1 1 0 0
0 0 0 -1 0 0 0 -1
1 1 0 0 1 1 0 0
1 0 0 0 0 1 0 0
0 1 1 -1 1 0 -2 -1
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,-1,0)
the Blanchfield form on it
2t^-3-6t^-2+10t^-1-13+10t-6t^2+2t^3
87
First homology
of the double branched cover of 12a_1285
Z/87
2 2
12a_1286
2

detected by
the Nakanishi index
-3+7t-8t^2+9t^3-8t^4+7t^5-3t^6
Seifert matrix of 12a_1286
1 0 0 0 0 0
1 1 0 0 0 1
1 1 1 0 1 1
0 -1 -1 -3 -1 0
1 1 0 0 1 1
1 0 0 0 0 1
2
45
First homology
of the double branched cover of 12a_1286
Z/15+Z/3
4 4
12a_1287
1

detected by
an unknotting move
-9+19t-9t^2
Seifert matrix of 12a_1287
3 0
-1 -3
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
3t^-1-6+3t
37
First homology
of the double branched cover of 12a_1287
Z/37
0 0
12a_1288
2

detected by
the Nakanishi index
1-3t+7t^2-14t^3+21t^4-25t^5+21t^6-14t^7+7t^8-3t^9+t^10
Seifert matrix of 12a_1288
-1 0 0 0 0 -1 -1 0 0 -1
0 1 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 1 0
0 1 1 1 0 0 0 1 1 0
-1 0 0 0 -1 -1 -1 0 0 -1
0 0 -1 -1 0 -1 -1 -1 0 -1
0 0 -1 -1 0 0 -1 -1 0 0
0 1 1 0 0 0 0 1 1 0
0 1 0 0 0 0 0 0 1 0
0 0 -1 -1 0 0 -1 -1 0 -1
2
117
First homology
of the double branched cover of 12a_1288
Z/39+Z/3
0 0
12n_0001
1

detected by
an unknotting move
-1+5t-13t^2+19t^3-13t^4+5t^5-t^6
Seifert matrix of 12n_0001
-1 0 0 0 0 -1
0 -2 1 1 1 0
0 0 1 0 0 0
0 1 -1 0 0 0
0 1 -1 -1 0 0
0 0 0 -1 -1 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
57
First homology
of the double branched cover of 12n_0001
Z/57
0 0
12n_0002
1

detected by
an unknotting move
-1+5t-11t^2+16t^3-17t^4+16t^5-11t^6+5t^7-t^8
Seifert matrix of 12n_0002
-1 0 -1 -1 -1 -1 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 -1 -1 0 0
0 1 -1 0 -1 0 0 0
0 1 -1 0 -1 -1 0 0
0 0 0 0 -1 -1 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(-t,0,1,0,1,1,-1,0)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-4+4t-3t^2+t^3
83
First homology
of the double branched cover of 12n_0002
Z/83
-2 2
12n_0003
1

detected by
an unknotting move
-1+7t-17t^2+23t^3-17t^4+7t^5-t^6
Seifert matrix of 12n_0003
-1 0 0 0 0 -1
0 0 1 1 1 0
0 0 1 0 0 0
0 1 -1 0 0 0
0 1 -1 -1 0 0
0 0 0 -1 -1 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+6t^-1-9+6t-t^2
73
First homology
of the double branched cover of 12n_0003
Z/73
0 0
12n_0004
1

detected by
an unknotting move
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 12n_0004
-1 0 -1 0 0 1
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 -1 -1 -1
0 0 0 0 0 -1
0 -1 1 0 -1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
1
81
First homology
of the double branched cover of 12n_0004
Z/81
0 0
12n_0005
1

detected by
an unknotting move
1-7t+21t^2-29t^3+21t^4-7t^5+t^6
Seifert matrix of 12n_0005
-1 0 -1 -1 1 -1
0 1 0 0 0 0
0 0 1 0 0 0
0 1 -1 0 2 -1
0 -1 1 1 1 0
0 1 -1 0 1 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+5t^-1-10+5t-t^2
87
First homology
of the double branched cover of 12n_0005
Z/87
2 2
12n_0006
2

detected by
the signature
1-5t+9t^2-6t^3+3t^4-6t^5+9t^6-5t^7+t^8
Seifert matrix of 12n_0006
-1 0 -1 -1 -1 -1 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 -1 -1 0 0
0 1 -1 0 -1 0 0 0
0 1 -1 0 -1 -1 0 0
0 0 0 0 -1 -1 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,-t,t^2)
the Blanchfield form on it
t^-3-4t^-2+5t^-1-2+5t-4t^2+t^3
45
First homology
of the double branched cover of 12n_0006
Z/45
-4 4
12n_0007
1

detected by
an unknotting move
1-5t+9t^2-9t^3+9t^4-5t^5+t^6
Seifert matrix of 12n_0007
1 0 0 0 0 0
-1 0 1 -1 0 -1
1 1 -2 0 1 1
0 0 0 -1 0 0
-1 -1 1 -1 0 -1
-1 0 1 -1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+6t^-1-11+6t-t^2
39
First homology
of the double branched cover of 12n_0007
Z/39
2 2
12n_0008
2

detected by
the signature
1-5t+9t^2-10t^3+11t^4-10t^5+9t^6-5t^7+t^8
Seifert matrix of 12n_0008
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 -1 -1 -1
0 0 -1 0 0 0 0 0
-1 0 -1 -1 0 -1 -1 -1
0 0 0 0 1 0 0 0
-1 0 -1 0 -1 -1 -1 -1
-1 0 -1 0 -1 0 -1 0
-1 0 -1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
t^-3-5t^-2+8t^-1-7+8t-5t^2+t^3
61
First homology
of the double branched cover of 12n_0008
Z/61
-4 4
12n_0009
1

detected by
an unknotting move
1-7t+17t^2-21t^3+17t^4-7t^5+t^6
Seifert matrix of 12n_0009
1 0 0 0 0 0
-1 0 1 -1 0 -1
1 1 0 0 1 1
0 0 0 -1 0 0
-1 -1 1 -1 0 -1
-1 0 1 -1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+6t^-1-11+6t-t^2
71
First homology
of the double branched cover of 12n_0009
Z/71
2 2
12n_0010
2

detected by
the Lickorish test
1-5t+9t^2-9t^3+9t^4-5t^5+t^6
Seifert matrix of 12n_0010
1 0 0 0 0 0
-1 -1 0 -1 1 -1
0 0 1 0 0 0
-1 0 -1 0 1 -1
1 0 1 1 -2 1
-1 0 -1 0 1 0
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+10t^-1-17+10t-2t^2
39
First homology
of the double branched cover of 12n_0010
Z/39
2 2
12n_0011
1

detected by
an unknotting move
3-15t+25t^2-15t^3+3t^4
Seifert matrix of 12n_0011
1 0 0 0
1 1 -1 1
1 -1 -2 0
0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
61
First homology
of the double branched cover of 12n_0011
Z/61
0 0
12n_0012
1

detected by
an unknotting move
2-10t+18t^2-19t^3+18t^4-10t^5+2t^6
Seifert matrix of 12n_0012
1 0 0 0 0 0
-1 -1 0 -1 0 1
0 0 -1 0 0 0
-1 0 -1 -1 0 1
0 0 0 0 1 0
1 0 1 0 1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
79
First homology
of the double branched cover of 12n_0012
Z/79
-2 2
12n_0013
1

detected by
an unknotting move
1-7t+13t^2-7t^3+t^4
Seifert matrix of 12n_0013
1 0 0 0
1 1 -1 1
1 -1 0 0
0 0 0 -1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-t^-1+2-t
29
First homology
of the double branched cover of 12n_0013
Z/29
0 0
12n_0014
1

detected by
an unknotting move
-1+7t-21t^2+31t^3-21t^4+7t^5-t^6
Seifert matrix of 12n_0014
-2 -2 1 -3 0 -1
-1 -1 1 -2 0 -1
0 0 1 0 0 0
-2 -3 1 -4 0 -2
-1 0 0 -1 -1 -1
-1 -1 0 -2 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-2-6t^-1+11-6t+t^2
89
First homology
of the double branched cover of 12n_0014
Z/89
0 0
12n_0015
2

detected by
the Lickorish test
1-9t+27t^2-37t^3+27t^4-9t^5+t^6
Seifert matrix of 12n_0015
1 1 0 -1 0 1
0 -2 2 1 0 -1
0 0 1 0 0 0
0 1 -1 0 0 0
-1 0 0 0 -1 0
0 -2 1 1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+6t^-1-9+6t-t^2
111
First homology
of the double branched cover of 12n_0015
Z/111
2 2
12n_0016
2

detected by
the signature
1-5t+7t^2-5t^4+7t^6-5t^7+t^8
Seifert matrix of 12n_0016
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 -1 0 0 -1
0 0 0 0 0 1 0 -1
0 0 0 0 -1 0 -1 -1
0 -1 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,t,0,1)
the Blanchfield form on it
t^-3-3t^-2+2t^-1-1+2t-3t^2+t^3
21
First homology
of the double branched cover of 12n_0016
Z/21
-4 4
12n_0017
2

detected by
the Lickorish test
1-8t+22t^2-29t^3+22t^4-8t^5+t^6
Seifert matrix of 12n_0017
1 0 0 0 0 0
-1 -1 0 1 0 1
0 0 1 0 0 0
1 0 1 1 0 0
0 0 0 0 -1 -1
1 0 1 0 0 1
1
Generator of the Alexander module
(0,0,2-t,2-t,3+t-t^2,0)
the Blanchfield form on it
-2t^-2+11t^-1-15+11t-2t^2
91
First homology
of the double branched cover of 12n_0017
Z/91
2 2
12n_0018
1

detected by
an unknotting move
-1+8t-26t^2+39t^3-26t^4+8t^5-t^6
Seifert matrix of 12n_0018
1 0 0 0 0 0
-1 -1 0 1 0 1
0 0 1 0 0 0
1 0 1 -1 0 0
0 0 0 0 1 -1
1 0 1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+5t^-1-9+5t-t^2
109
First homology
of the double branched cover of 12n_0018
Z/109
0 0
12n_0019
1

detected by
an unknotting move
1-3t-t^2+7t^3-t^4-3t^5+t^6
Seifert matrix of 12n_0019
1 0 0 0 0 0
-1 -1 0 1 0 1
0 0 -1 -1 0 -1
1 0 0 0 0 -1
0 0 0 0 -1 -1
1 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,-t,1,1+t,0)
the Blanchfield form on it
-2t^-2+t^-1+7+t-2t^2
1
First homology
of the double branched cover of 12n_0019
0
0 0
12n_0020
1

detected by
an unknotting move
1-5t+11t^2-13t^3+11t^4-5t^5+t^6
Seifert matrix of 12n_0020
1 0 0 0 0 0
0 0 0 -1 0 -1
0 0 1 0 0 0
0 -1 1 -2 0 -2
0 -1 0 -1 -1 -1
-1 0 1 -1 0 0
1
Generator of the Alexander module
(0,0,0,1,1,0)
the Blanchfield form on it
t^-1-2+t
47
First homology
of the double branched cover of 12n_0020
Z/47
2 2
12n_0021
1

detected by
an unknotting move
2-12t+28t^2-35t^3+28t^4-12t^5+2t^6
Seifert matrix of 12n_0021
1 0 0 0 0 0
-1 -2 -1 0 0 -1
0 -1 -2 0 0 0
0 -1 -1 -1 0 0
0 -1 -1 0 -1 0
-1 0 1 1 0 0
1
Generator of the Alexander module
(0,8t-3t^2,0,1-5t+3t^2,9t-8t^2+3t^3,0)
the Blanchfield form on it
-2t^-1+4-2t
119
First homology
of the double branched cover of 12n_0021
Z/119
-2 2
12n_0022
1

detected by
an unknotting move
1-6t+16t^2-29t^3+37t^4-29t^5+16t^6-6t^7+t^8
Seifert matrix of 12n_0022
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 0
0 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 -1 -1
0 0 0 0 1 1 0 1
0 0 0 0 0 1 0 0
-1 0 -1 0 -1 0 -1 0
0 0 0 0 0 1 0 1
1
Generator of the Alexander module
(0,0,0,-1-3t^2+t^3-2t^4+t^5,2+3t^2-t^3+2t^4-t^5,0,-1-t-3t^2-t^3-t^4+t^5,0)
the Blanchfield form on it
x
141
First homology
of the double branched cover of 12n_0022
Z/141
0 0
12n_0023
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 12n_0023
-4 -2
-1 0
1
Generator of the Alexander module
(1-2t,1)
the Blanchfield form on it
-2
9
First homology
of the double branched cover of 12n_0023
Z/9
0 0
12n_0024
1

detected by
an unknotting move
-1+5t-11t^2+15t^3-11t^4+5t^5-t^6
Seifert matrix of 12n_0024
-1 1 0 1 0 1
0 0 0 -1 0 -1
0 0 1 0 0 0
0 -1 -1 -2 0 -2
-1 1 0 1 -1 1
0 0 -1 -1 0 0
1
Generator of the Alexander module
(0,1,0,0,1+t,2)
the Blanchfield form on it
t^-1-2+t
49
First homology
of the double branched cover of 12n_0024
Z/49
0 0
12n_0025
1

detected by
an unknotting move
-1+3t-3t^2+3t^3-t^4
Seifert matrix of 12n_0025
3 1 -1 5
2 1 -1 3
0 0 1 0
6 2 -1 9
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-1-1+t
11
First homology
of the double branched cover of 12n_0025
Z/11
2 2
12n_0026
1

detected by
an unknotting move
-2+10t-22t^2+29t^3-22t^4+10t^5-2t^6
Seifert matrix of 12n_0026
-1 0 0 0 -1 -1
0 -2 1 0 0 -1
0 0 1 0 0 0
0 0 0 0 0 -1
0 0 0 -1 0 -1
0 -1 1 -1 -1 -2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-2t^-1+5-2t
97
First homology
of the double branched cover of 12n_0026
Z/97
0 0
12n_0027
2

detected by
the Lickorish test
-1+6t-16t^2+25t^3-27t^4+25t^5-16t^6+6t^7-t^8
Seifert matrix of 12n_0027
-1 0 -1 -1 -1 0 -1 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 0 0
0 1 -1 -1 -1 0 0 0
0 0 0 -1 -1 1 -1 1
0 1 -1 -1 -1 0 -1 0
0 0 0 0 -1 0 -1 1
1
Generator of the Alexander module
(0,0,0,t,0,1,0,-t)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
123
First homology
of the double branched cover of 12n_0027
Z/123
-2 2
12n_0028
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 12n_0028
-2 1 0 -2
1 0 0 1
-2 1 0 -3
-3 1 -2 -4
1
Generator of the Alexander module
(0,0,1,-1+t)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
33
First homology
of the double branched cover of 12n_0028
Z/33
0 0
12n_0029
1

detected by
an unknotting move
2-12t+28t^2-35t^3+28t^4-12t^5+2t^6
Seifert matrix of 12n_0029
-1 0 0 -1 0 -1
0 -2 1 0 0 -1
0 0 1 0 0 0
0 0 0 0 0 -1
-1 0 0 0 -1 -1
0 -1 1 -1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-1+5-2t
119
First homology
of the double branched cover of 12n_0029
Z/119
-2 2
12n_0030
1

detected by
an unknotting move
1-6t+16t^2-29t^3+37t^4-29t^5+16t^6-6t^7+t^8
Seifert matrix of 12n_0030
-1 0 -1 -1 0 0 -1 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 0 0
0 0 0 0 1 0 -1 0
0 0 0 -1 1 1 -1 1
0 1 -1 -1 0 0 -1 0
0 0 0 -1 1 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,-1,-1,0,0)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
141
First homology
of the double branched cover of 12n_0030
Z/141
0 0
12n_0031
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 12n_0031
-7 -5
-6 -4
1
Generator of the Alexander module
(2-t-2t^2,1-t-2t^2)
the Blanchfield form on it
-2
9
First homology
of the double branched cover of 12n_0031
Z/9
0 0
12n_0032
1

detected by
an unknotting move
-2+10t-22t^2+29t^3-22t^4+10t^5-2t^6
Seifert matrix of 12n_0032
1 0 0 0 0 0
-1 0 1 1 0 -1
1 1 -2 -1 -1 1
1 1 -1 -2 -1 1
1 1 -1 -2 -2 1
-1 0 1 1 0 0
1
Generator of the Alexander module
(0,t,1,0,0,0)
the Blanchfield form on it
2t^-2-8t^-1+12-8t+2t^2
97
First homology
of the double branched cover of 12n_0032
Z/97
0 0
12n_0033
2

detected by
the Lickorish test
-1+6t-16t^2+25t^3-27t^4+25t^5-16t^6+6t^7-t^8
Seifert matrix of 12n_0033
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 -1
0 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1
0 0 0 0 1 1 0 0
0 0 0 0 0 1 0 0
-1 0 -1 0 -1 0 -1 0
-1 0 -1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,1,-1,t,0,0,-1,t)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
123
First homology
of the double branched cover of 12n_0033
Z/123
-2 2
12n_0034
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 12n_0034
2 0 1 0
0 0 1 0
0 1 0 -1
0 1 -1 -2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
33
First homology
of the double branched cover of 12n_0034
Z/33
0 0
12n_0035
1

detected by
an unknotting move
-1+6t-16t^2+23t^3-16t^4+6t^5-t^6
Seifert matrix of 12n_0035
-1 0 0 0 0 -1
0 0 0 0 -1 0
0 0 1 0 0 0
-1 0 0 1 0 0
0 -1 1 0 -2 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+4t^-1-7+4t-t^2
69
First homology
of the double branched cover of 12n_0035
Z/69
0 0
12n_0036
1

detected by
an unknotting move
1-8t+22t^2-29t^3+22t^4-8t^5+t^6
Seifert matrix of 12n_0036
0 2 -1 0 -1 0
1 1 1 0 0 0
0 0 1 0 0 0
0 0 0 -1 0 -1
0 1 -1 0 0 0
1 1 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+6t^-1-9+6t-t^2
91
First homology
of the double branched cover of 12n_0036
Z/91
2 2
12n_0037
2

detected by
the signature
1-5t+8t^2-5t^3+3t^4-5t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0037
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 -1 0
0 -1 -1 0 -1 0 0 0
0 -1 0 0 -1 -1 0 0
0 0 0 0 0 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+2t^-1-1+2t-3t^2+t^3
41
First homology
of the double branched cover of 12n_0037
Z/41
-4 4
12n_0038
1

detected by
an unknotting move
1-6t+16t^2-21t^3+16t^4-6t^5+t^6
Seifert matrix of 12n_0038
0 0 -1 0 1 0
1 1 -1 0 2 0
0 0 1 0 0 0
1 1 0 1 2 0
2 1 -1 0 4 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+4t^-1-7+4t-t^2
67
First homology
of the double branched cover of 12n_0038
Z/67
2 2
12n_0039
1

detected by
an unknotting move
-1+8t-22t^2+31t^3-22t^4+8t^5-t^6
Seifert matrix of 12n_0039
0 2 -1 -1 -1 -1
1 1 1 -1 0 -1
0 0 1 0 0 0
0 0 0 -1 0 -1
0 1 -1 0 0 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1-t,1+t-t^2,0)
the Blanchfield form on it
-t^-2+7t^-1-13+7t-t^2
93
First homology
of the double branched cover of 12n_0039
Z/93
0 0
12n_0040
2

detected by
the Lickorish test
-1+5t-10t^2+11t^3-9t^4+11t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0040
-1 -1 -1 0 -1 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 -1 0 -1 0 0 0
0 -1 0 0 -1 -1 0 0
0 0 0 1 0 0 1 0
0 0 0 1 0 -1 1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,2-t)
the Blanchfield form on it
t^-3-3t^-2+2t^-1-1+2t-3t^2+t^3
63
First homology
of the double branched cover of 12n_0040
Z/63
-2 2
12n_0041
1

detected by
an unknotting move
1-4t+4t^2-t^3+4t^4-4t^5+t^6
Seifert matrix of 12n_0041
1 0 0 0 0 0
-1 0 1 0 -1 0
1 1 -2 1 0 1
-1 -1 1 0 0 0
0 0 0 0 -1 0
-1 -1 1 -1 0 0
1
Generator of the Alexander module
(0,-1-t,t,0,0,1+t^2)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
19
First homology
of the double branched cover of 12n_0041
Z/19
2 2
12n_0042
1

detected by
an unknotting move
1-6t+14t^2-17t^3+14t^4-6t^5+t^6
Seifert matrix of 12n_0042
1 0 0 0 0 0
0 -1 0 0 -1 0
1 0 -2 0 0 1
0 -1 0 -1 -1 0
0 0 0 0 -1 0
-1 -1 1 -1 -1 0
1
Generator of the Alexander module
(0,0,-1,1,0,2)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
59
First homology
of the double branched cover of 12n_0042
Z/59
-2 2
12n_0043
1

detected by
an unknotting move
1-5t+10t^2-15t^3+19t^4-15t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0043
1 0 0 0 0 0 0 0
-1 -1 0 -1 0 0 -1 0
0 0 -1 0 0 0 0 0
-1 0 -1 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 1
-1 0 -1 0 -1 -1 -1 -1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
81
First homology
of the double branched cover of 12n_0043
Z/81
0 0
12n_0044
1

detected by
an unknotting move
1-6t+12t^2-13t^3+12t^4-6t^5+t^6
Seifert matrix of 12n_0044
1 0 0 0 0 0
0 -1 0 0 -1 0
1 0 0 0 0 1
0 -1 0 -1 -1 0
0 0 0 0 -1 0
-1 -1 1 -1 -1 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+2t^-1-2+2t-t^2
51
First homology
of the double branched cover of 12n_0044
Z/51
-2 2
12n_0045
1

detected by
an unknotting move
-1+4t-8t^2+11t^3-8t^4+4t^5-t^6
Seifert matrix of 12n_0045
0 1 -1 0 -1 0
1 -2 1 0 1 0
0 0 1 0 0 0
-1 0 0 -1 0 -1
0 1 -1 0 0 0
-1 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
37
First homology
of the double branched cover of 12n_0045
Z/37
0 0
12n_0046
1

detected by
an unknotting move
2-10t+17t^2-10t^3+2t^4
Seifert matrix of 12n_0046
1 0 0 0
0 -2 0 0
1 0 -2 1
-1 1 1 0
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-1+2-t
41
First homology
of the double branched cover of 12n_0046
Z/41
0 0
12n_0047
1

detected by
an unknotting move
2-9t+13t^2-11t^3+13t^4-9t^5+2t^6
Seifert matrix of 12n_0047
1 0 0 0 0 0
-1 -1 0 -1 -1 0
0 0 -1 0 0 0
-1 0 -1 -1 -1 0
-1 0 -1 0 -1 1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,0,1,1,0,0)
the Blanchfield form on it
-t^-2+2t^-1+2t-t^2
59
First homology
of the double branched cover of 12n_0047
Z/59
-2 2
12n_0048
1

detected by
an unknotting move
2-12t+21t^2-12t^3+2t^4
Seifert matrix of 12n_0048
1 0 0 0
0 -2 0 0
1 0 0 1
-1 1 1 0
1
Generator of the Alexander module
(0,1,-t,-t)
the Blanchfield form on it
t^-1-4+t
49
First homology
of the double branched cover of 12n_0048
Z/49
0 0
12n_0049
1

detected by
an unknotting move
4-20t+33t^2-20t^3+4t^4
Seifert matrix of 12n_0049
1 0 0 0
-1 -5 -4 -7
0 -4 -5 -6
-1 -6 -5 -8
1
Generator of the Alexander module
(0,4-2t+6t^2-4t^3,1+6t^2-4t^3,1+6t^2-4t^3)
the Blanchfield form on it
106t^-2-551t^-1+926-551t+106t^2
81
First homology
of the double branched cover of 12n_0049
Z/81
0 0
12n_0050
1

detected by
an unknotting move
2-11t+23t^2-27t^3+23t^4-11t^5+2t^6
Seifert matrix of 12n_0050
1 0 0 0 0 0
-1 -1 0 0 1 -1
0 0 -1 0 0 0
0 0 0 1 0 0
1 0 1 0 -2 1
-1 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,-1-t-34t^2+12t^3+64t^4-38t^5+44t^6+28t^7-56t^8+16t^9,1+2t+36t^2+26t^3-38t^4+72t^5-64t^6+16t^7,1+t+36t^2-10t^3+8t^4+18t^5-28t^6+8t^7,t+2t^2+37t^3+26t^4-2t^5+26t^6-10t^7-20t^8+8t^9,3+35t^2-46t^3+18t^4+10t^5-46t^6+36t^7-8t^8)
the Blanchfield form on it
x
99
First homology
of the double branched cover of 12n_0050
Z/99
-2 2
12n_0051
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 12n_0051
-11 2
1 0
1
Generator of the Alexander module
(-5+3t+2t^2,1)
the Blanchfield form on it
-1
9
First homology
of the double branched cover of 12n_0051
Z/9
0 0
12n_0052
2

detected by
the Lickorish test
1-9t+30t^2-43t^3+30t^4-9t^5+t^6
Seifert matrix of 12n_0052
1 0 0 0 0 0
-1 -1 0 0 1 -1
0 0 1 0 0 0
0 0 0 1 0 0
1 0 1 0 1 1
-1 0 -1 -1 0 -1
1 or 2
123
First homology
of the double branched cover of 12n_0052
Z/123
2 2
12n_0053
1

detected by
an unknotting move
3-14t+23t^2-14t^3+3t^4
Seifert matrix of 12n_0053
1 0 0 0
1 -2 -1 -3
1 -1 0 -2
2 -2 -2 -5
1
Generator of the Alexander module
(0,1,1,0)
the Blanchfield form on it
t^-1-2+t
57
First homology
of the double branched cover of 12n_0053
Z/57
0 0
12n_0054
2

detected by
the signature
-1+4t-6t^2+7t^3-6t^4+4t^5-t^6
Seifert matrix of 12n_0054
1 0 0 0 0 0
0 0 0 0 -1 -1
0 0 1 0 0 0
1 0 0 1 0 0
0 -1 -1 0 -2 -2
-1 0 -1 -1 -1 0
1
Generator of the Alexander module
(0,0,0,t^2,1+t-t^3,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
29
First homology
of the double branched cover of 12n_0054
Z/29
4 4
12n_0055
2

detected by
the Lickorish test
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 12n_0055
-1 -1 0 -1 0 0
0 -2 1 -4 0 -2
0 0 1 0 0 0
0 -4 2 -6 0 -3
0 -1 0 -1 -1 0
0 -1 1 -2 1 -2
2
111
First homology
of the double branched cover of 12n_0055
Z/111
-2 2
12n_0056
2

detected by
A(F_2)
1-2t+3t^2-2t^3+t^4
Seifert matrix of 12n_0056
-1 1 1 0
0 0 -1 0
0 0 2 -1
-1 0 -1 0
2
9
First homology
of the double branched cover of 12n_0056
Z/9
0 0
12n_0057
2

detected by
A(F_2)
1-2t+3t^2-2t^3+t^4
Seifert matrix of 12n_0057
0 -1 1 0
0 0 1 0
0 1 0 1
1 -1 1 1
2
9
First homology
of the double branched cover of 12n_0057
Z/9
0 0
12n_0058
2

detected by
the signature
-2+13t-30t^2+39t^3-30t^4+13t^5-2t^6
Seifert matrix of 12n_0058
0 3 -1 2 1 1
2 4 1 2 2 2
0 0 1 0 0 0
1 1 1 1 1 1
1 3 0 2 2 2
1 2 0 1 1 2
2
129
First homology
of the double branched cover of 12n_0058
Z/129
4 4
12n_0059
2

detected by
the signature
-1+3t-8t^3+13t^4-8t^5+3t^7-t^8
Seifert matrix of 12n_0059
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 -1 -1 0 0
0 -1 0 -1 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
21
First homology
of the double branched cover of 12n_0059
Z/21
-4 4
12n_0060
2

detected by
the Lickorish test
-1+5t-12t^2+20t^3-23t^4+20t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0060
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 1 1 0 0
0 0 0 0 0 1 0 0
0 -1 0 -1 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
99
First homology
of the double branched cover of 12n_0060
Z/99
-2 2
12n_0061
2

detected by
the Lickorish test
-1+5t-12t^2+20t^3-23t^4+20t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0061
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 -1 -1 0 0
0 -1 0 -1 0 0 1 1
0 0 0 0 0 0 0 1
2
99
First homology
of the double branched cover of 12n_0061
Z/99
-2 2
12n_0062
2

detected by
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0062
-1 0 0 -1 -1 -1
0 -2 1 -1 0 0
0 0 1 0 0 0
0 -1 1 -2 -1 -1
0 0 0 -1 0 0
0 0 0 -1 -1 0
2
81
First homology
of the double branched cover of 12n_0062
Z/81
0 0
12n_0063
2

detected by
the Lickorish test
-3+10t-13t^2+10t^3-3t^4
Seifert matrix of 12n_0063
0 1 0 0
1 0 -1 0
-1 0 7 3
0 1 3 2
2
39
First homology
of the double branched cover of 12n_0063
Z/39
2 2
12n_0064
2

detected by
the signature
1-5t+10t^2-12t^3+13t^4-12t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0064
-1 0 -1 -1 -1 -1 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 -1 -1 0 0
0 1 -1 0 -1 0 0 0
0 1 -1 0 -1 -1 0 0
0 0 0 -1 -1 -1 -1 0
0 0 0 0 0 0 -1 -1
2
69
First homology
of the double branched cover of 12n_0064
Z/69
-4 4
12n_0065
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 12n_0065
-2 -1 -1 -2
-1 0 0 -1
0 0 1 0
-1 0 -1 1
1
Generator of the Alexander module
(-t,0,0,1)
the Blanchfield form on it
t^-1-2+t
31
First homology
of the double branched cover of 12n_0065
Z/31
2 2
12n_0066
2

detected by
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0066
1 0 0 0 0 0
-1 0 1 -1 1 1
1 1 -2 1 -1 -1
-1 0 1 0 1 1
1 1 -1 1 -2 -1
1 1 -1 1 -2 -2
2
81
First homology
of the double branched cover of 12n_0066
Z/81
0 0
12n_0067
3

detected by
the signature
1-5t+8t^2-8t^3+7t^4-8t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0067
1 0 0 0 0 0 0 0
-1 -1 0 0 1 1 1 0
0 0 1 0 0 0 0 0
0 0 0 1 1 1 1 0
1 0 1 0 1 1 0 0
1 0 1 0 0 1 0 0
1 0 1 0 1 1 1 0
0 0 0 1 1 1 1 1
2
51
First homology
of the double branched cover of 12n_0067
Z/51
6 6
12n_0068
3

detected by
the signature
1-5t+7t^2-4t^3+t^4-4t^5+7t^6-5t^7+t^8
Seifert matrix of 12n_0068
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
-1 -1 0 -1 0 0 1 0
0 0 -1 -1 -1 -1 0 0
-1 -1 0 -1 0 -1 1 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 -1
1
Generator of the Alexander module
(0,-2+t+2t^2+4t^3,0,1-t^2-2t^3,0,-2t^2+t^3+2t^4+4t^5,0,t^2-t^4-2t^5)
the Blanchfield form on it
x
35
First homology
of the double branched cover of 12n_0068
Z/35
-6 6
12n_0069
1

detected by
an unknotting move
-1+7t-17t^2+23t^3-17t^4+7t^5-t^6
Seifert matrix of 12n_0069
1 0 0 0 0 1
0 -1 0 0 0 0
0 -1 -2 1 1 0
0 0 1 0 0 1
0 0 1 -1 0 1
0 0 0 0 0 -1
1
Generator of the Alexander module
(2t,0,1-t^2,0,t,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
73
First homology
of the double branched cover of 12n_0069
Z/73
0 0
12n_0070
1

detected by
an unknotting move
1-7t+19t^2-25t^3+19t^4-7t^5+t^6
Seifert matrix of 12n_0070
-1 0 0 0 0 1
0 -1 0 0 0 0
0 -1 -2 -1 -2 -2
0 -1 -1 0 -1 -1
0 -1 -1 -1 -2 -1
0 -1 -1 -1 -1 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
79
First homology
of the double branched cover of 12n_0070
Z/79
-2 2
12n_0071
1

detected by
an unknotting move
1-5t+9t^2-10t^3+9t^4-10t^5+9t^6-5t^7+t^8
Seifert matrix of 12n_0071
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 -1 0 0
0 0 -1 0 -1 -1 0 0
-1 -1 0 0 0 -1 1 0
0 0 0 0 0 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+3t^-1-3+3t-2t^2+t^3
59
First homology
of the double branched cover of 12n_0071
Z/59
-2 2
12n_0072
2

detected by
the signature
-1+9t-23t^2+31t^3-23t^4+9t^5-t^6
Seifert matrix of 12n_0072
-1 0 0 0 0 -1
0 -1 0 0 0 0
0 -1 -2 0 1 0
0 0 0 -1 -1 0
0 0 1 0 0 1
0 0 0 0 0 -1
1
Generator of the Alexander module
(1,0,-1,1,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
97
First homology
of the double branched cover of 12n_0072
Z/97
-4 4
12n_0073
2

detected by
the Lickorish test
1-5t+13t^2-17t^3+13t^4-5t^5+t^6
Seifert matrix of 12n_0073
1 0 0 0 0 0
0 -1 0 0 0 0
0 -1 -2 -2 -1 -2
0 -1 -1 0 -1 -1
0 -1 -1 -1 0 -1
1 -1 -1 -1 -1 0
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-1+1-t
55
First homology
of the double branched cover of 12n_0073
Z/55
2 2
12n_0074
4

detected by
the signature
-2+5t-7t^2+7t^3-7t^4+7t^5-7t^6+5t^7-2t^8
Seifert matrix of 12n_0074
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 1 0
0 0 0 -1 0 0 -1 0
0 0 -1 0 -1 0 1 0
0 0 0 0 0 -1 -1 0
1 1 0 0 0 0 -2 0
0 0 0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,t,0,1,0,-t)
the Blanchfield form on it
-2t^-3+3t^-2-3t^-1+2-3t+3t^2-2t^3
49
First homology
of the double branched cover of 12n_0074
Z/49
-8 8
12n_0075
1

detected by
an unknotting move
3-10t+18t^2-21t^3+18t^4-10t^5+3t^6
Seifert matrix of 12n_0075
1 0 0 0 0 0
0 -1 0 0 0 0
0 -1 -2 0 0 -1
0 0 0 1 0 0
1 0 0 0 1 0
1 0 -1 1 1 1
1
Generator of the Alexander module
(0,0,1-t,0,-t,0)
the Blanchfield form on it
-2t^-2+5t^-1-7+5t-2t^2
83
First homology
of the double branched cover of 12n_0075
Z/83
2 2
12n_0076
2

detected by
the signature
-1+6t-12t^2+15t^3-12t^4+6t^5-t^6
Seifert matrix of 12n_0076
-3 -2 0 0 -2 0
-3 -3 0 0 -2 0
0 0 -1 0 0 -1
-1 -1 0 -1 -1 0
-2 -2 0 0 -1 0
-1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,-t,1,0,0)
the Blanchfield form on it
-t^-2+5t^-1-6+5t-t^2
53
First homology
of the double branched cover of 12n_0076
Z/53
-4 4
12n_0077
3

detected by
the signature
3-7t+8t^2-7t^3+8t^4-7t^5+3t^6
Seifert matrix of 12n_0077
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 0 0 -1
0 0 0 -1 0 1
0 0 -1 0 -1 -1
-1 -1 0 0 0 -3
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
43
First homology
of the double branched cover of 12n_0077
Z/43
-6 6
12n_0078
2

detected by
the Lickorish test
5-16t+23t^2-16t^3+5t^4
Seifert matrix of 12n_0078
2 0 1 -1
0 -1 0 0
1 -1 -2 0
0 0 0 1
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
2t^-2-7t^-1+10-7t+2t^2
65
First homology
of the double branched cover of 12n_0078
Z/65
0 0
12n_0079
1

detected by
an unknotting move
-1+6t-9t^2+6t^3-t^4
Seifert matrix of 12n_0079
-4 -3 -3 0
-4 -4 -3 0
-3 -3 -2 0
-1 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
1
23
First homology
of the double branched cover of 12n_0079
Z/23
-2 2
12n_0080
1

detected by
an unknotting move
2-7t+15t^2-19t^3+15t^4-7t^5+2t^6
Seifert matrix of 12n_0080
-1 -1 -1 0 -1 0
0 0 -1 0 -1 -1
0 -1 0 0 -1 0
0 0 0 1 0 0
0 0 -1 0 0 -1
0 0 0 1 0 2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
4t^-2-11t^-1+15-11t+4t^2
67
First homology
of the double branched cover of 12n_0080
Z/67
2 2
12n_0081
2

detected by
the signature
-2+11t-23t^2+29t^3-23t^4+11t^5-2t^6
Seifert matrix of 12n_0081
-1 -1 -1 0 -1 0
0 -2 -1 0 -2 0
0 -1 0 0 -1 0
0 0 0 -1 0 -1
0 -1 -1 0 -2 0
0 1 0 0 1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
101
First homology
of the double branched cover of 12n_0081
Z/101
-4 4
12n_0082
1

detected by
an unknotting move
2-5t+7t^2-7t^3+7t^4-5t^5+2t^6
Seifert matrix of 12n_0082
-1 -1 -1 0 -1 0
0 0 -1 0 -1 -1
0 -1 -2 0 -1 0
0 0 0 1 0 0
0 0 -1 0 0 -1
0 0 0 1 0 2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
3t^-1-5+3t
35
First homology
of the double branched cover of 12n_0082
Z/35
2 2
12n_0083
2

detected by
the signature
-2+11t-24t^2+31t^3-24t^4+11t^5-2t^6
Seifert matrix of 12n_0083
-1 -1 -1 0 -1 0
0 -1 -1 0 -2 0
0 -1 -2 0 -1 0
0 0 0 -1 0 -1
0 -1 -1 0 -1 0
0 1 0 0 1 -2
1
Generator of the Alexander module
(2,0,0,-t+2t^2,0,1-2t)
the Blanchfield form on it
-6t^-2+25t^-1-32+25t-6t^2
105
First homology
of the double branched cover of 12n_0083
Z/105
-4 4
12n_0084
1

detected by
an unknotting move
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 12n_0084
-1 -1 -1 0 -1 0
0 -1 -1 0 -1 -1
0 -1 -2 0 -1 0
0 0 0 1 0 0
0 0 -1 0 -1 -1
0 0 0 1 0 2
1
Generator of the Alexander module
(-3+2t,0,0,0,-2+t,0)
the Blanchfield form on it
4t^-2-8t^-1+13-8t+4t^2
63
First homology
of the double branched cover of 12n_0084
Z/63
-2 2
12n_0085
2

detected by
the Lickorish test
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 12n_0085
-1 -1 0 -1 -1 -1
0 0 0 -1 -1 -1
0 0 -1 -1 -1 -1
0 -1 0 0 -1 -1
0 -1 0 -1 0 -1
0 -1 0 0 -1 0
1
Generator of the Alexander module
(1,0,-2+t,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
65
First homology
of the double branched cover of 12n_0085
Z/65
0 2
12n_0086
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 12n_0086
-1 -1 0 -1 -1 -1
0 0 0 -1 -1 -1
0 0 1 -1 -1 -1
0 -1 0 -2 -1 -2
0 -1 0 -1 -2 -1
0 -1 0 -1 -1 -2
1
Generator of the Alexander module
(t,0,1,0,1,0)
the Blanchfield form on it
3t^-1-4+3t
103
First homology
of the double branched cover of 12n_0086
Z/103
-2 2
12n_0087
1

detected by
an unknotting move
4-12t+17t^2-12t^3+4t^4
Seifert matrix of 12n_0087
-2 -1 -4 -4
-2 -2 -2 -3
-3 0 -5 -5
-4 -1 -6 -6
1
Generator of the Alexander module
(1,2,0,1)
the Blanchfield form on it
3t^-1-4+3t
49
First homology
of the double branched cover of 12n_0087
Z/49
0 0
12n_0088
3

detected by
the signature
4-14t+26t^2-31t^3+26t^4-14t^5+4t^6
Seifert matrix of 12n_0088
-1 -1 0 -1 -1 -1
0 -2 0 -1 -1 -1
0 0 -1 -1 -1 -1
0 -1 0 -2 -1 -2
0 -1 0 -1 -2 -1
0 -1 0 -1 -1 -2
1
Generator of the Alexander module
(1+2t-2t^3+2t^4-2t^5,0,2t^3-2t^4,0,2t^3-2t^4,0)
the Blanchfield form on it
12t^-2-24t^-1+31-24t+12t^2
119
First homology
of the double branched cover of 12n_0088
Z/119
-6 6
12n_0089
3

detected by
the signature
1-4t+6t^2-7t^3+7t^4-7t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0089
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
43
First homology
of the double branched cover of 12n_0089
Z/43
-6 6
12n_0090
2

detected by
the signature
-1+4t-10t^2+15t^3-17t^4+15t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0090
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 1 0 0 0 0
-1 -1 0 -1 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,t,2t,1,t,t,0,t)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
77
First homology
of the double branched cover of 12n_0090
Z/77
4 4
12n_0091
3

detected by
the signature
-1+6t^2-15t^3+19t^4-15t^5+6t^6-t^8
Seifert matrix of 12n_0091
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,t^2+t^3+t^5,-t+t^2+t^3+t^5,1+t^2+t^4,-t-t^2-t^3-t^4,1+t^2,-2t-2t^3,1-3t+2t^2-2t^3-t^4)
the Blanchfield form on it
x
59
First homology
of the double branched cover of 12n_0091
Z/59
-6 6
12n_0092
1

detected by
an unknotting move
-1+4t-12t^2+23t^3-29t^4+23t^5-12t^6+4t^7-t^8
Seifert matrix of 12n_0092
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
-1 -1 0 -1 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+10t^-1-13+10t-4t^2+t^3
109
First homology
of the double branched cover of 12n_0092
Z/109
0 0
12n_0093
3

detected by
the signature
1-4t+4t^2+t^3-5t^4+t^5+4t^6-4t^7+t^8
Seifert matrix of 12n_0093
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,1,-t,1)
the Blanchfield form on it
t^-3-6t^-2+13t^-1-17+13t-6t^2+t^3
11
First homology
of the double branched cover of 12n_0093
Z/11
-6 6
12n_0094
2

detected by
the signature
-2+9t-16t^2+19t^3-16t^4+9t^5-2t^6
Seifert matrix of 12n_0094
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 1 0 0
0 0 0 0 -1 1
1 1 0 1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
73
First homology
of the double branched cover of 12n_0094
Z/73
-4 4
12n_0095
2

detected by
the Lickorish test
2-9t+22t^2-29t^3+22t^4-9t^5+2t^6
Seifert matrix of 12n_0095
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 1 0 0
0 0 0 0 1 0
1 1 0 1 -1 2
1
Generator of the Alexander module
(0,t,1+t,0,0,-1-t)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
95
First homology
of the double branched cover of 12n_0095
Z/95
2 2
12n_0096
3

detected by
the signature
2-3t+3t^3-3t^5+2t^6
Seifert matrix of 12n_0096
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 -1 1
1 1 0 1 0 -2
1
Generator of the Alexander module
(0,0,1,0,1-2t,0)
the Blanchfield form on it
2t^-2-1+2t^2
7
First homology
of the double branched cover of 12n_0096
Z/7
-6 6
12n_0097
1

detected by
an unknotting move
-1+5t-9t^2+11t^3-9t^4+5t^5-t^6
Seifert matrix of 12n_0097
-1 -1 -1 -1 0 0
0 0 -1 -1 0 0
0 -1 0 -1 0 0
0 0 -1 0 0 0
0 1 0 1 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,-1)
the Blanchfield form on it
-t^-2+2t^-1-3+2t-t^2
41
First homology
of the double branched cover of 12n_0097
Z/41
0 2
12n_0098
2

detected by
the signature
-1+6t-14t^2+17t^3-17t^4+17t^5-14t^6+6t^7-t^8
Seifert matrix of 12n_0098
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 0
0 0 -1 1 0 -1 -1 1
0 0 -1 0 -1 0 -1 0
0 0 0 0 0 -1 0 0
-1 -1 0 0 0 0 -1 0
0 0 -1 0 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
93
First homology
of the double branched cover of 12n_0098
Z/93
-4 4
12n_0099
2

detected by
the Lickorish test
2-12t+32t^2-43t^3+32t^4-12t^5+2t^6
Seifert matrix of 12n_0099
-1 0 1 1 1 0
0 -1 0 0 0 0
0 -2 -6 -3 -3 -4
0 -1 -3 -2 -2 -2
0 -1 -2 -1 0 -1
0 -1 -4 -2 -2 -2
1
Generator of the Alexander module
(3-3t,0,0,0,-t,1)
the Blanchfield form on it
-9t^-2+34t^-1-49+34t-9t^2
135
First homology
of the double branched cover of 12n_0099
Z/135
-2 2
12n_0100
3

detected by
the signature
5-15t+23t^2-25t^3+23t^4-15t^5+5t^6
Seifert matrix of 12n_0100
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 1 1 1
1 1 0 -2 -1 -1
1 1 0 -1 -2 -1
1 1 0 0 -1 -2
1 or 2
111
First homology
of the double branched cover of 12n_0100
Z/111
-6 6
12n_0101
1

detected by
an unknotting move
-1+12t-34t^2+47t^3-34t^4+12t^5-t^6
Seifert matrix of 12n_0101
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 1 1 1
1 1 0 1 0 -1
1 1 0 0 1 0
1 1 0 0 0 1
1 or 2
141
First homology
of the double branched cover of 12n_0101
Z/141
0 0
12n_0102
2

detected by
the signature
-1+4t-4t^2+3t^3-4t^4+4t^5-t^6
Seifert matrix of 12n_0102
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 -1 -1 0 0
1 1 -1 0 -1 0
1 1 -1 1 0 -1
1 or 2
21
First homology
of the double branched cover of 12n_0102
Z/21
-4 4
12n_0103
3

detected by
the signature
1-4t+6t^2-8t^3+9t^4-8t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0103
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
47
First homology
of the double branched cover of 12n_0103
Z/47
-6 6
12n_0104
2

detected by
the signature
-1+4t-10t^2+14t^3-15t^4+14t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0104
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 0 1 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
73
First homology
of the double branched cover of 12n_0104
Z/73
4 4
12n_0105
3

detected by
the signature
-1+4t^2-8t^3+9t^4-8t^5+4t^6-t^8
Seifert matrix of 12n_0105
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,-t,1,-t,-t)
the Blanchfield form on it
-t^-3+4t^-1-7+4t-t^3
31
First homology
of the double branched cover of 12n_0105
Z/31
-6 6
12n_0106
1

detected by
an unknotting move
-1+4t-10t^2+16t^3-19t^4+16t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0106
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 0 1 0 1 1
1
Generator of the Alexander module
(0,0,1+t-t^2,0,1+t^2-t^3,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+7t^-1-9+7t-3t^2+t^3
81
First homology
of the double branched cover of 12n_0106
Z/81
0 0
12n_0107
3

detected by
the signature
1-4t+6t^2-6t^3+5t^4-6t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0107
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,-1-t^2,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+3t^-1-3+3t-3t^2+t^3
39
First homology
of the double branched cover of 12n_0107
Z/39
-6 6
12n_0108
2

detected by
the signature
-2+9t-15t^2+17t^3-15t^4+9t^5-2t^6
Seifert matrix of 12n_0108
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 1 0 0
0 0 0 0 -2 1
-1 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-10+9t-5t^2+t^3
69
First homology
of the double branched cover of 12n_0108
Z/69
-4 4
12n_0109
2

detected by
the Lickorish test
2-9t+23t^2-31t^3+23t^4-9t^5+2t^6
Seifert matrix of 12n_0109
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 1 0 0
0 0 0 0 2 0
-1 -1 0 -1 -1 1
1
Generator of the Alexander module
(0,0,-t,0,1,t)
the Blanchfield form on it
-t^-2+3t^-1-6+3t-t^2
99
First homology
of the double branched cover of 12n_0109
Z/99
2 2
12n_0110
2

detected by
the signature
2-t-7t^2+13t^3-7t^4-t^5+2t^6
Seifert matrix of 12n_0110
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 -2 1
-1 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,-1,0,1-2t,0)
the Blanchfield form on it
t^-2+t^-1-2+t+t^2
21
First homology
of the double branched cover of 12n_0110
Z/21
-4 4
12n_0111
1

detected by
an unknotting move
2-9t+21t^2-27t^3+21t^4-9t^5+2t^6
Seifert matrix of 12n_0111
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 2 0
-1 -1 0 -1 -1 1
1
Generator of the Alexander module
(0,t,t+t^2,0,1+t,t+t^2)
the Blanchfield form on it
2t^-2-7t^-1+11-7t+2t^2
91
First homology
of the double branched cover of 12n_0111
Z/91
-2 2
12n_0112
2

detected by
the signature
-2+9t-17t^2+21t^3-17t^4+9t^5-2t^6
Seifert matrix of 12n_0112
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 0
0 0 0 -1 0 0
0 0 0 0 -2 1
-1 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-14+11t-5t^2+t^3
77
First homology
of the double branched cover of 12n_0112
Z/77
-4 4
12n_0113
2

detected by
the signature
1-3t+7t^2-10t^3+11t^4-10t^5+7t^6-3t^7+t^8
Seifert matrix of 12n_0113
-1 -1 -1 0 0 -1 0 0
0 0 -1 1 1 -1 1 1
0 -1 0 0 0 -1 0 0
0 0 0 1 0 0 1 0
0 0 0 1 1 0 1 1
0 0 -1 1 1 0 1 1
0 0 0 0 0 0 1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(-1+t,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
53
First homology
of the double branched cover of 12n_0113
Z/53
4 4
12n_0114
3

detected by
the signature
1-5t+9t^2-12t^3+13t^4-12t^5+9t^6-5t^7+t^8
Seifert matrix of 12n_0114
-1 -1 -1 0 0 -1 0 0
0 -2 -1 0 0 -2 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 -1 -1 -1 0 -1
0 -1 0 0 -1 -1 0 0
0 -1 -1 0 0 -2 0 0
0 -1 0 -1 -1 -1 -1 -1
0 -1 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-11+9t-5t^2+t^3
67
First homology
of the double branched cover of 12n_0114
Z/67
-6 6
12n_0115
1

detected by
an unknotting move
1-t-t^2+4t^3-5t^4+4t^5-t^6-t^7+t^8
Seifert matrix of 12n_0115
-1 -1 -1 0 0 -1 0 0
0 0 -1 1 1 -1 1 1
0 -1 -2 0 0 -1 0 0
0 0 0 1 0 0 1 0
0 0 0 1 1 0 1 1
0 0 -1 1 1 0 1 1
0 0 0 0 0 0 1 0
0 0 0 1 0 0 1 1
1
Generator of the Alexander module
(t,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-1-2+t
11
First homology
of the double branched cover of 12n_0115
Z/11
2 2
12n_0116
1

detected by
an unknotting move
2-7t+16t^2-21t^3+16t^4-7t^5+2t^6
Seifert matrix of 12n_0116
-1 -1 -1 0 0 -1
0 0 -1 -1 1 -1
0 -1 0 0 0 -1
0 0 0 2 0 0
0 0 0 -1 1 0
0 0 -1 -1 1 0
1
Generator of the Alexander module
(-2+t-t^2,0,-t^2,1+t,-t,t)
the Blanchfield form on it
2t^-2-7t^-1+10-7t+2t^2
71
First homology
of the double branched cover of 12n_0116
Z/71
2 2
12n_0117
2

detected by
the signature
-2+11t-22t^2+27t^3-22t^4+11t^5-2t^6
Seifert matrix of 12n_0117
-1 -1 -1 0 0 -1
0 -2 -1 0 0 -2
0 -1 0 0 0 -1
0 1 0 -2 1 1
0 -1 0 0 -1 -1
0 -1 -1 0 0 -2
1
Generator of the Alexander module
(-4+3t-24t^2-23t^3-32t^4+19t^5-10t^6+40t^7,0,-20t^2-54t^3-58t^4-50t^5-40t^6,1+8t+5t^2+11t^3+16t^4+64t^5+20t^6+80t^7,4t+9t^2+20t^3+21t^4+20t^5,4+13t+17t^2+9t^3+20t^4)
the Blanchfield form on it
x
97
First homology
of the double branched cover of 12n_0117
Z/97
-4 4
12n_0118
1

detected by
an unknotting move
2-3t+3t^3-3t^5+2t^6
Seifert matrix of 12n_0118
-1 -1 -1 0 0 -1
0 0 -1 -1 1 -1
0 -1 -2 0 0 -1
0 0 0 2 0 0
0 0 0 -1 1 0
0 0 -1 -1 1 0
1
Generator of the Alexander module
(t,0,-t,1,0,0)
the Blanchfield form on it
2t^-2+t^-1-4+t+2t^2
7
First homology
of the double branched cover of 12n_0118
Z/7
2 2
12n_0119
2

detected by
the signature
-1+3t-3t^2+3t^3-3t^4+3t^5-t^6
Seifert matrix of 12n_0119
-1 -1 0 -1 0 0
0 0 0 -1 0 0
0 0 -1 -1 0 0
0 -1 0 0 0 0
0 0 0 1 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
17
First homology
of the double branched cover of 12n_0119
Z/17
-4 4
12n_0120
1

detected by
an unknotting move
1-2t+4t^2-5t^3+4t^4-2t^5+t^6
Seifert matrix of 12n_0120
-1 -1 0 1 0 0
0 0 0 1 0 0
0 0 1 0 0 1
0 1 -1 1 1 -1
0 0 0 0 1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(-1,0,0,2,0,0)
the Blanchfield form on it
t^-2-5t^-1+7-5t+t^2
19
First homology
of the double branched cover of 12n_0120
Z/19
2 2
12n_0121
1

detected by
an unknotting move
1-t^2+t^4
Seifert matrix of 12n_0121
-1 -1 0 -1
0 0 0 -1
0 0 1 0
0 -1 -1 2
1
Generator of the Alexander module
(1,0,0,1)
the Blanchfield form on it
t^-1-2+t
1
First homology
of the double branched cover of 12n_0121
0
0 2
12n_0122
1

detected by
an unknotting move
1-6t+14t^2-21t^3+23t^4-21t^5+14t^6-6t^7+t^8
Seifert matrix of 12n_0122
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 1 0 0
0 0 -1 -1 0 0 -1 0
0 0 0 0 1 0 -1 0
0 0 0 0 0 1 0 1
-1 -1 -1 0 0 1 -1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,t+2t^2,0,-1-t,t+t^2,-1-t,0,0)
the Blanchfield form on it
t^-3-6t^-2+14t^-1-19+14t-6t^2+t^3
107
First homology
of the double branched cover of 12n_0122
Z/107
-2 2
12n_0123
2

detected by
the signature
-2+14t-34t^2+45t^3-34t^4+14t^5-2t^6
Seifert matrix of 12n_0123
-2 -1 0 -1 -1 0
-2 -2 0 -1 -1 0
1 1 0 0 0 1
-1 -1 -1 -2 -1 0
-1 -1 0 -1 -2 0
-1 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-4t^-2+13t^-1-18+13t-4t^2
145
First homology
of the double branched cover of 12n_0123
Z/145
-4 4
12n_0124
1

detected by
an unknotting move
2-3t+2t^2
Seifert matrix of 12n_0124
1 1
0 2
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
-1
7
First homology
of the double branched cover of 12n_0124
Z/7
2 2
12n_0125
2

detected by
the signature
-1+6t-14t^2+17t^3-17t^4+17t^5-14t^6+6t^7-t^8
Seifert matrix of 12n_0125
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 1
0 0 -1 -1 0 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
-1 -1 -1 0 1 0 -1 1
0 0 0 0 1 -1 0 1
1
Generator of the Alexander module
(0,0,-t,-t,1,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+4t^-1-4+4t-4t^2+t^3
93
First homology
of the double branched cover of 12n_0125
Z/93
-4 4
12n_0126
2

detected by
the Lickorish test
2-12t+32t^2-43t^3+32t^4-12t^5+2t^6
Seifert matrix of 12n_0126
-2 -1 0 -1 -1 1
-2 -2 0 -1 -1 1
0 0 0 -1 -1 0
-1 -1 -1 -2 -1 1
0 0 0 0 -1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(-3+2t-3t^2+2t^3,0,-4-7t+6t^2,-2-2t+2t^2,2+2t-2t^2,0)
the Blanchfield form on it
288t^-2-1102t^-1+1623-1102t+288t^2
135
First homology
of the double branched cover of 12n_0126
Z/135
-2 2
12n_0127
1

detected by
an unknotting move
1-6t+14t^2-21t^3+23t^4-21t^5+14t^6-6t^7+t^8
Seifert matrix of 12n_0127
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 -1
0 0 -1 1 0 1 0 -1
0 0 -1 0 -1 0 0 -1
0 0 -1 0 0 1 0 0
0 0 0 0 0 0 1 -1
-1 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,t,1,-1,0,1)
the Blanchfield form on it
-t^-3+4t^-2-6t^-1+6-6t+4t^2-t^3
107
First homology
of the double branched cover of 12n_0127
Z/107
-2 2
12n_0128
2

detected by
the signature
-2+14t-34t^2+45t^3-34t^4+14t^5-2t^6
Seifert matrix of 12n_0128
-2 -1 0 0 0 0
-2 -2 0 0 0 0
0 0 2 1 0 0
0 0 1 0 0 0
0 0 1 1 -1 0
-1 -1 -2 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0,2,-1)
the Blanchfield form on it
-2t^-2+10t^-1-14+10t-2t^2
145
First homology
of the double branched cover of 12n_0128
Z/145
-4 4
12n_0129
1

detected by
an unknotting move
2-3t+2t^2
Seifert matrix of 12n_0129
4 9
10 23
1
Generator of the Alexander module
(1,3)
the Blanchfield form on it
-1
7
First homology
of the double branched cover of 12n_0129
Z/7
2 2
12n_0130
2

detected by
the Lickorish test
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 12n_0130
-1 -1 -1 -1 0 -1
0 0 -1 -1 0 -1
0 -1 0 0 0 -1
0 -1 -1 0 0 -1
0 0 -1 -1 -1 -1
0 -1 -1 -1 0 0
1
Generator of the Alexander module
(1,0,0,0,-2+t,0)
the Blanchfield form on it
2t^-1-3+2t
65
First homology
of the double branched cover of 12n_0130
Z/65
0 2
12n_0131
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 12n_0131
-1 -1 -1 -1 0 -1
0 0 -1 -1 0 -1
0 -1 -2 -1 0 -1
0 -1 -2 -2 0 -1
0 0 -1 -1 1 -1
0 -1 -1 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,2-t,0)
the Blanchfield form on it
-2t^-1+3-2t
103
First homology
of the double branched cover of 12n_0131
Z/103
-2 2
12n_0132
1

detected by
an unknotting move
4-12t+17t^2-12t^3+4t^4
Seifert matrix of 12n_0132
-5 0 -3 -5
-2 -2 -2 -3
-4 -1 -2 -4
-6 -1 -4 -6
1
Generator of the Alexander module
(0,2,1,1)
the Blanchfield form on it
3t^-1-4+3t
49
First homology
of the double branched cover of 12n_0132
Z/49
0 0
12n_0133
3

detected by
the signature
4-14t+26t^2-31t^3+26t^4-14t^5+4t^6
Seifert matrix of 12n_0133
-1 -1 -1 -1 0 -1
0 -2 -1 -1 0 -1
0 -1 -2 -1 0 -1
0 -1 -2 -2 0 -1
0 0 -1 -1 -1 -1
0 -1 -1 -1 0 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-3t^-3+12t^-2-23t^-1+28-23t+12t^2-3t^3
119
First homology
of the double branched cover of 12n_0133
Z/119
-6 6
12n_0134
3

detected by
the signature
1-4t+6t^2-7t^3+7t^4-7t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0134
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,-1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+t^-1-1+t-t^2
43
First homology
of the double branched cover of 12n_0134
Z/43
-6 6
12n_0135
2

detected by
the signature
-1+4t-10t^2+15t^3-17t^4+15t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0135
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
77
First homology
of the double branched cover of 12n_0135
Z/77
4 4
12n_0136
3

detected by
the signature
-1+6t^2-15t^3+19t^4-15t^5+6t^6-t^8
Seifert matrix of 12n_0136
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,t^2,1+t^2,t,-t^2,t+t^2,-t,0)
the Blanchfield form on it
-t^-3-t^-2+3t^-1-5+3t-t^2-t^3
59
First homology
of the double branched cover of 12n_0136
Z/59
-6 6
12n_0137
1

detected by
an unknotting move
-1+4t-12t^2+23t^3-29t^4+23t^5-12t^6+4t^7-t^8
Seifert matrix of 12n_0137
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 0 -1 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,-1+t-2t^2+t^3,0,0,-2+2t^4-t^5,0,0)
the Blanchfield form on it
109
First homology
of the double branched cover of 12n_0137
Z/109
0 0
12n_0138
3

detected by
the signature
1-4t+4t^2+t^3-5t^4+t^5+4t^6-4t^7+t^8
Seifert matrix of 12n_0138
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 -1 0 -1
-1 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-3-6t^-2+13t^-1-17+13t-6t^2+t^3
11
First homology
of the double branched cover of 12n_0138
Z/11
-6 6
12n_0139
2

detected by
the signature
-1+5t-11t^2+12t^3-11t^4+12t^5-11t^6+5t^7-t^8
Seifert matrix of 12n_0139
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 -1
-1 -1 0 -1 0 0 1 0
0 0 -1 -1 -1 0 0 -1
0 0 -1 0 0 1 0 -1
0 0 0 0 0 0 1 0
-1 -1 0 -1 0 0 1 -1
1 or 2
69
First homology
of the double branched cover of 12n_0139
Z/69
-4 4
12n_0140
1

detected by
an unknotting move
1-9t+27t^2-37t^3+27t^4-9t^5+t^6
Seifert matrix of 12n_0140
-2 -1 0 -1 0 1
-2 -2 0 -1 0 1
0 0 2 -1 1 2
-1 -1 0 0 0 1
0 0 1 0 0 1
0 0 0 0 0 -1
1
Generator of the Alexander module
(1,1,2,0,0,0)
the Blanchfield form on it
-t^-1+2-t
111
First homology
of the double branched cover of 12n_0140
Z/111
-2 2
12n_0141
1

detected by
an unknotting move
-1+5t-13t^2+19t^3-13t^4+5t^5-t^6
Seifert matrix of 12n_0141
-2 -1 -1 -1 0 -1
-2 -2 -1 -1 0 -1
0 0 -1 0 0 -1
-1 -1 -1 0 0 -1
1 1 0 1 1 1
-1 -1 -1 -1 0 0
1
Generator of the Alexander module
(0,0,2,0,1,2)
the Blanchfield form on it
-3t^-2+8t^-1-7+8t-3t^2
57
First homology
of the double branched cover of 12n_0141
Z/57
0 0
12n_0142
1

detected by
an unknotting move
1-5t+10t^2-11t^3+10t^4-5t^5+t^6
Seifert matrix of 12n_0142
2 1 0 0 -1 0
1 0 0 0 -1 0
0 1 -1 0 0 1
1 1 0 1 -1 1
0 0 0 0 -1 0
1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-10t^-1+17-10t+2t^2
43
First homology
of the double branched cover of 12n_0142
Z/43
-2 2
12n_0143
2

detected by
the signature
-1+3t-2t^2+t^3-2t^4+3t^5-t^6
Seifert matrix of 12n_0143
-1 0 0 0 0 -1
0 0 0 -1 -1 0
0 1 -1 1 0 0
0 -1 0 0 0 0
0 0 0 0 -1 0
0 0 0 1 0 -1
1
Generator of the Alexander module
(1,0,-t,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
13
First homology
of the double branched cover of 12n_0143
Z/13
-4 4
12n_0144
2

detected by
the Lickorish test
1-7t+18t^2-23t^3+18t^4-7t^5+t^6
Seifert matrix of 12n_0144
2 1 0 0 1 0
1 0 0 0 1 0
0 1 1 0 0 1
1 1 0 1 1 1
0 0 0 0 1 0
1 0 0 0 1 -1
2
75
First homology
of the double branched cover of 12n_0144
Z/75
2 2
12n_0145
2

detected by
the Lickorish test
1-6t+11t^2-6t^3+t^4
Seifert matrix of 12n_0145
3 2 0 1
2 1 0 1
0 1 1 1
2 1 0 0
2
25
First homology
of the double branched cover of 12n_0145
Z/25
0 0
12n_0146
1

detected by
an unknotting move
-2+12t-19t^2+12t^3-2t^4
Seifert matrix of 12n_0146
0 -1 0 0
0 5 2 0
1 3 2 1
0 0 0 1
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
-1
47
First homology
of the double branched cover of 12n_0146
Z/47
2 2
12n_0147
3

detected by
the new u==2 criterion
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 12n_0147
-1 0 0 0 0 -1
0 2 0 0 0 0
0 0 -1 0 -1 0
0 1 0 1 0 0
0 1 0 0 -1 0
0 -1 0 0 -1 -1
2
75
First homology
of the double branched cover of 12n_0147
Z/15+Z/5
-2 2
12n_0148
2

detected by
the signature
1+t-5t^2+7t^3-5t^4+t^5+t^6
Seifert matrix of 12n_0148
1 0 0 0 0 0
1 1 0 0 -1 0
0 0 1 0 1 0
1 0 0 1 0 0
1 0 0 0 1 0
0 0 1 0 1 1
1 or 2
17
First homology
of the double branched cover of 12n_0148
Z/17
4 4
12n_0149
2

detected by
the signature
2-t-t^2-t^3+2t^4
Seifert matrix of 12n_0149
1 0 0 0
1 1 1 0
-1 0 2 0
1 0 0 1
1
Generator of the Alexander module
(0,-t+t^2,1-t,1+t-t^2)
the Blanchfield form on it
11t^-2-6t^-1-6-6t+11t^2
5
First homology
of the double branched cover of 12n_0149
Z/5
4 4
12n_0150
2

detected by
the signature
-1+5t-10t^2+9t^3-7t^4+9t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0150
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 0
0 0 0 1 0 0 -1 0
0 0 0 0 -1 0 0 0
0 0 -1 0 0 -1 -1 0
-1 -1 0 0 0 0 -1 0
0 0 0 1 1 0 -1 1
1
Generator of the Alexander module
(0,-1+3t-t^2+2t^3-3t^4+2t^5,1-t+t^3,1-t^2+t^3,1+2t-3t^2+2t^3,-1-t^2-t^3+2t^4-2t^5,0,-1+t-4t^2+4t^3-2t^4)
the Blanchfield form on it
x
57
First homology
of the double branched cover of 12n_0150
Z/57
-4 4
12n_0151
2

detected by
the Lickorish test
1-8t+24t^2-33t^3+24t^4-8t^5+t^6
Seifert matrix of 12n_0151
-1 0 0 0 1 -1
0 -1 0 0 0 0
0 -1 -2 0 0 1
-1 0 0 -1 0 -1
0 0 0 0 1 0
0 0 1 0 0 0
1
Generator of the Alexander module
(0,0,1-3t+t^2,3-2t+3t^2-t^3,0,1-3t+t^2)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
99
First homology
of the double branched cover of 12n_0151
Z/99
-2 2
12n_0152
1

detected by
an unknotting move
-1+6t-16t^2+23t^3-16t^4+6t^5-t^6
Seifert matrix of 12n_0152
1 0 0 1 1 0
0 -1 0 0 0 0
0 -1 -2 -2 0 -1
0 -1 -1 0 0 -1
0 0 0 0 -1 0
0 -1 -1 -1 0 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-1
69
First homology
of the double branched cover of 12n_0152
Z/69
0 0
12n_0153
4

detected by
the signature
-2+4t-3t^2-t^3+3t^4-t^5-3t^6+4t^7-2t^8
Seifert matrix of 12n_0153
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 -1 1
-1 -1 0 -1 0 0 0 1
0 0 0 0 -1 0 0 -1
0 0 -1 -1 0 -1 -1 1
-1 -1 0 -1 0 0 -1 1
1 1 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+t^-2-1+t^2-t^3
13
First homology
of the double branched cover of 12n_0153
Z/13
-8 8
12n_0154
1

detected by
an unknotting move
2-6t+10t^2-11t^3+10t^4-6t^5+2t^6
Seifert matrix of 12n_0154
1 0 -1 0 1 0
0 -1 0 0 0 0
-1 -1 -2 1 0 1
1 0 1 0 0 0
0 0 0 0 1 0
1 0 1 -1 0 0
1
Generator of the Alexander module
(0,0,-1,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+7t^-1-8+7t-4t^2+t^3
47
First homology
of the double branched cover of 12n_0154
Z/47
2 2
12n_0155
2

detected by
the signature
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 12n_0155
-3 -2 -2 -2 0 -2
-3 -3 -2 -2 0 -2
-1 -1 -2 -2 0 -1
-1 -1 -1 -2 0 -1
-1 -1 -1 -1 -1 -1
-2 -2 -2 -2 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
89
First homology
of the double branched cover of 12n_0155
Z/89
-4 4
12n_0156
2

detected by
the signature
-1+5t-8t^2+3t^3+t^4+3t^5-8t^6+5t^7-t^8
Seifert matrix of 12n_0156
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 -1 -1
0 0 0 1 0 0 -1 0
0 0 0 0 1 0 0 -1
0 0 -1 0 0 -1 -1 -1
-1 -1 0 0 0 0 -1 -1
-1 -1 0 0 0 0 0 -1
1 or 2
33
First homology
of the double branched cover of 12n_0156
Z/33
-4 4
12n_0157
2

detected by
the Lickorish test
1-6t+18t^2-25t^3+18t^4-6t^5+t^6
Seifert matrix of 12n_0157
0 0 1 0 0 0
0 -1 0 0 0 0
1 -1 -2 0 0 1
0 0 0 -1 0 -1
-1 0 0 0 -1 0
-1 0 1 0 0 0
1 or 2
75
First homology
of the double branched cover of 12n_0157
Z/75
-2 2
12n_0158
1

detected by
an unknotting move
-1+8t-22t^2+31t^3-22t^4+8t^5-t^6
Seifert matrix of 12n_0158
-2 -1 -1 0 0 -1
-2 -2 -1 0 0 -1
0 0 -1 0 0 0
1 1 1 1 1 1
-1 -1 -1 0 1 -1
-1 -1 -1 0 0 0
1
Generator of the Alexander module
(-t^2,t,0,-2-t^2,t^2,-1)
the Blanchfield form on it
57t^-2-220t^-1+314-220t+57t^2
93
First homology
of the double branched cover of 12n_0158
Z/93
0 0
12n_0159
1

detected by
an unknotting move
2-6t+12t^2-15t^3+12t^4-6t^5+2t^6
Seifert matrix of 12n_0159
-1 -1 -1 -1 1 0
0 0 -1 -1 1 0
0 -1 0 -1 1 0
0 0 -1 0 1 0
0 0 1 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
4t^-2-10t^-1+13-10t+4t^2
55
First homology
of the double branched cover of 12n_0159
Z/55
2 2
12n_0160
1

detected by
an unknotting move
-1+6t-12t^2+15t^3-12t^4+6t^5-t^6
Seifert matrix of 12n_0160
-1 -1 0 -1 -1 0
0 0 0 -1 -1 0
0 0 1 0 0 -1
0 -1 0 0 -1 0
0 0 0 -1 0 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-2t^-2+11t^-1-17+11t-2t^2
53
First homology
of the double branched cover of 12n_0160
Z/53
0 2
12n_0161
2

detected by
the Lickorish test
1-8t+22t^2-29t^3+22t^4-8t^5+t^6
Seifert matrix of 12n_0161
-1 -1 0 -1 -1 0
0 -2 0 -1 -2 0
0 0 -1 0 0 -1
0 -1 0 0 -1 0
0 -1 0 -1 -2 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(2-t,0,-3+t,0,0,0)
the Blanchfield form on it
-t^-2+5t^-1-6+5t-t^2
91
First homology
of the double branched cover of 12n_0161
Z/91
-2 2
12n_0162
1

detected by
an unknotting move
-1+6t-14t^2+19t^3-14t^4+6t^5-t^6
Seifert matrix of 12n_0162
-1 -1 0 -1 -1 0
0 0 0 -1 -1 0
0 0 1 0 0 -1
0 -1 0 -2 -1 0
0 0 0 -1 0 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-1+3-t
61
First homology
of the double branched cover of 12n_0162
Z/61
0 0
12n_0163
3

detected by
the signature
1-5t+8t^2-7t^3+5t^4-7t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0163
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 -1 0 0
0 0 -1 0 -1 -1 0 0
-1 -1 0 0 0 -1 0 0
0 0 0 -1 0 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-3-3t^-2+2t^-1-1+2t-3t^2+t^3
47
First homology
of the double branched cover of 12n_0163
Z/47
-6 6
12n_0164
2

detected by
the Lickorish test
-1+8t-20t^2+27t^3-20t^4+8t^5-t^6
Seifert matrix of 12n_0164
1 0 0 0 0 0
0 -1 0 0 0 0
0 -1 -2 0 1 0
0 0 0 -1 -1 0
0 0 1 0 0 0
1 0 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-2t^-1+3-2t
85
First homology
of the double branched cover of 12n_0164
Z/85
0 0
12n_0165
1

detected by
an unknotting move
1-6t+16t^2-21t^3+16t^4-6t^5+t^6
Seifert matrix of 12n_0165
-1 0 0 -1 0 0
0 -1 0 0 0 0
0 -1 -2 -4 -1 -2
0 -2 -2 -3 -2 -1
0 -1 -1 -2 0 -1
0 -1 -1 0 -1 0
1
Generator of the Alexander module
(-t,0,0,1,0,0)
the Blanchfield form on it
t^-2-4t^-1+7-4t+t^2
67
First homology
of the double branched cover of 12n_0165
Z/67
-2 2
12n_0166
4

detected by
the signature
-2+4t-5t^2+6t^3-7t^4+6t^5-5t^6+4t^7-2t^8
Seifert matrix of 12n_0166
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 0 -1 0 0 -1 0 1
0 0 0 0 -1 0 -1 -1
1 1 0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+4t^-2-4t^-1+3-4t+4t^2-2t^3
41
First homology
of the double branched cover of 12n_0166
Z/41
-8 8
12n_0167
1

detected by
an unknotting move
3-9t+14t^2-15t^3+14t^4-9t^5+3t^6
Seifert matrix of 12n_0167
1 0 -1 1 1 1
0 -1 0 0 0 0
-1 -1 -2 0 0 0
0 0 0 1 0 0
0 0 0 1 1 1
0 0 0 1 0 1
1
Generator of the Alexander module
(-2+t,0,-3+2t,0,0,0)
the Blanchfield form on it
3t^-2-4t^-1+4-4t+3t^2
67
First homology
of the double branched cover of 12n_0167
Z/67
2 2
12n_0168
2

detected by
the signature
-1+5t-8t^2+9t^3-8t^4+5t^5-t^6
Seifert matrix of 12n_0168
-3 -2 0 0 0 -2
-3 -3 0 0 0 -2
0 0 -1 0 -1 0
0 0 -1 -1 -1 0
-1 -1 0 0 -1 -1
-2 -2 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
37
First homology
of the double branched cover of 12n_0168
Z/37
-4 4
12n_0169
3

detected by
the signature
4-9t+9t^2-7t^3+9t^4-9t^5+4t^6
Seifert matrix of 12n_0169
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 0 0 1
0 0 -1 -1 0 1
0 0 0 0 -2 0
1 1 0 0 -1 -2
1
Generator of the Alexander module
(0,-1,1+t,1,0,0)
the Blanchfield form on it
4t^-2-5t^-1+4-5t+4t^2
51
First homology
of the double branched cover of 12n_0169
Z/51
-6 6
12n_0170
1

detected by
an unknotting move
6-20t+29t^2-20t^3+6t^4
Seifert matrix of 12n_0170
1 0 -1 0
0 -1 0 0
-1 -1 -2 0
1 0 0 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
3t^-2-11t^-1+16-11t+3t^2
81
First homology
of the double branched cover of 12n_0170
Z/81
0 0
12n_0171
2

detected by
the Lickorish test
-2+10t-15t^2+10t^3-2t^4
Seifert matrix of 12n_0171
-9 -8 -4 -8
-9 -9 -4 -8
-3 -3 -2 -3
-8 -8 -4 -7
1
Generator of the Alexander module
(2,2,1,2)
the Blanchfield form on it
t^-2-5t^-1+8-5t+t^2
39
First homology
of the double branched cover of 12n_0171
Z/39
-2 2
12n_0172
3

detected by
the signature
1-5t+6t^2-t^3-3t^4-t^5+6t^6-5t^7+t^8
Seifert matrix of 12n_0172
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 -1 0
0 0 0 -1 0 0 0 0
-1 -1 0 0 -1 0 0 0
0 0 -1 0 -1 -1 -1 0
-1 -1 0 0 -1 0 -1 0
0 0 0 -1 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,1)
the Blanchfield form on it
-t^-3+t^-2-1+t^2-t^3
23
First homology
of the double branched cover of 12n_0172
Z/23
-6 6
12n_0173
2

detected by
the Lickorish test
1-6t+16t^2-25t^3+27t^4-25t^5+16t^6-6t^7+t^8
Seifert matrix of 12n_0173
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 -1 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 0 -1 -1 0
0 0 -1 0 1 0 -1 1
1
Generator of the Alexander module
(0,0,0,0,1+t,1+t,0,-t)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
123
First homology
of the double branched cover of 12n_0173
Z/123
-2 2
12n_0174
2

detected by
the Lickorish test
-1+6t-18t^2+35t^3-45t^4+35t^5-18t^6+6t^7-t^8
Seifert matrix of 12n_0174
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 1 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 -1 -1
-1 -1 1 -1 0 1 1 0
0 0 0 0 0 0 1 0
0 0 -1 0 0 0 -1 -1
1 or 2
165
First homology
of the double branched cover of 12n_0174
Z/165
0 0
12n_0175
1

detected by
an unknotting move
-1+4t-4t^2-5t^3+11t^4-5t^5-4t^6+4t^7-t^8
Seifert matrix of 12n_0175
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 -1 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 0 -1 -1 0
0 0 -1 0 1 0 -1 1
1
Generator of the Alexander module
(0,-4t-8t^3+13t^4-2t^5-3t^6+t^7,-4t-6t^2-14t^3+26t^4-4t^5-6t^6+2t^7,-2-3t-7t^2+13t^3-2t^4-3t^5+t^6,2+2t+7t^2-13t^3+15t^4-4t^5-11t^6+9t^7-2t^8,0,-1-3t-5t^2+2t^3+11t^4-9t^5+2t^6,1+t+t^2-10t^3-t^4+15t^5-10t^6+2t^7)
the Blanchfield form on it
x
3
First homology
of the double branched cover of 12n_0175
Z/3
-2 2
12n_0176
1

detected by
an unknotting move
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 12n_0176
-3 -2 -1 -2
-3 -3 -1 -2
-2 -2 0 -2
-2 -2 -1 -3
1 or 2
63
First homology
of the double branched cover of 12n_0176
Z/63
-2 2
12n_0177
3

detected by
the signature
4-11t+16t^2-17t^3+16t^4-11t^5+4t^6
Seifert matrix of 12n_0177
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 -1 1 1
1 1 0 0 -2 -1
1 1 0 0 0 -2
1 or 2
79
First homology
of the double branched cover of 12n_0177
Z/79
-6 6
12n_0178
1

detected by
an unknotting move
-1+9t-24t^2+33t^3-24t^4+9t^5-t^6
Seifert matrix of 12n_0178
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 -1 1 1
1 1 0 0 1 -1
1 1 1 0 0 1
1
Generator of the Alexander module
(-134-682t+922t^2+2030t^3-1238t^4-820t^5-1228t^6+1692t^7-980t^8-168t^9,67+341t-461t^2-1015t^3+619t^4+410t^5+614t^6-846t^7+490t^8+84t^9,0,-22-26t-135t^2+752t^3-533t^4+221t^5-618t^6+526t^7-224t^8-42t^9,23+135t-664t^2+457t^3-189t^4+624t^5-526t^6+224t^7+42t^8,88-163t-4t^2-1251t^3+2491t^4-1353t^5+910t^6-
the Blanchfield form on it
x
101
First homology
of the double branched cover of 12n_0178
Z/101
0 0
12n_0179
2

detected by
the signature
-1+3t-2t^2+t^3-2t^4+3t^5-t^6
Seifert matrix of 12n_0179
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 1 0 0
1 1 0 -1 -1 0
1 1 0 -1 1 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
13
First homology
of the double branched cover of 12n_0179
Z/13
-4 4
12n_0180
1

detected by
an unknotting move
-2+10t-22t^2+29t^3-22t^4+10t^5-2t^6
Seifert matrix of 12n_0180
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
1 1 0 -1 -1 0
1 1 1 -1 1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
97
First homology
of the double branched cover of 12n_0180
Z/97
0 0
12n_0181
1

detected by
an unknotting move
2-9t+19t^2-23t^3+19t^4-9t^5+2t^6
Seifert matrix of 12n_0181
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 1 0 0
1 1 0 -1 2 0
1 1 0 -1 1 -1
1
Generator of the Alexander module
(0,0,1-2t,0,-2,0)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
83
First homology
of the double branched cover of 12n_0181
Z/83
-2 2
12n_0182
1

detected by
an unknotting move
1-5t+10t^2-13t^3+13t^4-13t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0182
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 1 0 -1
0 0 0 1 0 0 0 -1
0 0 -1 0 -1 0 0 -1
0 0 0 0 0 1 1 0
0 0 0 0 0 0 1 0
-1 -1 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,t,0,1-t^2,0,-1,0,0)
the Blanchfield form on it
-2t^-3+4t^-2-5t^-1+4-5t+4t^2-2t^3
71
First homology
of the double branched cover of 12n_0182
Z/71
-2 2
12n_0183
2

detected by
the signature
-1+10t-26t^2+35t^3-26t^4+10t^5-t^6
Seifert matrix of 12n_0183
0 0 1 0 1 0
0 -1 0 0 0 0
1 -1 -2 0 -1 0
-1 0 0 -1 0 0
0 -1 -1 0 -2 0
0 0 0 0 1 -1
1 or 2
109
First homology
of the double branched cover of 12n_0183
Z/109
-4 4
12n_0184
1

detected by
an unknotting move
1-4t+10t^2-13t^3+10t^4-4t^5+t^6
Seifert matrix of 12n_0184
1 0 0 0 0 0
0 -1 0 0 0 0
0 -1 -2 -2 -1 1
0 -1 -1 0 -1 0
0 -1 -1 -1 0 0
1 0 0 0 0 1
1
Generator of the Alexander module
(0,1,1,0,1,0)
the Blanchfield form on it
2t^-2-5t^-1+6-5t+2t^2
43
First homology
of the double branched cover of 12n_0184
Z/43
2 2
12n_0185
3

detected by
the signature
1-4t+7t^2-10t^3+11t^4-10t^5+7t^6-4t^7+t^8
Seifert matrix of 12n_0185
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 0
-1 -1 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
-1 -1 0 -1 -1 -1 0 0
-1 -1 0 0 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-5+4t-3t^2+t^3
55
First homology
of the double branched cover of 12n_0185
Z/55
-6 6
12n_0186
2

detected by
the signature
-1+4t-11t^2+18t^3-21t^4+18t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0186
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 0 0
-1 -1 1 1 -1 1 0 0
0 0 0 0 1 0 0 0
-1 -1 1 0 -1 1 0 0
-1 -1 0 0 -1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+10t^-1-13+10t-4t^2+t^3
89
First homology
of the double branched cover of 12n_0186
Z/89
4 4
12n_0187
3

detected by
the signature
-1+5t^2-12t^3+15t^4-12t^5+5t^6-t^8
Seifert matrix of 12n_0187
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 0
-1 -1 0 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 0 -1 -1 -1 0 0
-1 -1 0 0 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,t,0,0,1,-t)
the Blanchfield form on it
-2t^-3-t^-2+11t^-1-18+11t-t^2-2t^3
47
First homology
of the double branched cover of 12n_0187
Z/47
-6 6
12n_0188
2

detected by
the signature
-1+4t-9t^2+12t^3-13t^4+12t^5-9t^6+4t^7-t^8
Seifert matrix of 12n_0188
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 0
-1 -1 0 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 0 -1 -1 -1 0 0
-1 -1 0 0 -1 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-10t^-1+13-10t+4t^2-t^3
65
First homology
of the double branched cover of 12n_0188
Z/65
-4 4
12n_0189
1

detected by
an unknotting move
1-4t+9t^2-16t^3+19t^4-16t^5+9t^6-4t^7+t^8
Seifert matrix of 12n_0189
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 -1 0 0 0
-1 -1 1 1 -1 1 0 0
0 0 0 0 -1 0 0 0
-1 -1 1 0 -1 1 0 0
-1 -1 0 0 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,-1,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-8+5t-3t^2+t^3
79
First homology
of the double branched cover of 12n_0189
Z/79
-2 2
12n_0190
2

detected by
the signature
1-3t+8t^2-13t^3+15t^4-13t^5+8t^6-3t^7+t^8
Seifert matrix of 12n_0190
-1 -1 -1 -1 0 -1 -1 0
0 0 -1 -1 1 -1 -1 1
0 0 0 -1 1 0 -1 1
0 -1 -1 0 0 -1 -1 0
0 0 0 0 1 0 0 1
0 0 -1 -1 1 0 -1 1
0 0 0 -1 1 0 0 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+3t^-2-7t^-1+9-7t+3t^2-t^3
65
First homology
of the double branched cover of 12n_0190
Z/65
4 4
12n_0191
3

detected by
the signature
1-5t+10t^2-15t^3+17t^4-15t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0191
-1 -1 -1 -1 0 -1 -1 0
0 -2 -2 -1 0 -2 -2 0
0 -1 -2 -1 0 -1 -2 0
0 -1 -1 0 0 -1 -1 0
0 -1 -1 0 -1 -1 -1 0
0 -1 -2 -1 0 -2 -2 0
0 -1 -1 -1 0 -1 -2 0
0 -1 -1 0 -1 -1 -1 -1
1
Generator of the Alexander module
(1,0,0,0,-2+2t-t^2,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+6t^-1-7+6t-4t^2+t^3
79
First homology
of the double branched cover of 12n_0191
Z/79
-6 6
12n_0192
1

detected by
an unknotting move
1-t-2t^2+7t^3-9t^4+7t^5-2t^6-t^7+t^8
Seifert matrix of 12n_0192
-1 -1 -1 -1 0 -1 -1 0
0 0 -1 -1 1 -1 -1 1
0 0 0 -1 1 0 -1 1
0 -1 -1 -2 0 -1 -1 0
0 0 0 0 1 0 0 1
0 0 -1 -1 1 0 -1 1
0 0 0 -1 1 0 0 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
23
First homology
of the double branched cover of 12n_0192
Z/23
2 2
12n_0193
1

detected by
an unknotting move
2-6t+13t^2-17t^3+13t^4-6t^5+2t^6
Seifert matrix of 12n_0193
-1 -1 1 -1 0 0
0 0 1 -1 1 1
0 0 1 1 -1 -1
0 -1 1 0 0 0
0 0 0 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+6t^-1-8+6t-3t^2+t^3
59
First homology
of the double branched cover of 12n_0193
Z/59
2 2
12n_0194
2

detected by
the signature
-2+10t-19t^2+23t^3-19t^4+10t^5-2t^6
Seifert matrix of 12n_0194
-1 -1 1 -1 0 0
0 -2 2 -1 0 0
0 1 -3 1 0 0
0 -1 1 0 0 0
0 -1 1 0 -1 0
0 -1 1 0 -1 -1
1
Generator of the Alexander module
(1+14t-6t^2-16t^3+7t^4,2+20t-10t^2-22t^3+10t^4,-1-6t+4t^2+6t^3-3t^4,3+t-23t^2+25t^3+23t^4-42t^5+12t^6,3-3t-14t^2+18t^3+10t^4-21t^5+6t^6,3-5t-22t^2+33t^3+20t^4-42t^5+12t^6)
the Blanchfield form on it
x
85
First homology
of the double branched cover of 12n_0194
Z/85
-4 4
12n_0195
1

detected by
an unknotting move
2-4t+3t^2-t^3+3t^4-4t^5+2t^6
Seifert matrix of 12n_0195
-1 -1 1 -1 0 0
0 0 1 -1 1 1
0 0 1 1 -1 -1
0 -1 1 -2 0 0
0 0 0 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(t,0,1,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-2t^-1-2t+3t^2-t^3
19
First homology
of the double branched cover of 12n_0195
Z/19
2 2
12n_0196
2

detected by
the signature
-2+6t-7t^2+7t^3-7t^4+6t^5-2t^6
Seifert matrix of 12n_0196
-1 -1 1 -1 0 0
0 -1 2 -1 0 0
0 1 0 1 0 0
0 -1 1 -2 0 0
0 -1 1 0 -1 0
0 -1 1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,-t,0,t)
the Blanchfield form on it
t^-2+t^2
37
First homology
of the double branched cover of 12n_0196
Z/37
-4 4
12n_0197
1

detected by
an unknotting move
2-10t+25t^2-33t^3+25t^4-10t^5+2t^6
Seifert matrix of 12n_0197
-1 -1 1 -1 0 0
0 -1 1 -1 1 1
0 0 -2 1 -1 -1
0 -1 1 -2 0 0
0 0 0 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(-t+t^4,-3t^4,-1+2t+t^4,1,0,0)
the Blanchfield form on it
-11t^-5+40t^-4-113t^-3+282t^-2-528t^-1+660-528t+282t^2-113t^3+40t^4-11t^5
107
First homology
of the double branched cover of 12n_0197
Z/107
-2 2
12n_0198
1

detected by
an unknotting move
1-4t+6t^2-5t^3+6t^4-4t^5+t^6
Seifert matrix of 12n_0198
-1 0 -1 0 0 -1
0 1 0 0 -1 0
0 0 0 0 0 -1
0 0 0 -1 0 -1
0 0 0 -1 -1 0
0 0 -1 0 0 0
1
Generator of the Alexander module
(0,t,0,0,1,0)
the Blanchfield form on it
t^-2-2t^-1+1-2t+t^2
27
First homology
of the double branched cover of 12n_0198
Z/27
-2 2
12n_0199
1

detected by
an unknotting move
1-t+2t^2-3t^3+2t^4-t^5+t^6
Seifert matrix of 12n_0199
-1 0 -1 1 0 0
0 1 0 0 1 0
0 0 0 1 0 0
0 1 1 1 1 1
0 0 0 0 1 0
0 1 0 0 1 1
1
Generator of the Alexander module
(-t,0,1,0,0,0)
the Blanchfield form on it
t^-2-2t^-1+2-2t+t^2
11
First homology
of the double branched cover of 12n_0199
Z/11
2 2
12n_0200 1 or 2
2-2t+t^2-2t^3+2t^4
Seifert matrix of 12n_0200
-1 0 -1 1
0 2 0 0
0 0 0 1
0 -1 1 1
1
Generator of the Alexander module
(-1,0,0,1)
the Blanchfield form on it
2t^-1-4+2t
9
First homology
of the double branched cover of 12n_0200
Z/9
0 2
12n_0201
2

detected by
the signature
-3+13t-23t^2+27t^3-23t^4+13t^5-3t^6
Seifert matrix of 12n_0201
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -2 0 -1 1
0 0 0 1 0 0
1 1 -1 1 -2 1
-1 -1 0 -1 0 -1
1 or 2
105
First homology
of the double branched cover of 12n_0201
Z/105
-4 4
12n_0202
2

detected by
the Lickorish test
3-13t+31t^2-41t^3+31t^4-13t^5+3t^6
Seifert matrix of 12n_0202
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 2 0 1 0
0 0 0 1 0 0
1 1 1 1 2 0
-1 -1 -1 -1 -1 1
1 or 2
135
First homology
of the double branched cover of 12n_0202
Z/135
2 2
12n_0203
3

detected by
the signature
3-5t+t^2+3t^3+t^4-5t^5+3t^6
Seifert matrix of 12n_0203
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -2 0 -1 1
0 0 0 -1 0 0
1 1 -1 1 -2 1
-1 -1 0 -1 0 -1
1 or 2
15
First homology
of the double branched cover of 12n_0203
Z/15
-6 6
12n_0204
2

detected by
the signature
-1+9t-22t^2+29t^3-22t^4+9t^5-t^6
Seifert matrix of 12n_0204
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 0
0 0 0 -1 0 0
1 1 0 1 -1 0
-1 -1 -1 -1 -1 1
1 or 2
93
First homology
of the double branched cover of 12n_0204
Z/93
-4 4
12n_0205
2

detected by
the signature
-1+5t-11t^2+14t^3-15t^4+14t^5-11t^6+5t^7-t^8
Seifert matrix of 12n_0205
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
0 0 0 1 0 0 0 0
0 0 -1 0 -1 -1 0 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 -1 -1 -1 0
0 0 -1 0 -1 0 0 1
1 or 2
77
First homology
of the double branched cover of 12n_0205
Z/77
-4 4
12n_0206
2

detected by
the Lickorish test
1-5t+13t^2-24t^3+29t^4-24t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0206
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 1 0 1 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 1 0
-1 -1 1 -1 1 1 1 0
0 0 0 0 0 0 1 0
0 0 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,1-3t+t^2+2t^3-7t^4-t^5+22t^6-50t^7+52t^8-12t^9-16t^10+11t^11-2t^12,2t+2t^2+2t^3-6t^4+18t^5-32t^6+44t^7-20t^8-18t^9+18t^10-4t^11,1+2t+4t^2-7t^3+10t^4-8t^5-6t^6+32t^7-30t^8+2t^9+7t^10-2t^11,-1-t^2-t^3-3t^4+20t^5-45t^6+72t^7-63t^8+14t^9+16t^10-11t^11+2t^12,t+2t^2+6t^3-12t^4+14t^5-9t^6-18t^7+52t^8-41
the Blanchfield form on it
x
115
First homology
of the double branched cover of 12n_0206
Z/115
2 2
12n_0207
2

detected by
the signature
1-3t-t^2+12t^3-19t^4+12t^5-t^6-3t^7+t^8
Seifert matrix of 12n_0207
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 0
0 0 0 -1 0 0 0 0
0 0 -1 0 -1 -1 0 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 -1 -1 -1 0
0 0 -1 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,1,0,1,0,0,t)
the Blanchfield form on it
t^-3-4t^-1+7-4t+t^3
37
First homology
of the double branched cover of 12n_0207
Z/37
-4 4
12n_0208
1

detected by
an unknotting move
3-11t+23t^2-29t^3+23t^4-11t^5+3t^6
Seifert matrix of 12n_0208
-1 -1 -1 -1 0 0
0 0 -1 -1 0 0
0 -1 0 -1 0 0
0 -1 -1 0 1 -1
0 0 0 0 1 0
0 1 0 0 -1 2
1
Generator of the Alexander module
(-1-t^2+t^3,0,0,t-t^2,-1+t,1-t)
the Blanchfield form on it
6t^-2-13t^-1+16-13t+6t^2
103
First homology
of the double branched cover of 12n_0208
Z/103
2 2
12n_0209
2

detected by
the signature
-3+15t-31t^2+39t^3-31t^4+15t^5-3t^6
Seifert matrix of 12n_0209
-1 -1 -1 -1 0 0
0 -2 -1 -1 0 -1
0 -1 0 -1 0 0
0 -1 -1 -2 0 0
0 0 0 -1 -1 1
0 0 0 1 0 -2
1
Generator of the Alexander module
(1-t+2t^2-t^3+t^4,0,-t+t^2-t^3,1,0,0)
the Blanchfield form on it
-6t^-2+15t^-1-20+15t-6t^2
137
First homology
of the double branched cover of 12n_0209
Z/137
-4 4
12n_0210
1

detected by
an unknotting move
1-t-t^2+3t^3-t^4-t^5+t^6
Seifert matrix of 12n_0210
-1 -1 -1 -1 0 0
0 0 -1 -1 0 0
0 -1 -2 -1 0 0
0 -1 -1 0 1 -1
0 0 0 0 1 0
0 1 0 0 -1 2
1
Generator of the Alexander module
(t^2,-2t,-t+2t^2+2t^4,1+t^2,-t,0)
the Blanchfield form on it
-5t^-2-18t^-1+25-18t-5t^2
1
First homology
of the double branched cover of 12n_0210
0
0 0
12n_0211
2

detected by
the Lickorish test
1-6t+12t^2-13t^3+12t^4-6t^5+t^6
Seifert matrix of 12n_0211
-1 -1 0 -1 0 -1
0 0 0 -1 0 -1
0 0 -1 -1 0 0
0 -1 0 0 0 -1
0 0 0 0 -1 -1
0 -1 0 0 0 0
1
Generator of the Alexander module
(0,0,0,0,-t,1)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
51
First homology
of the double branched cover of 12n_0211
Z/51
-2 2
12n_0212
1

detected by
an unknotting move
3-11t+23t^2-29t^3+23t^4-11t^5+3t^6
Seifert matrix of 12n_0212
-1 -1 -1 0 0 -1
0 0 -1 0 1 -1
0 -1 0 0 0 -1
0 1 0 2 1 0
0 0 0 0 1 0
0 -1 -1 -1 0 0
1
Generator of the Alexander module
(0,0,1-t,0,0,t)
the Blanchfield form on it
8t^-3-30t^-2+63t^-1-80+63t-30t^2+8t^3
103
First homology
of the double branched cover of 12n_0212
Z/103
2 2
12n_0213
2

detected by
the signature
-3+15t-31t^2+39t^3-31t^4+15t^5-3t^6
Seifert matrix of 12n_0213
-1 -1 -1 0 0 -1
0 -2 -1 -1 0 -1
0 -1 0 0 0 -1
0 0 0 -2 0 1
0 -1 0 -1 -1 0
0 -1 -1 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
137
First homology
of the double branched cover of 12n_0213
Z/137
-4 4
12n_0214
1

detected by
an unknotting move
1-t-t^2+3t^3-t^4-t^5+t^6
Seifert matrix of 12n_0214
-1 -1 -1 0 0 -1
0 0 -1 0 1 -1
0 -1 -2 0 0 -1
0 1 0 2 1 0
0 0 0 0 1 0
0 -1 -1 -1 0 0
1
Generator of the Alexander module
(-t,0,1,2t,-1,-t)
the Blanchfield form on it
-1
1
First homology
of the double branched cover of 12n_0214
0
0 0
12n_0215
2

detected by
the signature
-2+8t-13t^2+15t^3-13t^4+8t^5-2t^6
Seifert matrix of 12n_0215
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 1 -2 0 0
-1 -1 -1 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+7t^-1-8+7t-4t^2+t^3
61
First homology
of the double branched cover of 12n_0215
Z/61
-4 4
12n_0216
1

detected by
an unknotting move
2-8t+19t^2-25t^3+19t^4-8t^5+2t^6
Seifert matrix of 12n_0216
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 1 0 0 0
1 1 1 2 0 0
-1 -1 -1 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+9t^-1-12+9t-4t^2+t^3
83
First homology
of the double branched cover of 12n_0216
Z/83
2 2
12n_0217
2

detected by
the signature
2-2t-3t^2+7t^3-3t^4-2t^5+2t^6
Seifert matrix of 12n_0217
-1 0 0 0 0 0
-1 -1 0 0 0 0
0 0 -1 0 0 0
1 1 1 -2 0 0
-1 -1 -1 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+2t^-2-t^-1-t+2t^2-t^3
5
First homology
of the double branched cover of 12n_0217
Z/5
-4 4
12n_0218
1

detected by
an unknotting move
-1+4t-6t^2+7t^3-6t^4+4t^5-t^6
Seifert matrix of 12n_0218
-1 -1 0 0 0 -1
0 0 0 0 0 -1
0 0 -1 -1 0 -1
0 0 0 1 1 0
0 0 0 0 1 0
0 -1 0 0 0 0
1
Generator of the Alexander module
(t,0,1,0,0,0)
the Blanchfield form on it
-2t^-2+9t^-1-13+9t-2t^2
29
First homology
of the double branched cover of 12n_0218
Z/29
0 2
12n_0219
2

detected by
the Lickorish test
1-5t+12t^2-20t^3+23t^4-20t^5+12t^6-5t^7+t^8
Seifert matrix of 12n_0219
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 -1
0 0 0 1 0 0 0 -1
0 0 -1 0 1 0 1 -1
0 0 -1 0 0 -1 0 -1
0 0 -1 0 0 0 1 -1
-1 -1 0 0 0 0 0 -1
2
99
First homology
of the double branched cover of 12n_0219
Z/99
-2 2
12n_0220
2

detected by
the signature
1-3t+8t^3-13t^4+8t^5-3t^7+t^8
Seifert matrix of 12n_0220
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 -1
0 0 0 1 0 0 0 -1
0 0 -1 0 -1 0 0 -1
0 0 -1 0 0 -1 0 -1
0 0 -1 0 -1 0 -1 -1
-1 -1 0 0 0 0 0 -1
2
21
First homology
of the double branched cover of 12n_0220
Z/21
-4 4
12n_0221
2

detected by
A(F_2)
1-2t+3t^2-2t^3+t^4
Seifert matrix of 12n_0221
0 0 -1 -1
0 -2 1 0
0 1 0 0
-1 -1 1 0
2
9
First homology
of the double branched cover of 12n_0221
Z/9
0 0
12n_0222
2

detected by
the signature
-2+13t-30t^2+39t^3-30t^4+13t^5-2t^6
Seifert matrix of 12n_0222
-2 -1 0 0 0 0
-2 -2 0 0 0 0
0 0 2 0 1 0
-1 -1 -2 -1 -1 0
0 0 1 0 0 0
-1 -1 -1 0 0 -1
2
129
First homology
of the double branched cover of 12n_0222
Z/129
-4 4
12n_0223
2

detected by
the Lickorish test
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 12n_0223
-1 0 -1 0 -1 0
0 -1 0 0 0 0
0 -2 -6 -3 -3 -2
0 -1 -2 0 -1 -1
0 -1 -3 -1 -2 -1
0 -1 -2 -1 -1 0
2
111
First homology
of the double branched cover of 12n_0223
Z/111
-2 2
12n_0224
2

detected by
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0224
-1 -1 -1 -1 0 -1
0 0 -1 -1 0 -1
0 -1 0 -1 0 -1
0 0 -1 0 0 -1
0 0 0 0 -1 -1
0 -1 -1 -1 0 0
2
81
First homology
of the double branched cover of 12n_0224
Z/81
0 0
12n_0225
2

detected by
the Lickorish test
-3+10t-13t^2+10t^3-3t^4
Seifert matrix of 12n_0225
-2 -1 -2 -2
0 -2 -1 -2
-1 -1 -1 -2
-1 -1 -2 -3
2
39
First homology
of the double branched cover of 12n_0225
Z/39
-2 2
12n_0226
2

detected by
the signature
-1+5t-11t^2+14t^3-15t^4+14t^5-11t^6+5t^7-t^8
Seifert matrix of 12n_0226
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 -1
0 0 0 1 0 0 0 0
0 0 -1 0 1 0 -1 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 0 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1 or 2
77
First homology
of the double branched cover of 12n_0226
Z/77
-4 4
12n_0227
2

detected by
the Lickorish test
1-5t+13t^2-24t^3+29t^4-24t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0227
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 0 1 0
0 0 0 1 0 0 0 0
0 0 -1 0 -1 0 -1 0
-1 -1 1 -1 0 1 1 1
0 0 0 0 0 0 1 0
-1 -1 1 -1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+17-12t+5t^2-t^3
115
First homology
of the double branched cover of 12n_0227
Z/115
2 2
12n_0228
2

detected by
the signature
1-3t-t^2+12t^3-19t^4+12t^5-t^6-3t^7+t^8
Seifert matrix of 12n_0228
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 0 -1
0 0 0 -1 0 0 0 0
0 0 -1 0 1 0 -1 0
-1 -1 0 -1 0 -1 0 0
0 0 -1 0 0 -1 -1 -1
-1 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-4t^-1+7-4t+t^3
37
First homology
of the double branched cover of 12n_0228
Z/37
-4 4
12n_0229
3

detected by
the signature
1-5t+8t^2-8t^3+7t^4-8t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0229
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 -1 1 0
-1 -1 0 -1 0 0 1 0
0 0 -1 -1 -1 -1 0 0
-1 -1 0 -1 0 -1 1 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 1 -1
2
51
First homology
of the double branched cover of 12n_0229
Z/51
-6 6
12n_0230
1

detected by
an unknotting move
1-4t+4t^2-t^3+4t^4-4t^5+t^6
Seifert matrix of 12n_0230
-1 -1 0 0 0 0
0 1 0 0 0 0
-1 0 -1 -1 0 0
0 0 0 -1 0 0
-1 0 0 -1 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1-3t+t^2,-6t+2t^2+2t^5-6t^6+2t^7,3t+11t^2-4t^3-t^5-t^6+11t^7-4t^8,-3-11t+4t^2+4t^5-12t^6+4t^7)
the Blanchfield form on it
x
19
First homology
of the double branched cover of 12n_0230
Z/19
-2 2
12n_0231
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 12n_0231
0 0 1 1
1 3 1 1
1 1 0 0
1 2 1 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-1
31
First homology
of the double branched cover of 12n_0231
Z/31
2 2
12n_0232
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 12n_0232
0 0 1 -1
0 2 0 0
1 -1 2 -1
0 0 0 1
1
Generator of the Alexander module
(1,0,-1+t,0)
the Blanchfield form on it
2t^-1-4+2t
31
First homology
of the double branched cover of 12n_0232
Z/31
2 2
12n_0233
2

detected by
the signature
1-2t+4t^2-5t^3+5t^4-5t^5+4t^6-2t^7+t^8
Seifert matrix of 12n_0233
-1 -1 -1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 -1 -1 -1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 -1 -1 -1 0 -1 -1 -1
0 0 -1 -1 -1 0 -1 -1
0 0 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 0
1
Generator of the Alexander module
(-t,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+2t^-1-2+2t-2t^2+t^3
29
First homology
of the double branched cover of 12n_0233
Z/29
4 4
12n_0234
3

detected by
the signature
1-4t+6t^2-7t^3+7t^4-7t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0234
-1 -1 -1 -1 -1 -1 -1 -1
0 -2 -2 -2 -1 -2 -2 -2
0 -1 -2 -2 -1 -1 -2 -2
0 -1 -1 -2 -1 -1 -1 -2
0 -1 -1 -1 0 -1 -1 -1
0 -1 -2 -2 -1 -2 -2 -2
0 -1 -1 -2 -1 -1 -2 -2
0 -1 -1 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(-t,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-2t^-2+2t^-1-2+2t-2t^2+t^3
43
First homology
of the double branched cover of 12n_0234
Z/43
-6 6
12n_0235
2

detected by
the signature
1-2t+2t^2-t^3+t^4-t^5+2t^6-2t^7+t^8
Seifert matrix of 12n_0235
-1 -1 -1 -1 -1 -1 -1 -1
0 0 -1 -1 -1 -1 -1 -1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 -1 -1 -1 -2 -1 -1 -1
0 0 -1 -1 -1 0 -1 -1
0 0 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 0
1
Generator of the Alexander module
(t,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3+t^3
13
First homology
of the double branched cover of 12n_0235
Z/13
4 4
12n_0236
1

detected by
an unknotting move
2-5t+10t^2-13t^3+10t^4-5t^5+2t^6
Seifert matrix of 12n_0236
-1 -1 -1 1 -1 -1
0 0 -1 1 -1 -1
0 0 0 1 -1 0
0 0 0 1 1 0
0 -1 -1 1 0 -1
0 0 -1 1 -1 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
4t^-2-8t^-1+9-8t+4t^2
47
First homology
of the double branched cover of 12n_0236
Z/47
2 2
12n_0237
2

detected by
the signature
-2+9t-16t^2+19t^3-16t^4+9t^5-2t^6
Seifert matrix of 12n_0237
-1 -1 -1 1 -1 -1
0 -2 -2 2 -1 -2
0 -1 -2 2 -1 -1
0 1 1 -3 1 1
0 -1 -1 1 0 -1
0 -1 -2 2 -1 -2
1
Generator of the Alexander module
(t,0,0,-1,0,0)
the Blanchfield form on it
2t^-2-3t^-1+4-3t+2t^2
73
First homology
of the double branched cover of 12n_0237
Z/73
-4 4
12n_0238
1

detected by
an unknotting move
2-5t+6t^2-5t^3+6t^4-5t^5+2t^6
Seifert matrix of 12n_0238
-1 -1 -1 1 -1 -1
0 0 -1 1 -1 -1
0 0 0 1 -1 0
0 0 0 1 1 0
0 -1 -1 1 -2 -1
0 0 -1 1 -1 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
31
First homology
of the double branched cover of 12n_0238
Z/31
2 2
12n_0239
1

detected by
an unknotting move
2-5t+9t^2-11t^3+9t^4-5t^5+2t^6
Seifert matrix of 12n_0239
-1 -1 1 1 -1 1
0 0 1 1 -1 1
0 0 1 0 1 0
0 0 1 1 1 1
0 -1 1 1 0 1
0 0 1 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
4t^-2-9t^-1+11-9t+4t^2
43
First homology
of the double branched cover of 12n_0239
Z/43
2 2
12n_0240
2

detected by
the signature
-2+9t-17t^2+21t^3-17t^4+9t^5-2t^6
Seifert matrix of 12n_0240
-1 -1 1 1 -1 1
0 -2 2 2 -1 2
0 1 -3 -3 1 -3
0 1 -2 -3 1 -2
0 -1 1 1 0 1
0 1 -2 -3 1 -3
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
77
First homology
of the double branched cover of 12n_0240
Z/77
-4 4
12n_0241
1

detected by
an unknotting move
2-7t+13t^2-15t^3+13t^4-7t^5+2t^6
Seifert matrix of 12n_0241
-1 -1 1 1 -1 1
0 0 1 1 -1 1
0 0 1 0 1 0
0 0 1 1 1 1
0 -1 1 1 -2 1
0 0 1 0 1 1
1
Generator of the Alexander module
(2t,0,1,1,t,1)
the Blanchfield form on it
2t^-2-3t^-1+4-3t+2t^2
59
First homology
of the double branched cover of 12n_0241
Z/59
2 2
12n_0242
4

detected by
the signature
-1+t-t^3+t^4-t^5+t^6-t^7+t^9-t^10
Seifert matrix of 12n_0242
-1 0 0 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 -1 -1 -1
-1 -1 0 -1 -1 -1 0 0 -1 -1
-1 -1 0 0 -1 -1 0 0 0 -1
-1 -1 0 0 0 -1 0 0 0 0
0 0 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 0 -1 -1 -1 0 -1 -1 -1
-1 -1 0 0 -1 -1 0 0 -1 -1
-1 -1 0 0 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0,t,0,0,0)
the Blanchfield form on it
-t^-4-t^4
1
First homology
of the double branched cover of 12n_0242
0
-8 8
12n_0243
4

detected by
the signature
-2+3t-t^2-2t^3+3t^4-2t^5-t^6+3t^7-2t^8
Seifert matrix of 12n_0243
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 1 -1 0 -1
-1 -1 0 -1 1 -1 0 0
1 1 0 0 -2 1 0 0
-1 -1 0 0 0 -1 0 0
0 0 -1 -1 1 -1 -1 -1
-1 -1 0 -1 1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-4-2t^-3+t^-2+t^-1-2+t+t^2-2t^3+t^4
5
First homology
of the double branched cover of 12n_0243
Z/5
-8 8
12n_0244
4

detected by
the signature
-2+4t-4t^2+2t^3-t^4+2t^5-4t^6+4t^7-2t^8
Seifert matrix of 12n_0244
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 1 1 -1 0 1
1 1 0 -2 -2 1 0 -2
1 1 0 -1 -2 1 0 -1
-1 -1 0 0 0 -1 0 0
0 0 -1 1 1 -1 -1 1
1 1 0 -1 -2 1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-2t^-3+3t^-2-t^-1-1-t+3t^2-2t^3
25
First homology
of the double branched cover of 12n_0244
Z/25
-8 8
12n_0245
3

detected by
the signature
4-8t+6t^2-3t^3+6t^4-8t^5+4t^6
Seifert matrix of 12n_0245
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 1 0 1
1 1 0 -2 0 -1
0 0 -1 1 -1 1
1 1 0 0 0 -2
1 or 2
39
First homology
of the double branched cover of 12n_0245
Z/39
-6 6
12n_0246
1

detected by
an unknotting move
5-17t+25t^2-17t^3+5t^4
Seifert matrix of 12n_0246
1 0 -1 0
0 -1 0 0
-1 -1 -2 -1
-1 0 -1 1
1
Generator of the Alexander module
(0,0,3t-2t^2,1-4t+2t^2)
the Blanchfield form on it
-5t^-1+7-5t
69
First homology
of the double branched cover of 12n_0246
Z/69
0 0
12n_0247
2

detected by
the Lickorish test
-3+13t-19t^2+13t^3-3t^4
Seifert matrix of 12n_0247
-3 -2 2 -2
-3 -3 2 -2
1 1 -3 1
-2 -2 2 -1
1
Generator of the Alexander module
(-2-5t+10t^2-5t^3,-3-6t+12t^2-6t^3,1+2t-4t^2+2t^3,-2-4t+8t^2-4t^3)
the Blanchfield form on it
247t^-2-1076t^-1+1580-1076t+247t^2
51
First homology
of the double branched cover of 12n_0247
Z/51
-2 2
12n_0248
2

detected by
the Lickorish test
3-6t+7t^2-6t^3+3t^4
Seifert matrix of 12n_0248
-1 -1 -1 -1
0 0 -1 -1
0 -1 0 -1
0 0 -1 2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
6t^-1-11+6t
25
First homology
of the double branched cover of 12n_0248
Z/25
0 2
12n_0249
1

detected by
an unknotting move
-3+12t-17t^2+12t^3-3t^4
Seifert matrix of 12n_0249
-1 -1 -1 -1
0 -2 -1 -2
0 -1 0 -1
0 -1 -1 -4
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
47
First homology
of the double branched cover of 12n_0249
Z/47
-2 2
12n_0250
1

detected by
an unknotting move
3-10t+15t^2-10t^3+3t^4
Seifert matrix of 12n_0250
-1 -1 -1 -1
0 0 -1 -1
0 -1 -2 -1
0 0 -1 2
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
1
41
First homology
of the double branched cover of 12n_0250
Z/41
0 0
12n_0251
3

detected by
the signature
3-5t+2t^2+t^3+2t^4-5t^5+3t^6
Seifert matrix of 12n_0251
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 -1
-1 -1 0 -1 0 0
0 0 -1 -1 -1 -1
-1 -1 0 -1 0 -3
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+2t^-2-t^-1-t+2t^2-t^3
19
First homology
of the double branched cover of 12n_0251
Z/19
-6 6
12n_0252
1

detected by
an unknotting move
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 12n_0252
-1 -1 0 -1 0 -1
0 0 0 -1 1 -1
0 1 -1 0 1 1
0 -1 0 0 0 -1
0 0 0 0 1 0
0 -1 0 -1 0 0
1
Generator of the Alexander module
(-t,0,1,0,0,1)
the Blanchfield form on it
-4t^-2+16t^-1-24+16t-4t^2
89
First homology
of the double branched cover of 12n_0252
Z/89
0 2
12n_0253
2

detected by
the Lickorish test
2-6t+12t^2-15t^3+12t^4-6t^5+2t^6
Seifert matrix of 12n_0253
-1 -1 0 -1 0 -1
0 0 0 -1 1 -1
0 1 1 0 1 1
0 -1 0 0 0 -1
0 0 0 0 1 0
0 -1 0 -1 0 0
1
Generator of the Alexander module
(-t,0,1,0,0,1)
the Blanchfield form on it
2t^-1-4+2t
55
First homology
of the double branched cover of 12n_0253
Z/55
2 2
12n_0254
2

detected by
the signature
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 12n_0254
-1 -1 0 -1 0 -1
0 -2 0 -1 0 -1
0 1 -1 0 1 1
0 -1 0 0 0 -1
0 -1 0 0 -1 0
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
65
First homology
of the double branched cover of 12n_0254
Z/65
-4 4
12n_0255
1

detected by
an unknotting move
2-12t+30t^2-39t^3+30t^4-12t^5+2t^6
Seifert matrix of 12n_0255
-1 -1 0 -1 0 -1
0 -2 0 -1 0 -1
0 1 1 0 1 1
0 -1 0 0 0 -1
0 -1 0 0 -1 0
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
127
First homology
of the double branched cover of 12n_0255
Z/127
-2 2
12n_0256
2

detected by
the Lickorish test
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 12n_0256
-8 -6 -6 0
-8 -6 -6 -1
-7 -5 -5 0
-3 -3 -2 -2
1
Generator of the Alexander module
(0,4,0,3)
the Blanchfield form on it
-44t^-1+80-44t
25
First homology
of the double branched cover of 12n_0256
Z/25
0 0
12n_0257
2

detected by
the Nakanishi index
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 12n_0257
0 2 2 0
0 0 0 1
1 2 3 1
1 2 2 -1
2
25
First homology
of the double branched cover of 12n_0257
Z/5+Z/5
0 0
12n_0258
1

detected by
an unknotting move
-1+4t-5t^2+4t^3-t^4
Seifert matrix of 12n_0258
-1 1 0 -1
-1 -1 -2 0
-1 0 -1 -1
0 1 0 -2
1
Generator of the Alexander module
(0,2,1,0)
the Blanchfield form on it
1
15
First homology
of the double branched cover of 12n_0258
Z/15
-2 2
12n_0259
3

detected by
the signature
4-12t+20t^2-23t^3+20t^4-12t^5+4t^6
Seifert matrix of 12n_0259
-1 -1 0 -1 0 -1
0 -2 0 -1 0 -1
0 1 -1 0 1 1
0 -1 0 -2 0 -1
0 -1 0 0 -1 0
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
6t^-2-18t^-1+25-18t+6t^2
95
First homology
of the double branched cover of 12n_0259
Z/95
-6 6
12n_0260 1 or 2
3-5t+5t^2-5t^3+3t^4
Seifert matrix of 12n_0260
-1 1 -1 1
0 1 1 0
0 1 0 1
0 -1 1 1
1 or 2
21
First homology
of the double branched cover of 12n_0260
Z/21
0 2
12n_0261
2

detected by
the signature
-1+5t-10t^2+12t^3-13t^4+12t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0261
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 -1
0 0 0 1 0 0 0 -1
0 0 -1 0 -1 0 -1 -1
0 0 0 0 0 1 0 0
0 0 -1 0 0 0 -1 -1
-1 -1 0 0 0 -1 0 -1
2
69
First homology
of the double branched cover of 12n_0261
Z/69
-4 4
12n_0262
1

detected by
an unknotting move
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 12n_0262
-1 -1 0 0 -1 -1
0 0 0 0 -1 -1
0 1 -1 -1 0 0
0 0 0 1 0 0
0 -1 0 0 0 -1
0 -1 0 1 -1 0
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
89
First homology
of the double branched cover of 12n_0262
Z/89
0 2
12n_0263
1

detected by
an unknotting move
2-12t+30t^2-39t^3+30t^4-12t^5+2t^6
Seifert matrix of 12n_0263
-1 -1 0 0 -1 -1
0 -2 0 0 -1 -1
0 1 1 -1 0 0
0 0 0 -1 0 -1
0 -1 0 0 0 -1
0 -1 0 0 -1 -2
1
Generator of the Alexander module
(-1,0,1,0,0,0)
the Blanchfield form on it
-2t^-1+4-2t
127
First homology
of the double branched cover of 12n_0263
Z/127
-2 2
12n_0264
2

detected by
the Lickorish test
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 12n_0264
-2 -2 -1 0
-3 -4 -3 0
-2 -4 -3 1
0 0 0 1
1
Generator of the Alexander module
(1,1,0,0)
the Blanchfield form on it
-t^-2+3t^-1-4+3t-t^2
25
First homology
of the double branched cover of 12n_0264
Z/25
0 0
12n_0265
1

detected by
an unknotting move
2-8t+14t^2-15t^3+14t^4-8t^5+2t^6
Seifert matrix of 12n_0265
-1 -1 0 -1 -1 0
0 0 0 -1 -1 0
0 1 -1 0 1 0
0 -1 0 0 -1 0
0 -1 0 -1 0 0
0 0 -1 0 1 -1
1
Generator of the Alexander module
(1+5t+3t^3+4t^4-2t^5-3t^6+t^7,-6t-3t^2+2t^3-11t^4+4t^5+3t^6-t^7,-1+t-14t^2+19t^3-21t^4+9t^5-2t^6+9t^7-9t^8+2t^9,1+8t+2t^3+10t^4-7t^5-2t^6+t^7,-1-6t+16t^2-28t^3+27t^4-13t^5+12t^6-12t^7+9t^8-2t^9,-3t+12t^2-16t^3+35t^4-23t^5+20t^6-10t^7+7t^8-8t^9+2t^10)
the Blanchfield form on it
x
63
First homology
of the double branched cover of 12n_0265
Z/63
-2 2
12n_0266
2

detected by
the Lickorish test
-2+10t-24t^2+33t^3-24t^4+10t^5-2t^6
Seifert matrix of 12n_0266
-1 -1 0 -1 -1 0
0 -2 0 -1 -1 0
0 1 1 0 1 1
0 -1 0 0 -1 0
0 -1 0 -1 -2 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-6t^-1+7-6t+2t^2
105
First homology
of the double branched cover of 12n_0266
Z/105
0 0
12n_0267
2

detected by
the Lickorish test
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 12n_0267
-2 -5 -2 -1
-4 -6 -3 -1
-2 -3 -2 0
-2 -3 -1 -2
1
Generator of the Alexander module
(1+t,t,0,2t)
the Blanchfield form on it
2
63
First homology
of the double branched cover of 12n_0267
Z/63
-2 2
12n_0268
2

detected by
the Nakanishi index
-2+5t-2t^2
Seifert matrix of 12n_0268
0 -2
-1 -3
2
9
First homology
of the double branched cover of 12n_0268
Z/3+Z/3
0 0
12n_0269
2

detected by
the Nakanishi index
-1+9t-28t^2+41t^3-28t^4+9t^5-t^6
Seifert matrix of 12n_0269
-1 -1 0 0 0 0
0 1 0 0 0 0
0 0 -1 0 0 -1
0 0 0 1 0 0
1 0 0 -1 -1 0
-1 0 0 1 -1 1
2
117
First homology
of the double branched cover of 12n_0269
Z/39+Z/3
0 0
12n_0270
2

detected by
the Nakanishi index
-3+16t-25t^2+16t^3-3t^4
Seifert matrix of 12n_0270
0 1 2 1
0 1 0 0
1 0 3 1
1 0 2 2
2
63
First homology
of the double branched cover of 12n_0270
Z/21+Z/3
2 2
12n_0271
1

detected by
an unknotting move
-1+5t-12t^2+17t^3-12t^4+5t^5-t^6
Seifert matrix of 12n_0271
0 0 0 0 1 1
0 -1 -1 -1 0 1
-1 0 0 0 1 1
-1 0 -1 -1 0 1
0 0 0 0 2 1
1 0 1 0 0 0
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
1
53
First homology
of the double branched cover of 12n_0271
Z/53
0 0
12n_0272
1

detected by
an unknotting move
1-7t+20t^2-27t^3+20t^4-7t^5+t^6
Seifert matrix of 12n_0272
0 0 0 -1 0 -1
0 1 0 0 0 0
-1 0 0 -1 0 -1
-1 0 -1 0 0 0
0 0 -1 -1 -1 0
0 -1 0 1 0 2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-1-3+2t
83
First homology
of the double branched cover of 12n_0272
Z/83
2 2
12n_0273
2

detected by
the signature
-1+3t-3t^3+3t^5-t^6
Seifert matrix of 12n_0273
0 0 -1 0 -1 0
-1 -1 0 0 -1 0
0 0 0 0 1 0
-1 -1 0 -1 -1 0
-1 0 1 0 0 0
0 -1 0 -1 -1 -1
2
5
First homology
of the double branched cover of 12n_0273
Z/5
-4 4
12n_0274
2

detected by
the Lickorish test
-3+14t-21t^2+14t^3-3t^4
Seifert matrix of 12n_0274
-1 -3 -2 -1
-2 -3 -4 -2
-2 -4 -5 -2
-1 -3 -3 -2
2
55
First homology
of the double branched cover of 12n_0274
Z/55
-2 2
12n_0275
1

detected by
an unknotting move
2-9t+15t^2-9t^3+2t^4
Seifert matrix of 12n_0275
3 -1 2 0
0 1 -1 0
2 -1 1 0
1 0 1 -1
1
Generator of the Alexander module
(0,1,0,2-t)
the Blanchfield form on it
1
37
First homology
of the double branched cover of 12n_0275
Z/37
0 0
12n_0276
3

detected by
the Stoimenow criterion
1+t-7t^2+11t^3-7t^4+t^5+t^6
Seifert matrix of 12n_0276
1 0 0 0 0 0
0 1 0 0 0 0
1 0 1 0 0 0
1 0 0 1 0 0
1 1 -1 0 1 -1
1 0 1 0 0 1
2
25
First homology
of the double branched cover of 12n_0276
Z/5+Z/5
4 4
12n_0277
1

detected by
an unknotting move
2-8t+15t^2-17t^3+15t^4-8t^5+2t^6
Seifert matrix of 12n_0277
-1 -1 -1 0 -1 0
0 2 0 0 0 0
0 1 -1 0 0 0
-1 -1 -1 -1 -1 0
0 -1 -1 0 -1 0
0 1 0 0 0 1
1
Generator of the Alexander module
(-8-36t+10t^2+2t^3,3+2t+4t^2,-1-19t+15t^2+t^3-3t^4,-3+t-26t^2+31t^3+3t^4-19t^5+3t^6+9t^7,5t+7t^2+t^3-6t^4,3-3t-3t^2)
the Blanchfield form on it
x
67
First homology
of the double branched cover of 12n_0277
Z/67
-2 2
12n_0278
2

detected by
the Lickorish test
4-16t+25t^2-16t^3+4t^4
Seifert matrix of 12n_0278
-2 1 1 0
0 2 0 0
0 1 -1 0
0 1 0 1
1 or 2
65
First homology
of the double branched cover of 12n_0278
Z/65
0 0
12n_0279
1

detected by
an unknotting move
1-6t+11t^2-6t^3+t^4
Seifert matrix of 12n_0279
-15 -12 -10 -8
-11 -9 -7 -6
-10 -8 -6 -5
-5 -4 -3 -2
1
Generator of the Alexander module
(0,1,0,-1)
the Blanchfield form on it
9t^-1-18+9t
25
First homology
of the double branched cover of 12n_0279
Z/25
0 0
12n_0280
1

detected by
an unknotting move
1-6t+12t^2-13t^3+12t^4-6t^5+t^6
Seifert matrix of 12n_0280
-1 0 -1 -1 1 0
1 -2 1 1 -2 0
0 0 -1 -1 0 0
0 0 0 1 0 0
1 -1 1 1 -1 0
-1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,2-t)
the Blanchfield form on it
t^-2-6t^-1+11-6t+t^2
51
First homology
of the double branched cover of 12n_0280
Z/51
-2 2
12n_0281
1

detected by
an unknotting move
-1+6t-18t^2+27t^3-18t^4+6t^5-t^6
Seifert matrix of 12n_0281
-1 0 -1 -1 1 0
1 -2 1 1 -2 0
0 0 -1 -1 0 0
0 0 0 1 0 0
1 -1 1 1 -1 0
-1 0 -1 0 0 1
1
Generator of the Alexander module
(0,1+t,0,1,-1+t,-t)
the Blanchfield form on it
1
77
First homology
of the double branched cover of 12n_0281
Z/77
0 0
12n_0282
1

detected by
an unknotting move
1-5t+9t^2-5t^3+t^4
Seifert matrix of 12n_0282
0 0 -1 1
1 -1 0 -1
0 -1 -1 1
0 0 0 1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
t^-1-2+t
21
First homology
of the double branched cover of 12n_0282
Z/21
0 0
12n_0283
2

detected by
the Lickorish test
-1+6t-14t^2+16t^3-13t^4+16t^5-14t^6+6t^7-t^8
Seifert matrix of 12n_0283
-1 0 -1 -1 -1 0 0 -1
0 1 0 0 0 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 1 -1 -1 -1 1 0 -1
0 1 0 0 0 1 0 0
0 0 -1 0 0 0 -1 -1
0 0 -1 -1 0 1 0 -1
1
Generator of the Alexander module
(2t^2+3t^3-15t^4+13t^5+2t^6-9t^7+5t^8-t^9,0,2+7t-8t^2-5t^3+3t^4+3t^5+4t^6-9t^7+5t^8-t^9,-t+t^2+13t^3-20t^4+8t^5+4t^6-4t^7+t^8,-2t-3t^2+15t^3-13t^4-2t^5+9t^6-5t^7+t^8,0,1+3t-7t^2-6t^3+18t^4-t^5-12t^6+t^7+8t^8-5t^9+t^10,1+3t-6t^2+2t^3-7t^4+8t^5+3t^6-9t^7+5t^8-t^9)
the Blanchfield form on it
x
87
First homology
of the double branched cover of 12n_0283
Z/87
-2 2
12n_0284
1

detected by
an unknotting move
-1+5t-13t^2+19t^3-13t^4+5t^5-t^6
Seifert matrix of 12n_0284
1 0 0 0 0 0
-1 -2 -1 0 -1 -1
0 0 -1 0 0 -1
0 -1 -1 -1 0 0
-1 0 0 1 0 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,-1,1,0)
the Blanchfield form on it
-t^-2+2t^-1-1+2t-t^2
57
First homology
of the double branched cover of 12n_0284
Z/57
0 0
12n_0285
1

detected by
an unknotting move
1-5t+9t^2-9t^3+9t^4-5t^5+t^6
Seifert matrix of 12n_0285
1 0 0 0 0 0
-1 -2 -1 0 -1 -1
0 0 -1 0 0 -1
0 -1 -1 -1 0 0
-1 0 0 1 0 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,-1,0)
the Blanchfield form on it
t^-2-6t^-1+11-6t+t^2
39
First homology
of the double branched cover of 12n_0285
Z/39
-2 2
12n_0286
1

detected by
an unknotting move
2-11t+19t^2-11t^3+2t^4
Seifert matrix of 12n_0286
1 0 0 0
-1 -1 0 1
1 1 -3 -2
1 1 -2 -1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
45
First homology
of the double branched cover of 12n_0286
Z/45
0 0
12n_0287
1

detected by
an unknotting move
-1+6t-15t^2+22t^3-23t^4+22t^5-15t^6+6t^7-t^8
Seifert matrix of 12n_0287
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 -1 0 0
0 0 1 0 0 0 0 0
0 0 1 1 0 0 -1 1
-1 0 -1 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
0 0 1 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,-t-8t^2+23t^3-35t^4+40t^5-39t^6+27t^7-11t^8+2t^9,0,-t-8t^2+23t^3-35t^4+40t^5-39t^6+27t^7-11t^8+2t^9,1-t+7t^2-31t^3+58t^4-75t^5+79t^6-66t^7+38t^8-13t^9+2t^10,0,0)
the Blanchfield form on it
x
111
First homology
of the double branched cover of 12n_0287
Z/111
2 2
12n_0288
1

detected by
an unknotting move
4-12t+17t^2-12t^3+4t^4
Seifert matrix of 12n_0288
-1 0 1 0
0 1 2 -1
0 2 0 -1
0 0 0 1
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
t^-1-1+t
49
First homology
of the double branched cover of 12n_0288
Z/49
0 0
12n_0289
3

detected by
the signature
4-12t+19t^2-21t^3+19t^4-12t^5+4t^6
Seifert matrix of 12n_0289
-1 0 -1 0 0 0
0 -1 0 0 0 0
0 0 -2 0 0 0
0 -1 -1 -1 0 1
0 0 0 0 -1 -1
0 1 1 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
91
First homology
of the double branched cover of 12n_0289
Z/91
-6 6
12n_0290
2

detected by
the signature
-1+7t-16t^2+21t^3-16t^4+7t^5-t^6
Seifert matrix of 12n_0290
-1 0 1 0 0 0
0 0 1 0 0 0
0 -1 -3 -2 -1 -1
0 -2 0 -2 -1 -1
0 0 0 0 -1 0
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(-t,0,0,2,0,1)
the Blanchfield form on it
2t^-1-3+2t
69
First homology
of the double branched cover of 12n_0290
Z/69
-4 4
12n_0291
1

detected by
an unknotting move
3-11t+22t^2-27t^3+22t^4-11t^5+3t^6
Seifert matrix of 12n_0291
-1 -2 0 -1 0 -1
0 -6 0 -3 0 -3
0 1 1 1 0 1
0 -3 0 -1 0 -1
0 1 1 1 1 1
0 -4 0 -2 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-3t^-2+9t^-1-13+9t-3t^2
99
First homology
of the double branched cover of 12n_0291
Z/99
2 2
12n_0292
4

detected by
the signature
2-4t+2t^2+4t^3-7t^4+4t^5+2t^6-4t^7+2t^8
Seifert matrix of 12n_0292
-1 0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
0 -1 0 -1 -1 -1 0 -1
0 -1 0 -1 0 -1 0 0
0 0 0 0 -1 -1 -1 -1
0 -1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(1-2t,0,0,-1,0,0,0,0)
the Blanchfield form on it
2t^-3-t^-2-t^-1+3-t-t^2+2t^3
1
First homology
of the double branched cover of 12n_0292
0
-8 8
12n_0293
1

detected by
an unknotting move
2-3t+2t^2
Seifert matrix of 12n_0293
-8 2
3 -1
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
-t^-1+2-t
7
First homology
of the double branched cover of 12n_0293
Z/7
-2 2
12n_0294
2

detected by
the signature
1-5t+8t^2-6t^3+5t^4-6t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0294
1 0 0 0 0 0 0 0
-1 -1 0 0 -1 0 0 -1
0 0 -1 -1 0 0 -1 0
0 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 0 -1 -1
0 0 0 0 0 1 0 0
0 0 0 -1 0 0 -1 0
-1 0 -1 -1 0 -1 -1 -1
2
45
First homology
of the double branched cover of 12n_0294
Z/45
-4 4
12n_0295
1

detected by
an unknotting move
1-9t+26t^2-35t^3+26t^4-9t^5+t^6
Seifert matrix of 12n_0295
0 2 0 -1 -1 2
1 1 0 1 0 0
0 0 -1 0 0 0
0 0 0 1 0 0
0 1 0 -1 0 1
1 1 -1 1 0 1
1 or 2
107
First homology
of the double branched cover of 12n_0295
Z/107
2 2
12n_0296
2

detected by
the signature
1-5t+8t^2-4t^3+t^4-4t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0296
-1 -1 0 -1 -1 -1 0 0
0 -1 0 -1 0 -1 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 0 -1 -1 -1 0 0
0 0 1 -1 0 -1 0 0
0 -1 0 0 -1 -1 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(-3+3t-4t^2+3t^3-t^4,0,-3-t^2+2t^3-t^4,0,0,0,1-3t+6t^2-4t^3+4t^4-2t^6+t^7,-t+3t^2-6t^3+4t^4-4t^5+2t^7-t^8)
the Blanchfield form on it
x
37
First homology
of the double branched cover of 12n_0296
Z/37
-4 4
12n_0297
2

detected by
the Lickorish test
2-11t+22t^2-25t^3+22t^4-11t^5+2t^6
Seifert matrix of 12n_0297
-1 1 -1 -1 0 0
0 -2 1 1 0 0
0 0 -1 -1 0 0
0 0 0 1 0 0
0 1 -1 0 -1 -1
0 0 0 0 0 1
2
95
First homology
of the double branched cover of 12n_0297
Z/95
-2 2
12n_0298
1

detected by
an unknotting move
-1+7t-21t^2+31t^3-21t^4+7t^5-t^6
Seifert matrix of 12n_0298
1 0 0 0 0 0
-1 -2 0 -1 0 -1
0 -1 -1 -1 0 0
0 0 0 1 0 0
0 -1 0 -1 -1 0
-1 0 1 0 0 0
1
Generator of the Alexander module
(0,2,-2t,3,0,2+2t)
the Blanchfield form on it
t^-2-4t^-1+7-4t+t^2
89
First homology
of the double branched cover of 12n_0298
Z/89
0 0
12n_0299
2

detected by
the signature
-3+12t-18t^2+19t^3-18t^4+12t^5-3t^6
Seifert matrix of 12n_0299
1 0 0 0 0 0
-1 -1 -1 0 -1 0
-1 0 -1 1 -1 1
0 0 0 -2 0 -1
-1 0 0 0 -1 1
0 0 0 -1 0 -2
1
Generator of the Alexander module
(0,-t-t^3+t^4,0,0,1-t^3,0)
the Blanchfield form on it
9t^-2-9t^-1+6-9t+9t^2
85
First homology
of the double branched cover of 12n_0299
Z/85
-4 4
12n_0300
1

detected by
an unknotting move
-1+7t-18t^2+25t^3-18t^4+7t^5-t^6
Seifert matrix of 12n_0300
0 0 2 -1 1 0
0 -1 0 0 -1 -1
1 0 1 1 1 1
0 0 0 1 0 0
1 0 1 0 0 0
1 0 2 -1 1 1
1
Generator of the Alexander module
(0,4-3t,-1+t,1-t,t-t^3,-1+3t-2t^2)
the Blanchfield form on it
-t^-1+4-t
77
First homology
of the double branched cover of 12n_0300
Z/77
0 0
12n_0301
1

detected by
an unknotting move
-1+5t-10t^2+12t^3-11t^4+12t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0301
-1 0 -1 -1 0 -1 0 0
0 1 0 0 0 -1 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 1 0 0 1 -1 0 0
0 0 -1 -1 0 -1 0 0
0 0 -1 0 0 -1 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+5t^-2-11t^-1+15-11t+5t^2-t^3
67
First homology
of the double branched cover of 12n_0301
Z/67
-2 2
12n_0302
1

detected by
an unknotting move
1-9t+27t^2-37t^3+27t^4-9t^5+t^6
Seifert matrix of 12n_0302
1 0 0 0 0 0
-1 -1 0 1 1 1
0 0 -2 1 0 1
1 0 0 -1 -1 -2
1 0 -1 -1 -2 -1
1 0 0 -1 -1 -1
1
Generator of the Alexander module
(-2-2t,2t^3,-t,1+t,-t,-2t-2t^2)
the Blanchfield form on it
2683t^-2-10971t^-1+15761-10971t+2683t^2
111
First homology
of the double branched cover of 12n_0302
Z/111
-2 2
12n_0303
2

detected by
the signature
-1+5t-9t^2+11t^3-9t^4+5t^5-t^6
Seifert matrix of 12n_0303
-1 0 0 0 -1 0
0 0 0 0 -1 0
0 0 -1 -1 0 -1
0 0 0 -1 0 -1
0 -1 0 0 -3 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
41
First homology
of the double branched cover of 12n_0303
Z/41
-4 4
12n_0304
1

detected by
an unknotting move
3-9t+15t^2-17t^3+15t^4-9t^5+3t^6
Seifert matrix of 12n_0304
-1 0 1 0 0 0
0 4 1 0 2 0
0 2 -1 0 1 0
0 2 1 1 1 1
0 1 0 0 1 0
0 2 1 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-2-3t^-1+3-3t+2t^2
71
First homology
of the double branched cover of 12n_0304
Z/71
2 2
12n_0305
4

detected by
the signature
2-4t+4t^2-3t^3+3t^4-3t^5+4t^6-4t^7+2t^8
Seifert matrix of 12n_0305
-1 0 -1 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 -2 0 0 0 0 0
0 0 0 -1 0 -1 0 -1
0 -1 -1 0 -1 0 0 0
0 -1 0 0 -1 -1 0 0
0 0 0 -1 0 -1 -1 -1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(-1+2t,0,0,0,1,0,0,0)
the Blanchfield form on it
2t^-3-t^-2+t^-1-1+t-t^2+2t^3
29
First homology
of the double branched cover of 12n_0305
Z/29
-8 8
12n_0306
1

detected by
an unknotting move
-2+9t-13t^2+9t^3-2t^4
Seifert matrix of 12n_0306
-1 0 -1 0
0 0 -1 0
0 -2 -6 -2
0 -1 -3 -2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
1
35
First homology
of the double branched cover of 12n_0306
Z/35
-2 2
12n_0307
1

detected by
an unknotting move
6-19t+27t^2-19t^3+6t^4
Seifert matrix of 12n_0307
-1 0 1 0
0 2 1 0
0 1 -1 0
0 1 1 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
3t^-2-10t^-1+14-10t+3t^2
77
First homology
of the double branched cover of 12n_0307
Z/77
0 2
12n_0308
3

detected by
the signature
4-10t+12t^2-11t^3+12t^4-10t^5+4t^6
Seifert matrix of 12n_0308
-1 0 -1 0 0 0
0 -1 -1 0 0 0
0 0 -2 0 0 0
0 0 0 -2 0 1
0 -1 -1 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-3+6t^-2-8t^-1+8-8t+6t^2-2t^3
63
First homology
of the double branched cover of 12n_0308
Z/63
-6 6
12n_0309
1

detected by
an unknotting move
1-t-t^2+3t^3-t^4-t^5+t^6
Seifert matrix of 12n_0309
-1 0 1 0 0 0
0 0 1 0 1 0
0 1 -1 0 1 0
0 1 1 1 1 1
0 0 0 0 1 0
0 1 1 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
t^-1-1+t
1
First homology
of the double branched cover of 12n_0309
0
0 0
12n_0310
1

detected by
an unknotting move
2-5t+7t^2-5t^3+2t^4
Seifert matrix of 12n_0310
-1 0 1 0
0 0 1 0
0 1 -1 0
0 1 1 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
21
First homology
of the double branched cover of 12n_0310
Z/21
0 2
12n_0311
1

detected by
an unknotting move
-3+13t-19t^2+13t^3-3t^4
Seifert matrix of 12n_0311
1 1 0 0
0 1 0 0
-1 0 1 -1
-1 1 -1 -2
1
Generator of the Alexander module
(0,0,-2+t,-1)
the Blanchfield form on it
t^-1-2+t
51
First homology
of the double branched cover of 12n_0311
Z/51
2 2
12n_0312
1

detected by
an unknotting move
-1+5t-11t^2+15t^3-11t^4+5t^5-t^6
Seifert matrix of 12n_0312
-1 0 0 0 0 -1
0 -2 0 1 0 -1
0 -1 0 0 0 -1
0 0 0 1 0 0
0 -1 -1 0 0 -1
0 -1 -1 1 -1 -2
1
Generator of the Alexander module
(-3+4t-t^2,0,0,0,2-t,0)
the Blanchfield form on it
-t^-2+4t^-1-5+4t-t^2
49
First homology
of the double branched cover of 12n_0312
Z/49
0 0
12n_0314
1

detected by
an unknotting move
1-6t+13t^2-15t^3+13t^4-6t^5+t^6
Seifert matrix of 12n_0314
1 0 0 0 0 0
-1 -2 0 -1 -1 -1
0 -1 -1 -1 0 0
0 0 0 1 0 0
-1 0 1 0 0 0
0 0 0 1 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
t^-1-2+t
55
First homology
of the double branched cover of 12n_0314
Z/55
2 2
12n_0315
1

detected by
an unknotting move
-1+6t-14t^2+19t^3-14t^4+6t^5-t^6
Seifert matrix of 12n_0315
0 0 0 0 1 -1
1 -1 -1 0 1 0
1 0 -1 0 1 0
1 1 1 1 1 0
0 0 0 0 1 0
-1 -1 0 0 0 0
1
Generator of the Alexander module
(0,0,1,0,0,-1)
the Blanchfield form on it
t^-1-1+t
61
First homology
of the double branched cover of 12n_0315
Z/61
0 0
12n_0316
2

detected by
the signature
-1+7t-15t^2+19t^3-15t^4+7t^5-t^6
Seifert matrix of 12n_0316
-4 -1 0 -3 -3 -2
-2 -1 0 -3 -2 -1
-1 0 -1 -1 -1 0
-4 -2 0 -5 -4 -2
-4 -1 0 -3 -4 -2
-1 0 0 -1 -1 -1
1 or 2
65
First homology
of the double branched cover of 12n_0316
Z/65
-4 4
12n_0317
2

detected by
the Lickorish test
-2+9t-19t^2+25t^3-19t^4+9t^5-2t^6
Seifert matrix of 12n_0317
-1 0 0 2 1 0
0 0 0 1 0 0
0 -1 1 1 1 0
0 2 -2 -6 -4 -2
0 0 -1 -2 -1 -1
0 -1 1 1 1 1
1
Generator of the Alexander module
(t,0,0,2,1,0)
the Blanchfield form on it
-2t^-2+6t^-1-7+6t-2t^2
85
First homology
of the double branched cover of 12n_0317
Z/85
0 0
12n_0318
1

detected by
an unknotting move
1-t-t^2+3t^3-t^4-t^5+t^6
Seifert matrix of 12n_0318
-1 0 1 0 0 1
0 1 1 1 1 1
0 0 0 0 1 -1
0 2 1 2 1 1
0 0 0 0 1 0
0 1 0 0 1 0
1
Generator of the Alexander module
(-1-t,0,0,0,0,-1)
the Blanchfield form on it
3t^-2+t^-1-5+t+3t^2
1
First homology
of the double branched cover of 12n_0318
0
0 0
12n_0319
2

detected by
the signature
-2+6t-8t^2+9t^3-8t^4+6t^5-2t^6
Seifert matrix of 12n_0319
-1 -1 1 -1 0 1
0 -4 0 -2 0 -2
0 -1 -1 0 0 -1
0 -1 0 0 0 -1
-1 -1 1 -1 -1 1
0 -1 -1 0 0 -2
1
Generator of the Alexander module
(0,2-10t-2t^2+5t^3-3t^4,1+t,1-4t-t^2+2t^3-t^4,-1-t+4t^2-2t^4+t^5,2+6t-2t^3+2t^4)
the Blanchfield form on it
41t^-4+172t^-3-990t^-2+1904t^-1-2328+1904t-990t^2+172t^3+41t^4
41
First homology
of the double branched cover of 12n_0319
Z/41
-4 4
12n_0320
1

detected by
an unknotting move
-2+11t-25t^2+33t^3-25t^4+11t^5-2t^6
Seifert matrix of 12n_0320
-1 0 1 0 0 1
0 2 1 1 1 1
0 0 -1 0 1 -1
0 2 1 2 1 1
0 0 0 0 1 0
0 1 0 0 1 -1
1
Generator of the Alexander module
(-t,1,0,0,0,t)
the Blanchfield form on it
2t^-2-5t^-1+8-5t+2t^2
109
First homology
of the double branched cover of 12n_0320
Z/109
0 0
12n_0321
1

detected by
an unknotting move
3-5t+3t^2
Seifert matrix of 12n_0321
-23 4
5 -1
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
-t^-1+2-t
11
First homology
of the double branched cover of 12n_0321
Z/11
-2 2
12n_0322
1

detected by
an unknotting move
-2+6t-7t^2+6t^3-2t^4
Seifert matrix of 12n_0322
-1 0 0 -1
1 -1 -2 -1
2 -2 -3 -1
2 -2 -4 -4
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-1+1-t
23
First homology
of the double branched cover of 12n_0322
Z/23
-2 2
12n_0323
1

detected by
an unknotting move
4-13t+19t^2-13t^3+4t^4
Seifert matrix of 12n_0323
-13 -12 -7 -10
-16 -16 -8 -12
-6 -5 -3 -4
-12 -11 -6 -8
1 or 2
53
First homology
of the double branched cover of 12n_0323
Z/53
0 0
12n_0324
1

detected by
an unknotting move
-5+17t-23t^2+17t^3-5t^4
Seifert matrix of 12n_0324
-3 -7 -6 -5
-10 -30 -25 -20
-8 -23 -19 -16
-6 -17 -15 -11
1 or 2
67
First homology
of the double branched cover of 12n_0324
Z/67
-2 2
12n_0325
1

detected by
an unknotting move
-2+11t-26t^2+35t^3-26t^4+11t^5-2t^6
Seifert matrix of 12n_0325
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 -1 -2 -1 -2 0
0 1 0 1 0 0
0 0 -1 -1 -2 0
0 1 1 1 1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
113
First homology
of the double branched cover of 12n_0325
Z/113
0 0
12n_0326
2

detected by
the signature
-1+4t-8t^2+9t^3-9t^4+9t^5-8t^6+4t^7-t^8
Seifert matrix of 12n_0326
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 1 1 0 0 0
0 0 0 0 1 0 0 0
0 0 -1 -1 0 -1 0 0
-1 -1 0 -1 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,-2t,0,1)
the Blanchfield form on it
-3t^-3+19t^-2-51t^-1+63-51t+19t^2-3t^3
53
First homology
of the double branched cover of 12n_0326
Z/53
-4 4
12n_0327
2

detected by
the signature
-1+4t-9t^2+11t^3-11t^4+11t^5-9t^6+4t^7-t^8
Seifert matrix of 12n_0327
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 0 1 0 0
0 0 0 1 1 0 0 0
0 0 0 0 1 0 0 0
0 0 0 -1 0 1 0 0
-1 -1 0 -1 -1 0 1 1
0 0 0 0 0 0 0 1
1 or 2
61
First homology
of the double branched cover of 12n_0327
Z/61
4 4
12n_0328
3

detected by
the signature
-1+3t^2-5t^3+5t^4-5t^5+3t^6-t^8
Seifert matrix of 12n_0328
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 -1 -1 0 0 0
0 0 -1 -1 0 -1 0 0
-1 -1 0 -1 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,-1,0,0,0,0,0,1-t)
the Blanchfield form on it
-t^-3+4t^-1-7+4t-t^3
19
First homology
of the double branched cover of 12n_0328
Z/19
-6 6
12n_0329
2

detected by
the signature
1+t-6t^2+9t^3-6t^4+t^5+t^6
Seifert matrix of 12n_0329
1 0 0 0 0 0
0 1 0 0 0 0
1 0 1 0 -1 0
0 0 0 1 1 0
1 1 0 0 1 0
0 0 0 1 1 1
1 or 2
21
First homology
of the double branched cover of 12n_0329
Z/21
4 4
12n_0330
1

detected by
an unknotting move
2-9t+20t^2-25t^3+20t^4-9t^5+2t^6
Seifert matrix of 12n_0330
1 0 0 0 0 0
0 -1 0 0 -1 0
1 0 1 0 -1 0
0 0 0 -1 0 -1
1 0 0 -1 -2 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,-2t^2,-1-2t,1,0,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
87
First homology
of the double branched cover of 12n_0330
Z/87
-2 2
12n_0331
2

detected by
the signature
-2+7t-9t^2+9t^3-9t^4+7t^5-2t^6
Seifert matrix of 12n_0331
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 0 -1 0
0 0 0 1 1 0
1 1 0 0 1 0
0 0 0 1 1 1
1
Generator of the Alexander module
(1-16t^2+8t^3,0,1-16t^2+8t^3,-16t^2,2+t-8t^2+8t^4,-2-3t+31t^2+8t^3-8t^4-8t^5)
the Blanchfield form on it
3907t^-2-13158t^-1+16307-13158t+3907t^2
45
First homology
of the double branched cover of 12n_0331
Z/45
4 4
12n_0332
2

detected by
the Nakanishi index
2-2t+t^2-2t^3+2t^4
Seifert matrix of 12n_0332
1 0 0 0
0 1 0 0
1 0 1 1
-1 -1 0 2
2
9
First homology
of the double branched cover of 12n_0332
Z/3+Z/3
4 4
12n_0333
2

detected by
the Nakanishi index
3-11t+17t^2-11t^3+3t^4
Seifert matrix of 12n_0333
1 0 0 0
0 -1 0 1
1 0 1 1
-1 0 0 -3
2
45
First homology
of the double branched cover of 12n_0333
Z/15+Z/3
0 0
12n_0334
2

detected by
the Nakanishi index
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 12n_0334
1 0 0 0
0 1 0 0
1 0 -2 1
-1 -1 0 2
2
63
First homology
of the double branched cover of 12n_0334
Z/21+Z/3
2 2
12n_0335
2

detected by
the Lickorish test
2-10t+22t^2-27t^3+22t^4-10t^5+2t^6
Seifert matrix of 12n_0335
-2 1 0 0 -1 0
0 1 0 0 0 0
-1 1 1 0 -1 0
-1 0 0 -1 0 0
0 0 0 0 -1 0
-1 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,t,0,t^2)
the Blanchfield form on it
2
95
First homology
of the double branched cover of 12n_0335
Z/95
-2 2
12n_0336
2

detected by
the signature
-1+2t-t^3+2t^5-t^6
Seifert matrix of 12n_0336
-5 -1 -1 -2 -2 -1
-2 0 -1 -1 -1 -1
0 0 1 0 0 0
-1 0 0 0 0 0
-2 0 0 -1 0 0
-2 0 -1 -1 -1 0
1
Generator of the Alexander module
(2,1,0,0,1-t,1)
the Blanchfield form on it
t^-2+t^2
5
First homology
of the double branched cover of 12n_0336
Z/5
4 4
12n_0337
1

detected by
an unknotting move
1-9t+25t^2-33t^3+25t^4-9t^5+t^6
Seifert matrix of 12n_0337
-1 0 -1 0 0 1
0 -1 0 0 0 0
0 0 1 0 0 0
-1 0 0 1 1 0
0 0 0 0 1 0
0 -1 1 0 0 1
1
Generator of the Alexander module
(0,2-t,-2+t,1-2t^2+t^3,1+2t-t^2,2t-t^2)
the Blanchfield form on it
-t^-2+8t^-1-16+8t-t^2
103
First homology
of the double branched cover of 12n_0337
Z/103
2 2
12n_0338
4

detected by
the signature
2-4t+4t^2-2t^3+t^4-2t^5+4t^6-4t^7+2t^8
Seifert matrix of 12n_0338
-1 0 0 0 0 0 0 0
0 -1 0 -1 0 0 -1 1
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 0 0 0 1
0 0 0 0 -1 0 0 -1
0 -1 0 -1 0 -1 -1 1
0 0 0 -1 0 0 -1 1
1 0 1 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-t^-2+t^-1-1+t-t^2+t^3
25
First homology
of the double branched cover of 12n_0338
Z/25
-8 8
12n_0339
2

detected by
the Lickorish test
3-11t+21t^2-25t^3+21t^4-11t^5+3t^6
Seifert matrix of 12n_0339
1 0 0 -1 1 0
1 -1 0 1 0 0
0 0 -1 0 0 0
-1 0 -1 -2 0 0
0 0 0 0 1 0
1 -1 0 1 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
3t^-2-9t^-1+13-9t+3t^2
95
First homology
of the double branched cover of 12n_0339
Z/95
-2 2
12n_0340
1

detected by
an unknotting move
-1+3t-3t^2+3t^3-3t^4+3t^5-t^6
Seifert matrix of 12n_0340
-3 -2 -2 -2 0 -2
-2 -1 -2 -2 0 -1
-3 -2 -3 -2 0 -2
-2 -1 -2 -1 0 -1
-1 -1 -1 -1 -1 -1
-2 -2 -2 -2 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
1
17
First homology
of the double branched cover of 12n_0340
Z/17
0 2
12n_0341
3

detected by
the signature
4-10t+13t^2-13t^3+13t^4-10t^5+4t^6
Seifert matrix of 12n_0341
-1 0 0 0 0 0
0 -2 0 1 0 -1
-1 0 -1 0 0 0
-1 0 -1 -1 0 1
0 0 0 0 -1 -1
1 0 1 0 0 -2
1 or 2
67
First homology
of the double branched cover of 12n_0341
Z/67
-6 6
12n_0342
1

detected by
an unknotting move
4-13t+19t^2-13t^3+4t^4
Seifert matrix of 12n_0342
5 6 2 -2
5 5 2 -2
2 2 0 -1
0 0 0 1
1
Generator of the Alexander module
(-6t+4t^2+11t^3-20t^4+14t^5-4t^6,-6t+4t^2+11t^3-20t^4+14t^5-4t^6,1-10t+2t^2+27t^3-42t^4+28t^5-8t^6,0)
the Blanchfield form on it
4t^-1-1+4t
53
First homology
of the double branched cover of 12n_0342
Z/53
0 0
12n_0343
1

detected by
an unknotting move
-4+15t-21t^2+15t^3-4t^4
Seifert matrix of 12n_0343
-5 -4 -4 -2
-4 -2 -4 -2
-5 -4 -5 -2
-1 -1 -1 -1
1
Generator of the Alexander module
(-35+38t-38t^2,34-34t+34t^2,-31+26t-26t^2,-42+38t-38t^2)
the Blanchfield form on it
10065t^-3-67579t^-2+162292t^-1-214238+162292t-67579t^2+10065t^3
59
First homology
of the double branched cover of 12n_0343
Z/59
-2 2
12n_0344
2

detected by
the signature
1-4t+10t^2-15t^3+17t^4-15t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0344
-1 0 -1 -1 0 0 -1 0
0 1 0 0 1 0 0 0
0 0 0 -1 0 1 -1 1
0 1 -1 0 1 0 -1 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 1
0 0 0 -1 0 1 0 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
2t^-3-5t^-2+8t^-1-9+8t-5t^2+2t^3
77
First homology
of the double branched cover of 12n_0344
Z/77
4 4
12n_0345
1

detected by
an unknotting move
-1+4t-8t^2+13t^3-15t^4+13t^5-8t^6+4t^7-t^8
Seifert matrix of 12n_0345
-1 0 -1 -1 0 0 -1 0
0 1 0 0 1 0 0 0
0 0 -2 -1 0 0 -2 0
0 1 -1 0 1 0 -1 0
0 0 0 0 1 0 0 0
0 0 -1 0 0 -1 -1 0
0 0 -1 -1 0 0 -2 0
0 0 -1 0 0 -1 -1 -1
1
Generator of the Alexander module
(-t,0,1,1,0,-t,1,-1)
the Blanchfield form on it
t^-2-2t^-1+3-2t+t^2
67
First homology
of the double branched cover of 12n_0345
Z/67
-2 2
12n_0346
1

detected by
an unknotting move
1-2t+2t^2-t^3+t^4-t^5+2t^6-2t^7+t^8
Seifert matrix of 12n_0346
-1 0 -1 -1 0 0 -1 0
0 -1 0 -1 0 0 0 0
0 0 0 -1 0 1 -1 1
0 0 -1 -2 0 0 -1 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 0 1 0 1
0 0 0 -1 0 1 0 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,1,0,0,0)
the Blanchfield form on it
2t^-3-3t^-2+t^-1+2+t-3t^2+2t^3
13
First homology
of the double branched cover of 12n_0346
Z/13
0 2
12n_0347
1

detected by
an unknotting move
1-3t+7t^2-9t^3+7t^4-3t^5+t^6
Seifert matrix of 12n_0347
-1 0 -1 0 1 0
0 1 0 1 0 0
0 1 0 1 1 0
0 0 0 1 0 0
0 0 1 0 1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1+t,0,0,0,-t^2,0)
the Blanchfield form on it
t^-1-2+t
31
First homology
of the double branched cover of 12n_0347
Z/31
2 2
12n_0348
1

detected by
an unknotting move
1-7t+19t^2-25t^3+19t^4-7t^5+t^6
Seifert matrix of 12n_0348
0 -1 0 0 -1 -1
-1 0 0 0 0 -1
-1 -1 -1 0 -1 -1
-1 -1 0 1 -1 -1
-1 -1 0 0 0 -1
-2 -1 -1 0 -1 -1
1
Generator of the Alexander module
(0,1-2t,-2,-1,2t,-2)
the Blanchfield form on it
-19t^-2+126t^-1-200+126t-19t^2
79
First homology
of the double branched cover of 12n_0348
Z/79
2 2
12n_0349
2

detected by
the signature
-1+4t-2t^2-t^3-2t^4+4t^5-t^6
Seifert matrix of 12n_0349
1 0 1 0 0 0
0 1 1 0 1 0
0 0 1 0 0 0
-1 -1 0 1 -1 -1
0 0 1 0 1 0
-1 0 0 0 0 -1
1
Generator of the Alexander module
(0,1,0,2,0,1)
the Blanchfield form on it
-t^-2-14t^-1+26-14t-t^2
13
First homology
of the double branched cover of 12n_0349
Z/13
4 4
12n_0350
1

detected by
an unknotting move
1-8t+25t^2-35t^3+25t^4-8t^5+t^6
Seifert matrix of 12n_0350
2 1 1 0 1 1
1 2 1 0 2 1
0 0 1 0 0 0
-1 -1 0 -1 -1 -1
1 1 1 0 2 1
0 1 0 0 1 0
1
Generator of the Alexander module
(0,0,0,2-t,-1,1)
the Blanchfield form on it
-1
103
First homology
of the double branched cover of 12n_0350
Z/103
2 2
12n_0351
1

detected by
an unknotting move
1-5t+7t^2-5t^3+7t^4-5t^5+t^6
Seifert matrix of 12n_0351
1 0 -1 -2 -1 0
0 -1 0 2 1 -1
0 0 -1 0 0 0
0 0 -1 -2 -1 0
0 0 -1 -1 0 0
0 0 0 2 1 -1
1
Generator of the Alexander module
(-2,2,0,-1,0,1)
the Blanchfield form on it
-t^-1+2-t
31
First homology
of the double branched cover of 12n_0351
Z/31
-2 2
12n_0352
1

detected by
an unknotting move
1-3t+t^2+3t^3+t^4-3t^5+t^6
Seifert matrix of 12n_0352
0 0 0 0 -1 0
-1 -1 0 0 -1 -1
0 0 1 0 0 -1
-1 0 0 -1 -1 0
-2 -1 0 0 -1 -1
-1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,1,0,0,1,0)
the Blanchfield form on it
1
7
First homology
of the double branched cover of 12n_0352
Z/7
-2 2
12n_0353
1

detected by
an unknotting move
1-9t+25t^2-33t^3+25t^4-9t^5+t^6
Seifert matrix of 12n_0353
1 0 0 1 0 0
-1 0 0 0 -1 -1
0 0 -1 0 0 -1
0 0 0 1 0 0
-1 -1 0 1 0 -1
-1 0 0 0 -1 0
1
Generator of the Alexander module
(5t^2-3t^3+12t^4-23t^5-147t^6-9t^7-31t^8+74t^9-6t^10+72t^11,t+t^2+21t^3+6t^4+18t^5,2-4t-2t^2-31t^3-113t^4-21t^5+5t^6+74t^7-6t^8+72t^9,0,-6+11t+6t^2+76t^3+270t^4+18t^5-46t^6-148t^7+12t^8-144t^9,1+2t+5t^2-3t^3-6t^4-18t^5)
the Blanchfield form on it
x
103
First homology
of the double branched cover of 12n_0353
Z/103
2 2
12n_0354
1

detected by
an unknotting move
1-4t+5t^2-3t^3+5t^4-4t^5+t^6
Seifert matrix of 12n_0354
2 0 2 1 0 1
0 -1 1 1 1 0
1 0 2 1 0 1
1 0 2 2 0 1
1 0 2 1 1 1
0 0 1 1 0 0
1
Generator of the Alexander module
(0,t,1,1,3,-6)
the Blanchfield form on it
-26t^-2+111t^-1-97+111t-26t^2
23
First homology
of the double branched cover of 12n_0354
Z/23
2 2
12n_0355
2

detected by
A(F_2)
1-3t+2t^2+t^3+2t^4-3t^5+t^6
Seifert matrix of 12n_0355
1 0 0 0 0 0
0 1 1 0 1 -1
1 0 1 0 0 -1
0 0 0 -1 0 -1
1 0 0 -1 1 -1
0 0 0 0 0 -1
2
11
First homology
of the double branched cover of 12n_0355
Z/11
2 2
12n_0356
2

detected by
A(F_2)
-1+5t-14t^2+21t^3-14t^4+5t^5-t^6
Seifert matrix of 12n_0356
1 0 0 0 0 0
0 1 1 0 1 -1
1 0 1 0 0 -1
0 0 0 -1 0 -1
1 0 0 -1 -1 -1
0 0 0 0 0 -1
2
61
First homology
of the double branched cover of 12n_0356
Z/61
0 0
12n_0357
2

detected by
the Lickorish test
1-9t+24t^2-31t^3+24t^4-9t^5+t^6
Seifert matrix of 12n_0357
1 0 0 0 0 0
0 1 1 0 1 -1
1 0 -1 0 0 -1
0 0 0 -1 0 -1
1 0 0 -1 -1 -1
0 0 0 0 0 -1
2
99
First homology
of the double branched cover of 12n_0357
Z/99
-2 2
12n_0358
1

detected by
an unknotting move
-3+11t-15t^2+11t^3-3t^4
Seifert matrix of 12n_0358
1 0 0 0
1 1 2 3
1 2 3 4
0 2 2 5
1
Generator of the Alexander module
(0,1,1,0)
the Blanchfield form on it
t^-1-2+t
43
First homology
of the double branched cover of 12n_0358
Z/43
2 2
12n_0359
1

detected by
an unknotting move
3-17t+29t^2-17t^3+3t^4
Seifert matrix of 12n_0359
5 -9 6 2
-8 13 -8 -3
6 -9 5 3
2 -3 2 2
1
Generator of the Alexander module
(0,0,-1,1)
the Blanchfield form on it
-16t^-2+65t^-1-98+65t-16t^2
69
First homology
of the double branched cover of 12n_0359
Z/69
0 0
12n_0360
1

detected by
an unknotting move
3-12t+19t^2-12t^3+3t^4
Seifert matrix of 12n_0360
0 -1 -1 -1
-2 -3 -2 -2
-2 -3 -2 -3
-3 -3 -3 -4
1
Generator of the Alexander module
(0,-2+3t,-1+t,1-2t)
the Blanchfield form on it
-10t^-1+25-10t
49
First homology
of the double branched cover of 12n_0360
Z/49
0 0
12n_0361
2

detected by
the signature
-3+11t-15t^2+15t^3-15t^4+11t^5-3t^6
Seifert matrix of 12n_0361
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 -2 0 -1 -1
0 0 0 -1 0 -1
1 -1 -1 -1 -2 -1
0 0 0 0 0 -1
1 or 2
73
First homology
of the double branched cover of 12n_0361
Z/73
-4 4
12n_0362
1

detected by
an unknotting move
1-4t+7t^2-7t^3+7t^4-4t^5+t^6
Seifert matrix of 12n_0362
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 -2 0 -1 -1
0 0 0 1 0 0
1 -1 -1 -1 0 -1
0 0 0 1 0 1
1
Generator of the Alexander module
(0,t,1,0,1,-t)
the Blanchfield form on it
-1
31
First homology
of the double branched cover of 12n_0362
Z/31
2 2
12n_0363
1

detected by
an unknotting move
1-8t+21t^2-27t^3+21t^4-8t^5+t^6
Seifert matrix of 12n_0363
2 0 1 1 1 1
0 -1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
1 1 1 1 2 1
0 0 0 1 1 0
1
Generator of the Alexander module
(-5+10t-9t^2-7t^3+22t^4-13t^5+2t^6+8t^7-8t^8+2t^9,0,0,0,2t-5t^2+3t^4-5t^5+4t^6-t^7,-2+4t-7t^2+t^3+3t^4-5t^5+4t^6-t^7)
the Blanchfield form on it
x
87
First homology
of the double branched cover of 12n_0363
Z/87
2 2
12n_0364
2

detected by
the Lickorish test
2-11t+23t^2-27t^3+23t^4-11t^5+2t^6
Seifert matrix of 12n_0364
2 0 -1 0 0 0
1 -1 -1 0 0 0
0 0 -1 0 0 0
0 1 0 -1 0 1
1 0 -1 0 1 1
1 -1 -1 0 0 -1
1
Generator of the Alexander module
(49+47t-10t^2+40t^3-124t^4-136t^5-156t^6+702t^7-1200t^8+1532t^9-1016t^10+304t^11-32t^12,5-10t+8t^2-6t^3-66t^4+154t^5-194t^6+180t^7-88t^8+16t^9,7+127t+17t^2+140t^3+536t^4-1238t^5+622t^6+36t^7-1130t^8+1372t^9-448t^10-48t^11+32t^12,40-10t+64t^2+64t^3-388t^4+588t^5-684t^6+460t^7-144t^8+16t^9,-47-36t-31t
the Blanchfield form on it
x
99
First homology
of the double branched cover of 12n_0364
Z/99
-2 2
12n_0365
2

detected by
the Lickorish test
2-11t+23t^2-27t^3+23t^4-11t^5+2t^6
Seifert matrix of 12n_0365
1 0 0 0 0 0
-1 -1 -1 1 0 0
0 0 1 0 1 0
0 0 -1 0 -1 1
0 0 0 0 1 0
-1 0 -1 2 -1 1
1
Generator of the Alexander module
(0,28t+4t^2-134t^3+105t^4-26t^5,-29+107t-136t^2+15t^3+33t^4-13t^5,-57-11t+90t^2-59t^3+13t^4,-86+153t-149t^2+15t^3+33t^4-13t^5,-115t+146t^2-193t^3+118t^4-26t^5)
the Blanchfield form on it
12t^-2-34t^-1+35-34t+12t^2
99
First homology
of the double branched cover of 12n_0365
Z/99
2 2
12n_0366
2

detected by
the signature
1+2t-8t^2+11t^3-8t^4+2t^5+t^6
Seifert matrix of 12n_0366
1 0 0 0 0 0
0 1 1 0 1 0
1 0 1 0 0 -1
0 1 1 1 1 0
1 0 0 0 1 0
1 0 0 0 0 1
1 or 2
29
First homology
of the double branched cover of 12n_0366
Z/29
4 4
12n_0367
1

detected by
an unknotting move
-1+10t-30t^2+43t^3-30t^4+10t^5-t^6
Seifert matrix of 12n_0367
1 0 0 0 0 0
0 1 1 0 1 0
1 0 -1 0 0 -1
0 1 1 1 1 0
1 0 0 0 -1 -1
1 0 0 0 -1 -2
1
Generator of the Alexander module
(0,-t^2,1-t,0,0,0)
the Blanchfield form on it
t^-2-8t^-1+13-8t+t^2
125
First homology
of the double branched cover of 12n_0367
Z/125
0 0
12n_0368
3

detected by
the signature
-1+4t-5t^2+3t^3-t^4+3t^5-5t^6+4t^7-t^8
Seifert matrix of 12n_0368
-1 0 0 0 0 0 0 0
0 -1 0 -1 -1 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 0 0 -1 -1 -1 0 0
-1 0 -1 0 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1-t^2,0,0,0,-2t+t^3,2t^2-t^4)
the Blanchfield form on it
-2t^-3+5t^-2-t^-1+1-t+5t^2-2t^3
27
First homology
of the double branched cover of 12n_0368
Z/27
-6 6
12n_0369
1

detected by
an unknotting move
-1+4t-9t^2+15t^3-17t^4+15t^5-9t^6+4t^7-t^8
Seifert matrix of 12n_0369
-1 0 0 0 0 0 0 0
0 1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 1 -1 1 -1 1 0 0
0 0 0 0 -1 0 0 0
0 1 0 0 -1 1 0 0
-1 0 -1 0 -1 0 -1 0
0 0 0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,-2t^2-t^4,2t^2+t^4,0,1+2t+3t^3+t^5,0,0)
the Blanchfield form on it
-t^-1+2-t
75
First homology
of the double branched cover of 12n_0369
Z/75
-2 2
12n_0370
1

detected by
an unknotting move
-1+2t-t^3+2t^5-t^6
Seifert matrix of 12n_0370
-1 0 -1 1 0 0
0 1 0 0 0 0
0 0 0 0 0 -1
0 1 1 -1 0 1
0 0 0 -1 -1 0
0 1 0 1 0 0
1
Generator of the Alexander module
(t,0,-1,1,0,0)
the Blanchfield form on it
1
5
First homology
of the double branched cover of 12n_0370
Z/5
0 2
12n_0371
1

detected by
an unknotting move
1-2t+2t^2-t^3+2t^4-2t^5+t^6
Seifert matrix of 12n_0371
-1 0 -1 1 0 0
0 -1 0 -1 0 -1
0 0 -2 1 0 0
0 0 2 -1 1 -1
0 0 0 0 1 0
0 0 1 -1 0 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
1
11
First homology
of the double branched cover of 12n_0371
Z/11
-2 2
12n_0372
1

detected by
an unknotting move
1-4t+10t^2-13t^3+10t^4-4t^5+t^6
Seifert matrix of 12n_0372
-1 0 -1 1 0 0
0 -1 0 -1 0 -1
0 0 -2 1 0 0
0 0 2 -1 1 -1
0 0 0 0 1 0
0 0 1 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
1
43
First homology
of the double branched cover of 12n_0372
Z/43
-2 2
12n_0373
2

detected by
the signature
-1+8t-18t^2+23t^3-18t^4+8t^5-t^6
Seifert matrix of 12n_0373
-1 0 -1 1 0 0
0 -1 0 -1 0 -1
0 0 -2 1 0 0
0 0 2 -3 0 -1
0 0 0 -1 -1 0
0 0 1 -1 0 0
1 or 2
77
First homology
of the double branched cover of 12n_0373
Z/77
-4 4
12n_0374
3

detected by
the signature
-2+3t-6t^3+9t^4-6t^5+3t^7-2t^8
Seifert matrix of 12n_0374
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 -1
-1 -1 0 -1 0 0 0 0
0 0 0 -1 -1 1 0 0
0 0 0 1 0 -2 0 0
0 0 -1 0 0 -1 -1 -1
-1 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,-t^2,t,0,1+t^2,-t^2,0,0)
the Blanchfield form on it
-2t^-2+5t^-1-7+5t-2t^2
11
First homology
of the double branched cover of 12n_0374
Z/11
-6 6
12n_0375
2

detected by
the signature
-1+6t-13t^2+17t^3-13t^4+6t^5-t^6
Seifert matrix of 12n_0375
-3 -2 -4 0 -2 0
0 -1 0 0 0 0
-5 -2 -6 0 -3 0
-2 0 -2 -1 -1 0
-2 -1 -2 1 -2 -1
1 0 1 1 0 -1
1
Generator of the Alexander module
(0,0,-2,0,0,1)
the Blanchfield form on it
-14t^-2+43t^-1-60+43t-14t^2
57
First homology
of the double branched cover of 12n_0375
Z/57
-4 4
12n_0376
1

detected by
an unknotting move
1-4t+10t^2-19t^3+23t^4-19t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0376
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 0 0 0 1 0
-1 -1 0 -1 0 0 0 0
0 0 0 -1 -1 1 0 0
0 0 1 1 0 -1 1 1
0 0 0 0 0 0 1 0
-1 -1 1 0 0 0 1 1
1
Generator of the Alexander module
(0,0,6t-4t^2,3t-2t^2,t-t^2,1-t,0,0)
the Blanchfield form on it
-74t^-3+236t^-2-327t^-1+367-327t+236t^2-74t^3
91
First homology
of the double branched cover of 12n_0376
Z/91
-2 2
12n_0377
1

detected by
an unknotting move
1-4t+9t^2-11t^3+9t^4-4t^5+t^6
Seifert matrix of 12n_0377
0 0 1 0 0 -1
0 -1 0 0 0 0
1 -1 -2 0 0 1
0 0 1 1 1 -1
0 0 0 0 1 0
0 0 0 0 -1 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-t^-2+2t^-1-4+2t-t^2
39
First homology
of the double branched cover of 12n_0377
Z/39
2 2
12n_0378
1

detected by
an unknotting move
3-12t+24t^2-29t^3+24t^4-12t^5+3t^6
Seifert matrix of 12n_0378
-1 0 0 1 0 0
-1 -1 0 1 0 0
1 1 1 1 0 1
1 1 0 2 1 0
0 0 0 0 1 0
0 0 0 1 0 1
1
Generator of the Alexander module
(-6t-t^2-4t^3+16t^4-10t^5+14t^6-7t^7+t^8,-1+4t-3t^3+2t^4-4t^5+t^6,8-13t+6t^2+26t^3-67t^4+96t^5-103t^6+72t^7-42t^8+15t^9-2t^10,4-6t+t^2+14t^3-16t^4+35t^5-39t^6+38t^7-54t^8+34t^9-27t^10+13t^11-2t^12,1-4t+2t^2+t^3-t^4+14t^5-21t^6+18t^7-16t^8+7t^9-t^10,2-2t+t^2+10t^3-20t^4+18t^5-16t^6+7t^7-t^8)
the Blanchfield form on it
x
107
First homology
of the double branched cover of 12n_0378
Z/107
2 2
12n_0379
2

detected by
the Nakanishi index
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 12n_0379
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 0 0 -1 0 -1
0 0 -1 0 -1 -1
0 1 0 0 2 0
0 0 0 -1 0 0
2
63
First homology
of the double branched cover of 12n_0379
Z/21+Z/3
2 2
12n_0380
2

detected by
the Nakanishi index
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0380
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 0 -2 -1 0 -2
0 0 -1 0 -1 -1
0 1 0 0 2 0
0 0 -1 -1 0 -2
2
81
First homology
of the double branched cover of 12n_0380
Z/27+Z/3
0 0
12n_0381
1

detected by
an unknotting move
-3+15t-23t^2+15t^3-3t^4
Seifert matrix of 12n_0381
-5 -2 2 -3
-2 -2 1 -1
0 0 -2 -1
-4 -1 0 -3
1
Generator of the Alexander module
(-t+2t^2,2+2t-4t^2,0,-1+4t^2)
the Blanchfield form on it
-12t^-1+21-12t
59
First homology
of the double branched cover of 12n_0381
Z/59
-2 2
12n_0382
1

detected by
an unknotting move
-1+5t-7t^2+5t^3-t^4
Seifert matrix of 12n_0382
-3 -2 2 -5
-2 -2 1 -3
0 0 -2 1
-4 -3 4 -7
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
3t^-1-4+3t
19
First homology
of the double branched cover of 12n_0382
Z/19
-2 2
12n_0383
1

detected by
an unknotting move
-3+13t-19t^2+13t^3-3t^4
Seifert matrix of 12n_0383
-3 -6 -6 -5
-6 -10 -9 -9
-4 -6 -8 -7
-4 -7 -8 -7
1
Generator of the Alexander module
(1,0,-1,3)
the Blanchfield form on it
71t^-1-104+71t
51
First homology
of the double branched cover of 12n_0383
Z/51
-2 2
12n_0384
2

detected by
the signature
-3+13t-25t^2+31t^3-25t^4+13t^5-3t^6
Seifert matrix of 12n_0384
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 0 -2 -1 0 -1
0 -1 -2 -2 0 -1
0 0 0 -1 -1 -1
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(-t,0,1,0,t,0)
the Blanchfield form on it
-3t^-2+10t^-1-12+10t-3t^2
113
First homology
of the double branched cover of 12n_0384
Z/113
-4 4
12n_0385
1

detected by
an unknotting move
-1+7t-17t^2+23t^3-17t^4+7t^5-t^6
Seifert matrix of 12n_0385
-1 0 -1 -1 0 -1
0 1 0 0 0 0
0 0 -2 -1 0 -1
0 -1 -2 -2 0 -1
0 0 0 -1 1 -1
0 0 -1 -1 0 0
1
Generator of the Alexander module
(t,0,0,1,t,0)
the Blanchfield form on it
t^-1-2+t
73
First homology
of the double branched cover of 12n_0385
Z/73
0 0
12n_0386
4

detected by
the signature
-2+4t-3t^2-2t^3+5t^4-2t^5-3t^6+4t^7-2t^8
Seifert matrix of 12n_0386
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 -1
-1 -1 0 -1 0 0 0 0
0 0 -1 -1 -1 1 0 -1
0 0 1 1 0 -2 0 1
0 0 0 0 0 -1 -1 0
-1 -1 0 -1 0 0 0 -1
2
9
First homology
of the double branched cover of 12n_0386
Z/3+Z/3
-8 8
12n_0387
3

detected by
the signature
-1+5t-6t^2+2t^3+t^4+2t^5-6t^6+5t^7-t^8
Seifert matrix of 12n_0387
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 -1
-1 0 -1 0 -1 0 0 0
0 0 0 -1 -1 -1 0 -1
0 -1 0 0 0 -1 1 0
-1 0 -1 0 -1 0 0 -1
2
27
First homology
of the double branched cover of 12n_0387
Z/9+Z/3
-6 6
12n_0388
2

detected by
the Nakanishi index
-1+5t-10t^2+13t^3-10t^4+5t^5-t^6
Seifert matrix of 12n_0388
0 1 0 1 -1 2
0 -2 -1 -1 0 -2
0 0 -1 0 0 0
1 -2 -1 -2 1 -4
0 1 0 1 0 2
1 -2 -2 -3 1 -5
2
45
First homology
of the double branched cover of 12n_0388
Z/15+Z/3
0 0
12n_0389
2

detected by
the Nakanishi index
1-9t+24t^2-31t^3+24t^4-9t^5+t^6
Seifert matrix of 12n_0389
-2 0 -1 -1 -1 0
0 1 0 0 0 0
-2 0 -2 -1 -1 0
0 0 0 -1 0 0
-1 0 -1 -1 0 0
0 -1 0 0 -1 -1
2
99
First homology
of the double branched cover of 12n_0389
Z/33+Z/3
-2 2
12n_0390
1

detected by
an unknotting move
1-6t+14t^2-17t^3+14t^4-6t^5+t^6
Seifert matrix of 12n_0390
-1 0 0 0 0 0
0 2 0 1 0 1
-1 0 -1 0 0 0
-1 0 -1 1 0 0
0 0 0 -1 -1 -1
0 1 0 1 0 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-1+3-t
59
First homology
of the double branched cover of 12n_0390
Z/59
-2 2
12n_0391
2

detected by
the Lickorish test
3-12t+26t^2-33t^3+26t^4-12t^5+3t^6
Seifert matrix of 12n_0391
-1 0 0 0 0 0
0 2 0 1 0 1
-1 0 -1 0 0 0
-1 0 -1 1 0 0
0 0 0 -1 1 -1
0 1 0 1 0 2
1
Generator of the Alexander module
(2+4t+t^2+2t^3,-2-3t+13t^2-9t^3+12t^4+2t^5+4t^6,-2-4t,1-t+4t^2,1+2t,6t-5t^2-4t^3)
the Blanchfield form on it
x
115
First homology
of the double branched cover of 12n_0391
Z/115
2 2
12n_0392
1

detected by
an unknotting move
1-8t+24t^2-33t^3+24t^4-8t^5+t^6
Seifert matrix of 12n_0392
1 0 0 0 0 0
-1 -1 0 -1 1 -1
0 0 -1 0 1 -1
-1 0 0 -1 1 0
0 0 0 0 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,2-t,-1,0,0)
the Blanchfield form on it
1
99
First homology
of the double branched cover of 12n_0392
Z/99
-2 2
12n_0393
2

detected by
A(F_2)
3-12t+19t^2-12t^3+3t^4
Seifert matrix of 12n_0393
-8 -3 -3 -6
-6 -3 -2 -4
-2 -1 0 -1
-7 -3 -2 -4
2
49
First homology
of the double branched cover of 12n_0393
Z/49
0 0
12n_0394
2

detected by
the Lickorish test
1-6t+11t^2-6t^3+t^4
Seifert matrix of 12n_0394
0 -1 -1 0
-2 -3 -2 0
0 -1 -2 1
-1 -1 0 0
2
25
First homology
of the double branched cover of 12n_0394
Z/25
0 0
12n_0395
2

detected by
the signature
-1+8t-18t^2+23t^3-18t^4+8t^5-t^6
Seifert matrix of 12n_0395
1 0 0 0 0 0
0 1 0 0 0 1
1 0 1 1 0 0
-1 -1 0 -1 0 0
1 1 0 1 1 1
0 0 0 0 0 1
1 or 2
77
First homology
of the double branched cover of 12n_0395
Z/77
4 4
12n_0396
1

detected by
an unknotting move
1-7t+16t^2-19t^3+16t^4-7t^5+t^6
Seifert matrix of 12n_0396
1 0 0 0 0 0
0 1 0 0 0 1
1 0 0 1 -1 0
-1 -1 0 -1 0 0
1 1 -1 1 -2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,-1+t-t^2,0,-2+2t-t^2,0)
the Blanchfield form on it
-t^-2+4t^-1-4+4t-t^2
67
First homology
of the double branched cover of 12n_0396
Z/67
2 2
12n_0397
2

detected by
the Nakanishi index
-1+5t-11t^2+15t^3-11t^4+5t^5-t^6
Seifert matrix of 12n_0397
0 0 0 -1 0 0
-1 -1 0 -1 1 0
-1 0 -1 -1 0 0
-2 -1 0 -1 0 0
0 0 0 0 1 1
0 0 0 0 0 1
2
49
First homology
of the double branched cover of 12n_0397
Z/7+Z/7
0 0
12n_0398
2

detected by
the signature
-1+4t-4t^2+3t^3-4t^4+4t^5-t^6
Seifert matrix of 12n_0398
1 0 1 0 0 0
-1 -1 0 -1 1 0
0 0 1 0 0 0
-1 -1 1 0 0 0
0 0 0 0 1 1
0 0 0 0 0 1
1 or 2
21
First homology
of the double branched cover of 12n_0398
Z/21
4 4
12n_0399
1

detected by
an unknotting move
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 12n_0399
1 0 1 0 0 0
-1 0 0 -1 1 0
0 0 1 0 0 0
-1 -1 1 0 0 0
0 0 0 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,1,0,1)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
81
First homology
of the double branched cover of 12n_0399
Z/81
0 0
12n_0400
1

detected by
an unknotting move
1-8t+23t^2-31t^3+23t^4-8t^5+t^6
Seifert matrix of 12n_0400
2 0 1 0 1 0
0 -1 0 -1 -1 0
0 0 0 0 1 0
1 0 1 1 1 0
1 0 1 0 2 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,-t,0,t,1,0)
the Blanchfield form on it
t^-1-4+t
95
First homology
of the double branched cover of 12n_0400
Z/95
2 2
12n_0401
2

detected by
the Lickorish test
1-7t+21t^2-29t^3+21t^4-7t^5+t^6
Seifert matrix of 12n_0401
-1 0 0 0 0 -1
0 1 1 2 1 0
0 1 1 1 1 -1
0 1 0 0 1 0
0 2 1 2 1 0
0 0 0 0 0 -1
1 or 2
87
First homology
of the double branched cover of 12n_0401
Z/87
-2 2
12n_0402
2

detected by
the Nakanishi index
1+t-3t^2+3t^3-3t^4+t^5+t^6
Seifert matrix of 12n_0402
1 0 0 0 0 0
1 1 0 1 0 0
1 0 1 0 0 -1
1 0 0 1 0 0
1 1 0 1 1 0
1 0 0 0 0 1
2
9
First homology
of the double branched cover of 12n_0402
Z/3+Z/3
4 4
12n_0403
2

detected by
the Nakanishi index
-1+3t-t^2-t^3-t^4+3t^5-t^6
Seifert matrix of 12n_0403
1 0 0 0 0 0
1 0 0 0 -1 -1
1 0 1 0 0 -1
1 -1 0 0 -1 -1
1 0 0 0 0 -1
1 -1 0 -1 -1 -2
2
9
First homology
of the double branched cover of 12n_0403
Z/3+Z/3
4 4
12n_0404
1

detected by
an unknotting move
2+t-5t^2+t^3+2t^4
Seifert matrix of 12n_0404
1 0 0 0
-1 2 0 0
1 0 1 -1
1 0 0 1
1
Generator of the Alexander module
(0,-1,t,1)
the Blanchfield form on it
t^-1-2+t
3
First homology
of the double branched cover of 12n_0404
Z/3
2 2
12n_0405
2

detected by
the signature
1-6t+13t^2-12t^3+9t^4-12t^5+13t^6-6t^7+t^8
Seifert matrix of 12n_0405
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 0 0 -1 0
0 -1 0 -1 1 -1 -1 1
0 0 0 -1 0 -1 -1 0
-1 0 -1 0 0 0 -1 0
0 -1 0 -1 0 -1 0 1
1 or 2
73
First homology
of the double branched cover of 12n_0405
Z/73
-4 4
12n_0406
3

detected by
the signature
5-13t+16t^2-15t^3+16t^4-13t^5+5t^6
Seifert matrix of 12n_0406
-1 0 0 0 0 0
0 -2 0 0 -1 -1
-1 0 -1 0 0 0
-1 -1 -1 -1 -1 0
0 -1 0 0 -2 -1
1 0 1 0 -1 -2
1 or 2
83
First homology
of the double branched cover of 12n_0406
Z/83
-6 6
12n_0407
2

detected by
the signature
-1+5t-8t^2+9t^3-8t^4+5t^5-t^6
Seifert matrix of 12n_0407
-1 0 0 0 0 0
0 0 0 0 -1 -1
-1 0 -1 0 0 0
-1 -1 -1 -1 -1 0
0 -1 0 0 -2 -1
1 0 1 0 -1 -2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
37
First homology
of the double branched cover of 12n_0407
Z/37
-4 4
12n_0408
1

detected by
an unknotting move
-1+9t-24t^2+33t^3-24t^4+9t^5-t^6
Seifert matrix of 12n_0408
-1 0 0 0 0 0
0 0 0 1 1 0
-1 0 -1 0 0 0
-1 0 -1 1 0 0
0 1 0 1 2 1
1 1 1 0 1 2
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-3t^-2+9t^-1-13+9t-3t^2
101
First homology
of the double branched cover of 12n_0408
Z/101
0 0
12n_0409
2

detected by
the Lickorish test
1-3t+9t^2-13t^3+9t^4-3t^5+t^6
Seifert matrix of 12n_0409
-1 1 -1 0 0 0
0 1 1 0 1 0
0 1 0 1 0 1
0 0 0 1 0 1
0 1 1 1 2 1
0 0 0 0 0 1
1 or 2
39
First homology
of the double branched cover of 12n_0409
Z/39
2 2
12n_0410
2

detected by
the Lickorish test
2-10t+26t^2-35t^3+26t^4-10t^5+2t^6
Seifert matrix of 12n_0410
-1 1 -1 0 0 0
0 -3 1 0 -1 0
0 1 -1 1 0 1
0 0 0 1 0 1
0 -1 1 1 -1 1
0 0 0 0 0 1
1
Generator of the Alexander module
(42-44t+21t^2-750t^3+2306t^4-3140t^5+2210t^6-800t^7+120t^8,-42+72t+20t^2+312t^3-1138t^4+1400t^5-664t^6+96t^7,-35+135t-70t^2-56t^3-88t^4+354t^5-208t^6+24t^7,10-4t-42t^2+64t^3-24t^4,-7+26t+36t^2-194t^3+258t^4-136t^5+24t^6,7+18t-188t^2+388t^3-370t^4+160t^5-24t^6)
the Blanchfield form on it
x
111
First homology
of the double branched cover of 12n_0410
Z/111
-2 2
12n_0411
1

detected by
an unknotting move
5-9t+5t^2
Seifert matrix of 12n_0411
11 -3
-2 1
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
t^-1-2+t
19
First homology
of the double branched cover of 12n_0411
Z/19
2 2
12n_0412
1

detected by
an unknotting move
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 12n_0412
0 0 -1 0 1 -1
1 -1 0 0 1 0
-1 -1 0 0 0 0
1 1 0 1 1 0
0 0 0 0 1 0
-1 0 -1 0 0 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-1
75
First homology
of the double branched cover of 12n_0412
Z/75
2 2
12n_0413
2

detected by
the Lickorish test
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 12n_0413
-1 0 1 1 0 1
0 2 1 1 1 1
0 0 -1 -1 1 -1
0 1 0 -1 1 0
0 0 0 0 1 0
0 0 0 -1 1 -1
1
Generator of the Alexander module
(1+t,1,0,0,0,0)
the Blanchfield form on it
4t^-2-10t^-1+15-10t+4t^2
75
First homology
of the double branched cover of 12n_0413
Z/75
-2 2
12n_0414
2

detected by
the Nakanishi index
2-6t+9t^2-6t^3+2t^4
Seifert matrix of 12n_0414
1 1 -1 -1
2 0 0 0
-1 -1 0 0
-1 0 -1 0
2
25
First homology
of the double branched cover of 12n_0414
Z/5+Z/5
0 0
12n_0415
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 12n_0415
-1 0 -1 -1 -1 0
0 1 0 0 0 0
0 -1 -2 -2 -2 0
0 0 -1 -2 -1 0
0 -1 -1 -2 -2 0
0 1 1 1 1 1
1
Generator of the Alexander module
(-t,0,1,1,1,0)
the Blanchfield form on it
t^-2-3t^-1+5-3t+t^2
103
First homology
of the double branched cover of 12n_0415
Z/103
-2 2
12n_0416
2

detected by
the signature
-1+4t-10t^2+15t^3-17t^4+15t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0416
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 1 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 0 1 0 0 1
-1 -1 0 0 1 -1 0 1
0 0 0 0 0 -1 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-6t^-1+7-6t+3t^2-t^3
77
First homology
of the double branched cover of 12n_0416
Z/77
-4 4
12n_0417
3

detected by
the signature
-1+4t^2-9t^3+11t^4-9t^5+4t^6-t^8
Seifert matrix of 12n_0417
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 1 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 0 0 1 -1 0 1
0 0 0 0 0 -1 -1 0
0 0 0 0 -1 0 0 -1
1 or 2
35
First homology
of the double branched cover of 12n_0417
Z/35
-6 6
12n_0418
3

detected by
the signature
1-4t+4t^2-t^3-t^4-t^5+4t^6-4t^7+t^8
Seifert matrix of 12n_0418
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 0 0
0 0 -1 -1 0 0 0 -1
0 0 0 0 1 0 0 0
-1 -1 0 0 1 -1 0 0
0 0 0 0 0 -1 -1 0
-1 -1 -1 0 1 0 0 -1
1 or 2
19
First homology
of the double branched cover of 12n_0418
Z/19
-6 6
12n_0419
3

detected by
the signature
1-4t+3t^2+3t^3-7t^4+3t^5+3t^6-4t^7+t^8
Seifert matrix of 12n_0419
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 -1 0
-1 -1 0 -1 0 0 0 0
0 0 -1 0 -1 -1 -1 0
-1 -1 0 0 0 -1 -1 0
0 0 0 0 0 0 1 0
0 0 0 -1 0 0 1 -1
1
Generator of the Alexander module
(-6t^4+8t^6-4t^8+2t^9,1+t^2+2t^3+32t^4+66t^5-36t^6-247t^7-60t^8+322t^9-5t^10-146t^11+68t^12,8t^2+11t^3-4t^4-54t^5+2t^6+50t^7+t^8-26t^9+12t^10,-4t-2t^2-2t^3-t^4+30t^5-17t^6+37t^7-103t^8+118t^9-74t^10+28t^11-6t^12,16t^2+25t^3-8t^4-124t^5+4t^6+118t^7+t^8-60t^9+28t^10,2t-10t^2-19t^3+9t^4+37t^5+19t^6-50t
the Blanchfield form on it
x
3
First homology
of the double branched cover of 12n_0419
Z/3
-6 6
12n_0420
2

detected by
the Nakanishi index
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 12n_0420
1 0 0 0 0 -1
0 -1 0 0 0 0
0 -1 -2 0 -1 -1
1 0 -1 1 -1 -1
0 -1 -1 0 0 0
0 -1 -1 0 -1 -2
2
81
First homology
of the double branched cover of 12n_0420
Z/27+Z/3
0 0
12n_0421
1

detected by
an unknotting move
-2+11t-27t^2+37t^3-27t^4+11t^5-2t^6
Seifert matrix of 12n_0421
-1 0 0 1 -1 1
0 2 0 0 0 0
0 1 -1 0 0 0
0 1 1 1 0 1
0 -1 -1 0 -1 0
0 1 1 0 0 1
1 or 2
117
First homology
of the double branched cover of 12n_0421
Z/117
0 0
12n_0422
1

detected by
an unknotting move
-2+11t-27t^2+37t^3-27t^4+11t^5-2t^6
Seifert matrix of 12n_0422
1 0 0 1 0 1
0 1 -1 -1 0 -1
0 0 -2 -1 0 -1
0 0 0 -1 0 0
1 -1 -1 0 1 0
0 0 0 -1 0 -1
1
Generator of the Alexander module
(8-8t-240t^2+1048t^3-784t^4-544t^5+928t^6-416t^7+64t^8,-3+3t+90t^2-393t^3+294t^4+204t^5-348t^6+156t^7-24t^8,-4+4t+120t^2-524t^3+392t^4+272t^5-464t^6+208t^7-32t^8,0,-4+2t+108t^2-337t^3-149t^4+668t^5-192t^6-300t^7+212t^8-40t^9,-2+t-3t^3-58t^4+40t^5+36t^6-36t^7+8t^8)
the Blanchfield form on it
x
117
First homology
of the double branched cover of 12n_0422
Z/117
0 0
12n_0423
2

detected by
the Lickorish test
1-3t+3t^2-t^3+3t^4-3t^5+t^6
Seifert matrix of 12n_0423
-1 0 0 0 -1 -1
0 1 0 0 0 0
0 1 1 1 0 0
0 1 1 1 0 1
0 0 1 2 1 1
0 1 1 2 0 0
1 or 2
15
First homology
of the double branched cover of 12n_0423
Z/15
2 2
12n_0424
1

detected by
an unknotting move
-1+5t-12t^2+19t^3-21t^4+19t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0424
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 1 0 0 1 0 1 0
-1 -1 -1 0 -1 -1 -1 0
0 0 0 0 0 0 1 0
0 -1 0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,-1,1,-1,0,1,0,1)
the Blanchfield form on it
1
95
First homology
of the double branched cover of 12n_0424
Z/95
-2 2
12n_0425
2

detected by
the signature
1-4t+7t^2-4t^3+t^4-4t^5+7t^6-4t^7+t^8
Seifert matrix of 12n_0425
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 1 0 0 1 0 1 0
-1 -1 -1 0 -1 1 -1 1
0 0 0 0 0 0 1 0
0 -1 0 0 0 0 -1 1
1 or 2
33
First homology
of the double branched cover of 12n_0425
Z/33
4 4
12n_0426
3

detected by
the signature
1-3t^2+4t^3-3t^4+4t^5-3t^6+t^8
Seifert matrix of 12n_0426
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 -1 0 -1 -1 -1 0
0 -1 0 0 -1 0 -1 0
0 -1 0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,1-7t^2+2t^4,-1+4t-2t^2,0,0,0,-3-2t+2t^2)
the Blanchfield form on it
117t^-3-242t^-2+282t^-1-250+282t-242t^2+117t^3
15
First homology
of the double branched cover of 12n_0426
Z/15
-6 6
12n_0427
2

detected by
the signature
1-5t+14t^2-23t^3+27t^4-23t^5+14t^6-5t^7+t^8
Seifert matrix of 12n_0427
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 -1 0 -1 1 -1 1
0 -1 0 0 -1 0 -1 0
0 -1 0 0 0 0 -1 1
1
Generator of the Alexander module
(0,1,-t,0,0,1-t,1,0)
the Blanchfield form on it
t^-3-5t^-2+13t^-1-17+13t-5t^2+t^3
113
First homology
of the double branched cover of 12n_0427
Z/113
-4 4
12n_0428
3

detected by
the signature
-1+4t-5t^2+4t^3-3t^4+4t^5-5t^6+4t^7-t^8
Seifert matrix of 12n_0428
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 -1 -1 0 -1 -1 -1 0
0 -1 0 0 -1 0 -1 0
0 -1 0 0 0 -1 -1 -1
1 or 2
31
First homology
of the double branched cover of 12n_0428
Z/31
-6 6
12n_0429
1

detected by
an unknotting move
-4+18t-27t^2+18t^3-4t^4
Seifert matrix of 12n_0429
10 6 3 6
3 1 1 2
4 2 2 3
5 3 2 4
1
Generator of the Alexander module
(3,0,1,1)
the Blanchfield form on it
t^-1-2+t
71
First homology
of the double branched cover of 12n_0429
Z/71
2 2
12n_0431
1

detected by
an unknotting move
-1+8t-24t^2+35t^3-24t^4+8t^5-t^6
Seifert matrix of 12n_0431
1 0 0 0 0 0
0 1 0 0 0 0
1 0 0 1 -1 0
-1 -1 0 -1 0 0
1 0 -1 1 -2 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,1,-1,0,1)
the Blanchfield form on it
-t^-1+3-t
101
First homology
of the double branched cover of 12n_0431
Z/101
0 0
12n_0432
2

detected by
the signature
3-4t+3t^2-4t^3+3t^4
Seifert matrix of 12n_0432
1 0 0 0
-1 2 0 1
1 1 1 1
0 1 0 2
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
2t^-2-3t^-1+2-3t+2t^2
17
First homology
of the double branched cover of 12n_0432
Z/17
4 4
12n_0433
1

detected by
an unknotting move
-1+2t+4t^2-9t^3+4t^4+2t^5-t^6
Seifert matrix of 12n_0433
1 0 0 0 0 0
0 1 1 1 1 -1
1 0 1 0 0 -1
1 0 0 1 1 -1
1 0 0 0 1 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,0,1,t,0,0)
the Blanchfield form on it
-t^-2+5t^-1-8+5t-t^2
11
First homology
of the double branched cover of 12n_0433
Z/11
2 2
12n_0434
1

detected by
an unknotting move
-1+6t-15t^2+21t^3-15t^4+6t^5-t^6
Seifert matrix of 12n_0434
1 0 0 0 0 0
0 -1 0 0 0 -1
1 -1 0 -1 -1 -1
1 -1 -1 0 0 -1
1 -1 -1 -1 0 0
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,5-6t-2t^2,1+4t-3t^2,1+t-4t^2-8t^3,2-4t,1)
the Blanchfield form on it
-136t^-2+358t^-1-403+358t-136t^2
65
First homology
of the double branched cover of 12n_0434
Z/65
0 0
12n_0435
1

detected by
an unknotting move
-1+6t-13t^2+17t^3-13t^4+6t^5-t^6
Seifert matrix of 12n_0435
0 -1 0 0 -1 0
-2 -1 0 0 -1 -1
0 0 1 0 0 -1
-1 -1 0 -1 -1 0
-1 -1 0 0 0 0
-1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,t,-1,0,1)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
57
First homology
of the double branched cover of 12n_0435
Z/57
0 2
12n_0436
2

detected by
the signature
-1+5t-6t^2+5t^3-6t^4+5t^5-t^6
Seifert matrix of 12n_0436
1 0 0 1 0 0
-1 0 0 1 0 -1
0 0 1 0 0 -1
0 0 0 1 0 0
0 0 0 1 1 0
-1 -1 0 0 -1 -1
2
29
First homology
of the double branched cover of 12n_0436
Z/29
4 4
12n_0437
1

detected by
an unknotting move
1+t-8t^2+13t^3-8t^4+t^5+t^6
Seifert matrix of 12n_0437
-1 1 0 0 0 0
0 -3 -1 0 -1 0
0 -1 0 1 -1 1
0 0 0 1 0 1
0 -1 0 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(2-t,0,2,1,1,0)
the Blanchfield form on it
2t^-1-3+2t
29
First homology
of the double branched cover of 12n_0437
Z/29
0 0
12n_0438
2

detected by
the signature
-1+3t-4t^2+5t^3-4t^4+3t^5-t^6
Seifert matrix of 12n_0438
-2 -1 -1 0 -1 -1
0 -1 -1 0 0 0
0 0 -1 0 0 0
-1 -1 -1 -1 -1 0
-2 -1 -1 0 -1 0
-1 -1 0 0 0 0
1
Generator of the Alexander module
(0,0,0,1+t-t^4,0,t^2)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
21
First homology
of the double branched cover of 12n_0438
Z/21
-4 4
12n_0439
1

detected by
an unknotting move
1-t+t^3-t^5+t^6
Seifert matrix of 12n_0439
-1 0 0 1 0 -1
1 0 0 1 1 0
1 1 1 1 1 0
0 0 0 1 0 0
-1 0 0 1 0 0
-1 -1 0 0 0 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-1-2+t
3
First homology
of the double branched cover of 12n_0439
Z/3
2 2
12n_0440
2

detected by
the Nakanishi index
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0440
-1 0 2 2 2 1
0 0 1 1 1 0
0 2 -6 -6 -7 -4
0 2 -7 -6 -7 -4
0 2 -6 -6 -6 -4
0 0 -2 -2 -2 -1
2
81
First homology
of the double branched cover of 12n_0440
Z/9+Z/9
0 0
12n_0441
2

detected by
the signature
-1+9t-22t^2+29t^3-22t^4+9t^5-t^6
Seifert matrix of 12n_0441
-16 -11 -8 -15 -8 -4
-12 -8 -6 -12 -6 -3
-5 -4 -4 -5 -3 -1
-16 -11 -8 -16 -8 -4
-7 -5 -4 -7 -4 -2
-5 -4 -3 -5 -3 -2
1 or 2
93
First homology
of the double branched cover of 12n_0441
Z/93
-4 4
12n_0442
2

detected by
the Lickorish test
-3+10t-13t^2+10t^3-3t^4
Seifert matrix of 12n_0442
-3 -2 -2 -1
-1 -2 -1 0
-3 -2 -2 0
-1 -1 0 0
2
39
First homology
of the double branched cover of 12n_0442
Z/39
-2 2
12n_0443
1

detected by
an unknotting move
3-8t+11t^2-8t^3+3t^4
Seifert matrix of 12n_0443
0 1 1 -1
2 1 2 0
0 1 1 0
-1 -1 0 0
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
t^-1-2+t
33
First homology
of the double branched cover of 12n_0443
Z/33
0 2
12n_0444
1

detected by
an unknotting move
-2+7t-9t^2+7t^3-2t^4
Seifert matrix of 12n_0444
-1 0 2 1
0 0 1 0
0 2 -5 -4
0 0 -2 -1
1 or 2
27
First homology
of the double branched cover of 12n_0444
Z/27
-2 2
12n_0445
2

detected by
the signature
-2+13t-30t^2+39t^3-30t^4+13t^5-2t^6
Seifert matrix of 12n_0445
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 -1 -2 0 -2 1
0 -1 -1 -1 -1 1
0 0 -1 0 -2 1
0 -1 0 0 0 -1
1 or 2
129
First homology
of the double branched cover of 12n_0445
Z/129
-4 4
12n_0446
1

detected by
an unknotting move
-1+2t+3t^2-7t^3+3t^4+2t^5-t^6
Seifert matrix of 12n_0446
-2 0 0 -1 -1 -2
0 -1 0 0 0 0
-2 0 0 -1 -1 -1
0 0 0 -1 0 -1
-1 0 0 0 -1 -1
0 1 1 0 0 0
1
Generator of the Alexander module
(0,0,1,-t,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
7
First homology
of the double branched cover of 12n_0446
Z/7
-2 2
12n_0447
1

detected by
an unknotting move
-2+8t-16t^2+21t^3-16t^4+8t^5-2t^6
Seifert matrix of 12n_0447
0 1 1 0 0 1
0 -1 0 0 0 0
1 0 0 1 0 -1
-1 1 1 0 0 1
-1 0 1 -1 -1 1
1 -1 -2 1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-2+6t^-1-7+6t-2t^2
73
First homology
of the double branched cover of 12n_0447
Z/73
0 0
12n_0448
1

detected by
an unknotting move
1-6t+14t^2-21t^3+25t^4-21t^5+14t^6-6t^7+t^8
Seifert matrix of 12n_0448
-1 0 -1 -1 0 0 -1 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 1 -1 -1 0 0 -1 0
-1 0 0 -1 1 1 -1 1
0 0 0 0 0 1 0 0
0 1 -1 0 0 0 -1 0
-1 0 0 -1 0 1 0 1
1
Generator of the Alexander module
(0,0,0,0,3-t+2t^2-t^3,1+2t^2-t^3,0,1+2t^2-t^3)
the Blanchfield form on it
t^-2-3t^-1+1-3t+t^2
109
First homology
of the double branched cover of 12n_0448
Z/109
0 2
12n_0449
1

detected by
an unknotting move
1-4t+8t^2-9t^3+8t^4-4t^5+t^6
Seifert matrix of 12n_0449
-1 0 -1 0 -1 0
0 -1 0 -1 0 0
0 0 0 0 -1 0
0 0 0 -1 0 0
0 0 -1 -1 0 -1
0 1 1 1 0 2
1
Generator of the Alexander module
(-t,0,1,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
35
First homology
of the double branched cover of 12n_0449
Z/35
-2 2
12n_0450
1

detected by
an unknotting move
1-8t+23t^2-31t^3+23t^4-8t^5+t^6
Seifert matrix of 12n_0450
-1 0 -1 0 -1 0
0 -1 0 -1 0 0
0 0 -2 0 -1 -1
0 0 0 -1 0 0
0 0 -1 -1 0 -1
0 1 0 1 0 1
1
Generator of the Alexander module
(-11t+10t^2+10t^3-7t^4+t^5,0,-21t+7t^2,1-9t+6t^2-t^3,3-13t-8t^2+7t^3-t^4,-3+t)
the Blanchfield form on it
-2t^-2+9t^-1-12+9t-2t^2
95
First homology
of the double branched cover of 12n_0450
Z/95
-2 2
12n_0451
2

detected by
the Lickorish test
1-3t+8t^2-11t^3+8t^4-3t^5+t^6
Seifert matrix of 12n_0451
-1 0 -1 0 -1 0
0 1 0 0 0 0
0 0 0 0 -1 0
0 1 0 1 0 0
0 0 -1 -1 0 -1
0 1 1 1 0 2
1 or 2
35
First homology
of the double branched cover of 12n_0451
Z/35
2 2
12n_0452
1

detected by
an unknotting move
-4+14t-19t^2+14t^3-4t^4
Seifert matrix of 12n_0452
-6 -6 -4 -5
-4 -3 -2 -4
-5 -4 -4 -4
-4 -5 -2 -4
1
Generator of the Alexander module
(2,1,1,2)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
55
First homology
of the double branched cover of 12n_0452
Z/55
-2 2
12n_0453
3

detected by
the signature
5-15t+24t^2-27t^3+24t^4-15t^5+5t^6
Seifert matrix of 12n_0453
-1 0 -1 0 -1 0
0 -1 0 -1 0 0
0 0 -2 0 -1 -1
0 0 0 -1 0 0
0 0 -1 -1 -2 0
0 1 0 1 1 -2
1 or 2
115
First homology
of the double branched cover of 12n_0453
Z/115
-6 6
12n_0454
1

detected by
an unknotting move
1-4t+11t^2-15t^3+11t^4-4t^5+t^6
Seifert matrix of 12n_0454
-1 1 -1 0 -1 0
0 1 1 0 1 0
0 1 0 1 -1 1
0 0 0 1 0 1
0 1 0 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1-t,0,0,-1,0,0)
the Blanchfield form on it
t^-1-2+t
47
First homology
of the double branched cover of 12n_0454
Z/47
2 2
12n_0455
2

detected by
the signature
-3+12t-21t^2+25t^3-21t^4+12t^5-3t^6
Seifert matrix of 12n_0455
-1 1 -1 0 -1 0
0 1 1 0 1 0
0 1 -2 0 -2 0
0 0 -1 -1 -1 0
0 1 -1 0 -2 0
0 0 -1 -1 -1 -1
1
Generator of the Alexander module
(t-2t^2+3t^3-3t^4+t^5,t-2t^2+3t^3-3t^4+t^5,-2t+4t^2-6t^3+6t^4-2t^5,0,1-3t+6t^2-7t^3+6t^4-2t^5,2-2t^4+t^5)
the Blanchfield form on it
4t^-7-102t^-6+650t^-5-2249t^-4+5316t^-3-9434t^-2+13128t^-1-14624+13128t-9434t^2+5316t^3-2249t^4+650t^5-102t^6+4t^7
97
First homology
of the double branched cover of 12n_0455
Z/97
-4 4
12n_0456
1

detected by
an unknotting move
1-5t^2+9t^3-5t^4+t^6
Seifert matrix of 12n_0456
-1 1 -1 0 -1 0
0 -3 1 0 1 0
0 1 0 1 -1 1
0 0 0 1 0 1
0 1 0 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(1,0,1,0,0,0)
the Blanchfield form on it
t^-1-2+t
17
First homology
of the double branched cover of 12n_0456
Z/17
0 0
12n_0457
1

detected by
an unknotting move
3-5t+3t^2
Seifert matrix of 12n_0457
3 3
4 5
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
-1
11
First homology
of the double branched cover of 12n_0457
Z/11
2 2
12n_0458
1

detected by
an unknotting move
1-6t+16t^2-26t^3+31t^4-26t^5+16t^6-6t^7+t^8
Seifert matrix of 12n_0458
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 0 -1
0 -1 0 0 1 -1 1 0
0 0 0 0 0 -1 0 0
0 -1 0 0 0 -1 1 0
0 0 0 0 1 -1 1 1
1
Generator of the Alexander module
(-2t^2-4t^3+4t^4-6t^5+6t^6-2t^7,-t^2,0,1+t-2t^2+3t^3-3t^4+t^5,-t^2-2t^3+2t^4-3t^5+3t^6-t^7,-4t^3,0,-2t^3)
the Blanchfield form on it
x
129
First homology
of the double branched cover of 12n_0458
Z/129
0 2
12n_0459
2

detected by
the signature
1-6t+15t^2-20t^3+21t^4-20t^5+15t^6-6t^7+t^8
Seifert matrix of 12n_0459
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 1 -1 0 -1 1
0 -1 0 0 -1 -1 -1 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 -1 -1 0
0 0 0 0 -1 0 0 1
1 or 2
105
First homology
of the double branched cover of 12n_0459
Z/105
-4 4
12n_0460
2

detected by
the Nakanishi index
1-6t+15t^2-19t^3+15t^4-6t^5+t^6
Seifert matrix of 12n_0460
1 0 0 0 0 0
0 1 0 -1 0 -1
1 0 -2 -1 0 -1
1 0 -2 -2 0 -1
0 1 -1 -1 1 -1
1 0 -1 -1 0 0
2
63
First homology
of the double branched cover of 12n_0460
Z/21+Z/3
2 2
12n_0461
1

detected by
an unknotting move
-1+7t-20t^2+29t^3-20t^4+7t^5-t^6
Seifert matrix of 12n_0461
0 0 -1 0 -1 0
0 0 -1 0 0 0
-1 0 0 -1 -1 0
0 0 0 -1 0 0
-1 0 -2 -1 -1 -1
-1 1 0 -1 -1 0
1
Generator of the Alexander module
(0,0,0,2-t,0,1)
the Blanchfield form on it
1
85
First homology
of the double branched cover of 12n_0461
Z/85
0 0
12n_0462
2

detected by
the Lickorish test
1-6t+11t^2-6t^3+t^4
Seifert matrix of 12n_0462
-2 0 1 1
0 0 0 -1
0 -1 0 -1
1 0 -1 1
2
25
First homology
of the double branched cover of 12n_0462
Z/25
0 0
12n_0463
1

detected by
an unknotting move
-1+7t-18t^2+25t^3-18t^4+7t^5-t^6
Seifert matrix of 12n_0463
2 0 0 1 -1 1
0 -1 -1 0 0 0
0 0 1 0 0 0
1 0 0 0 0 1
0 -1 -1 0 -1 0
0 1 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
77
First homology
of the double branched cover of 12n_0463
Z/77
0 0
12n_0464
1

detected by
an unknotting move
-1+4t-5t^2+4t^3-t^4
Seifert matrix of 12n_0464
0 0 -1 -1
0 -1 0 -1
0 0 -1 0
-1 0 -1 -2
1
Generator of the Alexander module
(0,-t,0,1)
the Blanchfield form on it
1
15
First homology
of the double branched cover of 12n_0464
Z/15
-2 2
12n_0465
1

detected by
an unknotting move
-1+6t-13t^2+15t^3-13t^4+15t^5-13t^6+6t^7-t^8
Seifert matrix of 12n_0465
-1 1 -1 0 0 0 1 0
0 -1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 -1 0 0 -1 0
-1 0 0 0 1 -1 0 1
-1 1 -1 1 0 -1 1 0
0 -1 0 0 0 0 -1 0
0 0 0 0 0 -1 0 1
1
Generator of the Alexander module
(0,t-3t^2+2t^4-2t^5+2t^6,-1+t+t^2+2t^3-4t^4+2t^5-2t^6,t-3t^2+2t^4-2t^5+2t^6,2t+2t^2-6t^3+4t^5-4t^6+4t^7,4t-3t^2+3t^3-6t^4+6t^5-2t^6+2t^7,t-3t^2+2t^4-2t^5+2t^6,-t+7t^2-9t^3+4t^4-2t^6+2t^7)
the Blanchfield form on it
x
83
First homology
of the double branched cover of 12n_0465
Z/83
-2 2
12n_0466
2

detected by
the signature
1-3t+7t^2-10t^3+11t^4-10t^5+7t^6-3t^7+t^8
Seifert matrix of 12n_0466
-1 0 -1 -1 -1 0 -1 -1
0 1 0 0 0 1 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 1 -1 -1 0 1 -1 -1
0 0 0 0 0 1 0 0
0 0 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 0
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
2t^-3-4t^-2+6t^-1-7+6t-4t^2+2t^3
53
First homology
of the double branched cover of 12n_0466
Z/53
4 4
12n_0467
1

detected by
an unknotting move
-1+3t-5t^2+8t^3-9t^4+8t^5-5t^6+3t^7-t^8
Seifert matrix of 12n_0467
-1 0 -1 -1 -1 0 -1 -1
0 1 0 0 0 1 0 0
0 0 -2 -2 -1 0 -2 -2
0 0 -1 -2 -1 0 -1 -2
0 1 -1 -1 0 1 -1 -1
0 0 0 0 0 1 0 0
0 0 -1 -2 -1 0 -2 -2
0 0 -1 -1 -1 0 -1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+3t^-2-4t^-1+5-4t+3t^2-t^3
43
First homology
of the double branched cover of 12n_0467
Z/43
-2 2
12n_0468
1

detected by
an unknotting move
1-3t+5t^2-6t^3+7t^4-6t^5+5t^6-3t^7+t^8
Seifert matrix of 12n_0468
-1 0 -1 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 0 -1 -1 -2 0 -1 -1
0 -1 0 0 -1 -1 0 0
0 0 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 0
1
Generator of the Alexander module
(1,0,0,0,0,1,0,0)
the Blanchfield form on it
2t^-3-5t^-2+6t^-1-4+6t-5t^2+2t^3
37
First homology
of the double branched cover of 12n_0468
Z/37
0 2
12n_0469
2

detected by
the Lickorish test
2-6t+12t^2-15t^3+12t^4-6t^5+2t^6
Seifert matrix of 12n_0469
-1 0 -1 1 -1 0
0 1 0 0 0 1
0 0 0 1 -1 0
0 0 0 1 1 0
0 1 -1 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
55
First homology
of the double branched cover of 12n_0469
Z/55
2 2
12n_0470
1

detected by
an unknotting move
-2+6t-8t^2+9t^3-8t^4+6t^5-2t^6
Seifert matrix of 12n_0470
-1 0 -1 1 -1 0
0 1 0 0 0 1
0 0 -2 2 -1 0
0 0 1 -3 1 0
0 1 -1 1 0 1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-4+4t-3t^2+t^3
41
First homology
of the double branched cover of 12n_0470
Z/41
0 2
12n_0471
1

detected by
an unknotting move
2-8t+16t^2-19t^3+16t^4-8t^5+2t^6
Seifert matrix of 12n_0471
-1 0 -1 1 -1 0
0 -1 0 0 -1 0
0 0 0 1 -1 0
0 0 0 1 1 0
0 0 -1 1 -2 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(1,0,0,0,0,1)
the Blanchfield form on it
4t^-2-14t^-1+22-14t+4t^2
71
First homology
of the double branched cover of 12n_0471
Z/71
-2 2
12n_0472
4

detected by
the signature
-1+t-2t^3+4t^4-5t^5+4t^6-2t^7+t^9-t^10
Seifert matrix of 12n_0472
-1 0 0 0 0 0 0 0 0 0
0 -1 0 -1 -1 -1 0 -1 -1 -1
-1 0 -1 0 0 0 0 0 0 0
-1 0 -1 -1 -1 -1 0 0 -1 -1
-1 0 -1 0 -1 -1 0 0 0 -1
-1 0 -1 0 0 -1 0 0 0 0
0 -1 0 -1 -1 -1 -1 -1 -1 -1
0 0 0 -1 -1 -1 0 -1 -1 -1
-1 0 -1 0 -1 -1 0 0 -1 -1
-1 0 -1 0 0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-4+t^-3-t^-1+1-t+t^3-t^4
13
First homology
of the double branched cover of 12n_0472
Z/13
-8 8
12n_0473
4

detected by
the signature
2-3t+t^2+3t^3-5t^4+3t^5+t^6-3t^7+2t^8
Seifert matrix of 12n_0473
-1 0 0 0 0 0 0 0
0 -1 0 -1 1 -1 0 -1
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 1 -1 0 0
1 0 1 0 -2 1 0 0
-1 0 -1 0 0 -1 0 0
0 -1 0 -1 1 -1 -1 -1
0 0 0 -1 1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1,-2t,0,0,0)
the Blanchfield form on it
-5t^-4+8t^-3-3t^-2-7t^-1+12-7t-3t^2+8t^3-5t^4
1
First homology
of the double branched cover of 12n_0473
0
-8 8
12n_0474
4

detected by
the signature
2-3t+2t^2-t^3+t^4-t^5+2t^6-3t^7+2t^8
Seifert matrix of 12n_0474
-1 0 0 0 0 0 0 0
0 -2 0 1 1 1 1 1
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 -1 -1 -1
-1 0 -1 0 -1 -1 0 -1
-1 0 -1 0 0 -1 0 0
-1 0 -1 0 -1 -1 -1 -1
-1 0 -1 0 0 -1 0 -1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
-t^-4+2t^-3-2t^-2+2t^-1-2+2t-2t^2+2t^3-t^4
17
First homology
of the double branched cover of 12n_0474
Z/17
-8 8
12n_0475
1

detected by
an unknotting move
1-2t+t^2+t^3+t^4-2t^5+t^6
Seifert matrix of 12n_0475
1 2 0 0 2 0
1 1 0 0 2 0
0 0 -1 0 1 0
2 2 1 1 1 1
0 0 0 0 1 0
2 2 1 0 1 1
1
Generator of the Alexander module
(1,0,0,0,0,-t)
the Blanchfield form on it
-2t^-2+t^-1+2+t-2t^2
7
First homology
of the double branched cover of 12n_0475
Z/7
2 2
12n_0476
2

detected by
the signature
-3+10t-15t^2+17t^3-15t^4+10t^5-3t^6
Seifert matrix of 12n_0476
-2 -1 -1 -1 -1 -1
-1 1 -1 -1 -1 -1
-2 -1 -2 -1 -1 -1
0 0 0 -1 -1 -1
0 0 0 0 -1 0
0 0 0 0 -1 -1
1
Generator of the Alexander module
(-2t,1-10t+20t^2-20t^3+24t^4-20t^5+6t^6,0,0,0,0)
the Blanchfield form on it
73
First homology
of the double branched cover of 12n_0476
Z/73
-4 4
12n_0477
3

detected by
the signature
4-8t+7t^2-5t^3+7t^4-8t^5+4t^6
Seifert matrix of 12n_0477
-1 0 0 0 0 0
0 -2 0 1 -1 1
-1 0 -1 0 0 0
-1 0 -1 -1 1 -1
1 0 1 0 -2 1
-1 0 -1 0 0 -1
1 or 2
43
First homology
of the double branched cover of 12n_0477
Z/43
-6 6
12n_0478
1

detected by
an unknotting move
2-7t+11t^2-7t^3+2t^4
Seifert matrix of 12n_0478
1 2 0 0
1 1 0 0
0 0 -1 0
2 2 1 2
1
Generator of the Alexander module
(3-2t,-3+2t,1-3t+2t^2,-1-6t+4t^2)
the Blanchfield form on it
89t^-2-494t^-1+728-494t+89t^2
29
First homology
of the double branched cover of 12n_0478
Z/29
0 0
12n_0479
1

detected by
an unknotting move
-6+21t-29t^2+21t^3-6t^4
Seifert matrix of 12n_0479
-3 -2 -2 -2
-2 0 -2 -2
-3 -2 -3 -2
-1 -1 -1 -2
1
Generator of the Alexander module
(3,2,3,1)
the Blanchfield form on it
-12t^-1+27-12t
83
First homology
of the double branched cover of 12n_0479
Z/83
-2 2
12n_0480
2

detected by
the Nakanishi index
-1+6t-19t^2+29t^3-19t^4+6t^5-t^6
Seifert matrix of 12n_0480
-2 -1 -1 1 -1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
-1 -1 0 0 0 0
-1 0 0 0 -1 -1
2
81
First homology
of the double branched cover of 12n_0480
Z/9+Z/9
0 0
12n_0481
2

detected by
the Lickorish test
-1+5t-15t^2+23t^3-15t^4+5t^5-t^6
Seifert matrix of 12n_0481
-1 0 0 0 0 0
-1 -1 0 -1 -1 0
0 0 1 0 0 0
0 0 0 1 0 0
-1 0 1 -1 -2 1
0 0 -1 1 1 0
1 or 2
65
First homology
of the double branched cover of 12n_0481
Z/65
0 0
12n_0482
1

detected by
an unknotting move
-1+6t-15t^2+21t^3-15t^4+6t^5-t^6
Seifert matrix of 12n_0482
0 -1 -1 0 0 -1
0 -1 -1 0 0 0
0 0 1 0 0 0
-1 0 0 -1 0 -2
-1 -1 0 0 0 -2
-2 -2 -2 0 -1 -5
1
Generator of the Alexander module
(0,0,0,1,0,2-t)
the Blanchfield form on it
t^-1-2+t
65
First homology
of the double branched cover of 12n_0482
Z/65
0 0
12n_0483
1

detected by
an unknotting move
-1+4t-5t^2+4t^3-t^4
Seifert matrix of 12n_0483
0 0 1 -1
0 -1 0 -1
0 0 -2 1
-1 0 2 -2
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
1
15
First homology
of the double branched cover of 12n_0483
Z/15
-2 2
12n_0484
1

detected by
an unknotting move
1-5t+12t^2-15t^3+12t^4-5t^5+t^6
Seifert matrix of 12n_0484
-2 -1 -1 0 -1 -1
0 -1 0 0 0 0
-1 -1 0 0 0 0
-1 -1 0 -1 -1 0
-2 -1 0 0 -1 0
-1 0 -1 0 0 0
1
Generator of the Alexander module
(0,0,0,-1,0,1)
the Blanchfield form on it
-t^-1+2-t
51
First homology
of the double branched cover of 12n_0484
Z/51
-2 2
12n_0485
1

detected by
an unknotting move
2-8t+16t^2-19t^3+16t^4-8t^5+2t^6
Seifert matrix of 12n_0485
-1 0 -1 -1 0 0
0 0 0 0 -1 -1
0 -1 -1 -1 1 1
0 0 0 -1 1 1
0 -2 0 0 2 2
0 -2 0 0 1 2
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-2-7t^-1+11-7t+2t^2
71
First homology
of the double branched cover of 12n_0485
Z/71
-2 2
12n_0486
2

detected by
the Lickorish test
2-7t+12t^2-13t^3+12t^4-7t^5+2t^6
Seifert matrix of 12n_0486
-1 1 -1 0 0 0
0 1 1 1 1 1
0 1 -2 -1 -1 -1
0 1 0 1 1 0
0 1 0 0 1 0
0 1 0 1 1 1
1
Generator of the Alexander module
(5-4t+2t^2-4t^3+2t^4,0,2t^2,-2-2t+2t^2,-2t+2t^2,2t^2-2t^3)
the Blanchfield form on it
t^-1+t
55
First homology
of the double branched cover of 12n_0486
Z/55
2 2
12n_0487
1

detected by
an unknotting move
-1+t+4t^2-7t^3+4t^4+t^5-t^6
Seifert matrix of 12n_0487
-1 1 -1 0 0 0
0 1 1 1 1 1
0 1 -2 -1 -1 -1
0 1 0 0 1 0
0 1 0 0 0 0
0 1 0 1 1 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
1
11
First homology
of the double branched cover of 12n_0487
Z/11
-2 2
12n_0488
1

detected by
an unknotting move
1-t-2t^2+5t^3-2t^4-t^5+t^6
Seifert matrix of 12n_0488
-1 1 -1 0 0 0
0 -3 1 -1 -1 -1
0 1 0 0 0 0
0 -1 1 0 0 -1
0 -1 1 -1 0 -1
0 -1 1 0 0 0
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
1
5
First homology
of the double branched cover of 12n_0488
Z/5
0 0
12n_0489
1

detected by
an unknotting move
2-11t+28t^2-37t^3+28t^4-11t^5+2t^6
Seifert matrix of 12n_0489
-1 1 -1 0 0 0
0 -3 1 -1 -1 -1
0 1 -2 -1 -1 -1
0 -1 0 -1 -1 -2
0 -1 0 -2 -1 -2
0 -1 0 -1 -1 -1
1
Generator of the Alexander module
(-2,0,0,0,1,0)
the Blanchfield form on it
4t^-2-16t^-1+27-16t+4t^2
119
First homology
of the double branched cover of 12n_0489
Z/119
-2 2
12n_0490
1

detected by
an unknotting move
5-19t+29t^2-19t^3+5t^4
Seifert matrix of 12n_0490
-1 1 -1 0
0 1 1 -1
0 1 -2 1
0 -1 0 2
1 or 2
77
First homology
of the double branched cover of 12n_0490
Z/77
0 0
12n_0491
1

detected by
an unknotting move
-1+7t-16t^2+21t^3-16t^4+7t^5-t^6
Seifert matrix of 12n_0491
-1 0 -1 -1 -1 0
0 -1 0 0 0 0
0 0 0 -1 -1 0
0 0 -1 0 0 -1
0 -1 -1 -1 0 -1
0 1 1 0 0 2
1
Generator of the Alexander module
(t-3t^2+2t^3-t^4,-t+t^2+4t^3-3t^4+t^5+3t^6-2t^7+t^8,-1+t+6t^2-5t^3-6t^4+6t^5-4t^6,5+10t+3t^2-13t^3+8t^4-12t^5-28t^6+14t^7+8t^8-38t^9+24t^10-10t^11,t-3t^2+2t^3-t^4,2+4t+2t^2-8t^3+6t^4-5t^5-15t^6+8t^7+3t^8-16t^9+10t^10-4t^11)
the Blanchfield form on it
x
69
First homology
of the double branched cover of 12n_0491
Z/69
0 2
12n_0492
1

detected by
an unknotting move
-2+9t-20t^2+27t^3-20t^4+9t^5-2t^6
Seifert matrix of 12n_0492
-2 -1 -1 0 -1 0
-1 1 -1 -1 -1 -1
-2 -1 -2 0 -1 0
1 0 1 1 0 0
0 0 0 0 -1 0
1 0 1 1 0 1
1
Generator of the Alexander module
(-2t-t^2+4t^3-4t^4,3-11t+17t^2-19t^3+12t^4-4t^5,0,3-9t+16t^2-16t^3+8t^4,-2+3t-2t^2,2t^2-3t^3+2t^4)
the Blanchfield form on it
-2819t^-5+17231t^-4-53938t^-3+111871t^-2-165725t^-1+187688-165725t+111871t^2-53938t^3+17231t^4-2819t^5
89
First homology
of the double branched cover of 12n_0492
Z/89
0 0
12n_0493
1

detected by
an unknotting move
-2+9t-21t^2+29t^3-21t^4+9t^5-2t^6
Seifert matrix of 12n_0493
-1 0 0 0 0 0
0 2 0 1 1 0
-1 0 -1 0 0 0
-1 0 -1 1 0 0
-1 0 -1 1 1 0
1 1 1 0 0 -1
1
Generator of the Alexander module
(0,1,-1,0,0,0)
the Blanchfield form on it
-2t^-2+3t^-1-1+3t-2t^2
93
First homology
of the double branched cover of 12n_0493
Z/93
0 0
12n_0494
3

detected by
the new u==2 criterion
-1+5t-8t^2+6t^3-5t^4+6t^5-8t^6+5t^7-t^8
Seifert matrix of 12n_0494
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 0 0 -1
-1 -1 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 -1 -1 -1 1 -1 -1
-1 -1 0 -1 -1 0 0 -1
2
45
First homology
of the double branched cover of 12n_0494
Z/15+Z/3
-4 4
12n_0495
2

detected by
the Nakanishi index
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 12n_0495
0 0 1 -1 -1 1
0 -1 0 0 0 0
1 -1 -2 1 1 -2
0 0 1 0 -1 1
0 0 0 0 1 0
0 -1 -1 0 0 0
2
27
First homology
of the double branched cover of 12n_0495
Z/9+Z/3
2 2
12n_0496
3

detected by
the new u==2 criterion
-1+11t-28t^2+37t^3-28t^4+11t^5-t^6
Seifert matrix of 12n_0496
-2 -1 -1 -1 0 -1
-2 -2 -1 -1 0 -1
0 0 -1 0 0 0
-1 -1 -1 -2 0 -1
0 0 0 0 -1 0
-1 -1 -1 0 1 0
2
117
First homology
of the double branched cover of 12n_0496
Z/39+Z/3
-4 4
12n_0497
2

detected by
the Lickorish test
-1+9t-25t^2+35t^3-25t^4+9t^5-t^6
Seifert matrix of 12n_0497
-1 0 0 0 0 0
0 2 0 0 0 1
-1 0 -1 0 0 0
-1 1 -1 1 -1 0
0 0 0 0 -1 -1
0 1 0 0 0 1
1 or 2
105
First homology
of the double branched cover of 12n_0497
Z/105
0 0
12n_0498
2

detected by
A(F_2)
-5+20t-29t^2+20t^3-5t^4
Seifert matrix of 12n_0498
-8 -6 -6 -5
-6 -6 -7 -4
-9 -9 -8 -6
-6 -5 -5 -4
2
79
First homology
of the double branched cover of 12n_0498
Z/79
-2 2
12n_0499
1

detected by
an unknotting move
-1+5t-10t^2+13t^3-10t^4+5t^5-t^6
Seifert matrix of 12n_0499
-1 0 -1 0 -1 0
0 1 0 -1 0 0
0 0 0 0 -1 0
0 0 0 -1 0 0
0 0 -1 -1 0 -1
0 1 1 0 0 2
1
Generator of the Alexander module
(2t-2t^2,0,4t,-2,2t,1)
the Blanchfield form on it
-1
45
First homology
of the double branched cover of 12n_0499
Z/45
0 0
12n_0500
1

detected by
an unknotting move
2-6t+11t^2-13t^3+11t^4-6t^5+2t^6
Seifert matrix of 12n_0500
0 1 0 -1 1 0
1 -2 1 1 -1 1
-1 1 0 -1 1 0
0 0 0 0 1 0
1 0 1 1 0 1
-1 1 -1 -1 1 0
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-2t^-2+6t^-1-9+6t-2t^2
51
First homology
of the double branched cover of 12n_0500
Z/51
2 2
12n_0501
1

detected by
an unknotting move
4-12t+17t^2-12t^3+4t^4
Seifert matrix of 12n_0501
0 0 1 -1
1 -1 0 0
1 0 1 1
-1 -1 0 0
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
2t^-2-6t^-1+8-6t+2t^2
49
First homology
of the double branched cover of 12n_0501
Z/49
0 0
12n_0502
4

detected by
the signature
2-3t+t^2+t^3-t^4+t^5+t^6-3t^7+2t^8
Seifert matrix of 12n_0502
-1 0 0 0 0 0 0 0
0 -2 0 0 0 1 0 0
-1 0 -1 0 0 0 0 0
-1 -1 -1 -1 -1 0 -1 -1
-1 -1 -1 0 -1 0 0 -1
-1 0 -1 0 0 -1 0 0
-1 -1 -1 0 -1 0 -1 -1
-1 -1 -1 0 0 0 0 -1
1
Generator of the Alexander module
(0,1,t,0,t,t,1,0)
the Blanchfield form on it
2t^-3-3t^-2+t^-1+1+t-3t^2+2t^3
9
First homology
of the double branched cover of 12n_0502
Z/9
-8 8
12n_0503
3

detected by
the signature
4-8t+5t^2-t^3+5t^4-8t^5+4t^6
Seifert matrix of 12n_0503
-1 0 0 0 0 0
0 -2 0 0 0 1
-1 0 -1 0 0 0
-1 -1 -1 -1 1 0
1 1 1 0 -2 0
-1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-2t^-3+5t^-2-4t^-1+2-4t+5t^2-2t^3
35
First homology
of the double branched cover of 12n_0503
Z/35
-6 6
12n_0504
1

detected by
an unknotting move
1-6t+15t^2-24t^3+29t^4-24t^5+15t^6-6t^7+t^8
Seifert matrix of 12n_0504
1 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 0 -1 0 0 -1 0
1 0 0 -1 1 -1 -1 1
0 0 0 -1 0 -1 -1 0
0 -1 0 0 0 0 -1 0
1 0 0 -1 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,2,1,0,0)
the Blanchfield form on it
t^-3-3t^-2+4t^-1-7+4t-3t^2+t^3
121
First homology
of the double branched cover of 12n_0504
Z/121
0 0
12n_0505
2

detected by
the Nakanishi index
1-8t+24t^2-33t^3+24t^4-8t^5+t^6
Seifert matrix of 12n_0505
0 0 0 -1 -1 0
0 -1 -1 0 0 0
0 0 1 0 0 0
-1 1 0 0 0 0
-1 0 0 -1 0 0
-1 1 0 0 0 1
2
99
First homology
of the double branched cover of 12n_0505
Z/33+Z/3
2 2
12n_0506
1

detected by
an unknotting move
1-6t+14t^2-17t^3+14t^4-6t^5+t^6
Seifert matrix of 12n_0506
-1 0 0 0 0 0
0 0 -1 0 0 0
-1 0 0 0 -1 0
0 0 -1 -1 -1 0
-1 0 -2 0 -1 -1
-1 1 0 0 -1 0
1
Generator of the Alexander module
(0,0,0,1,0,1)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
59
First homology
of the double branched cover of 12n_0506
Z/59
-2 2
12n_0507
1

detected by
an unknotting move
1-7t+18t^2-23t^3+18t^4-7t^5+t^6
Seifert matrix of 12n_0507
1 0 1 0 1 1
0 0 -1 0 0 0
0 0 2 0 1 1
0 0 1 -1 1 0
0 0 0 0 1 0
0 1 2 0 1 1
1
Generator of the Alexander module
(1,0,0,3-t,0,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
75
First homology
of the double branched cover of 12n_0507
Z/75
2 2
12n_0508
2

detected by
the Nakanishi index
-1+4t-10t^2+16t^3-19t^4+16t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0508
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 1 -1 1 0 -1 0
0 0 0 -1 0 0 -1 0
0 0 0 -1 1 0 -1 0
-1 -1 0 0 0 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 1 0 -1 1 -1
2
81
First homology
of the double branched cover of 12n_0508
Z/27+Z/3
-4 4
12n_0509
2

detected by
the Nakanishi index
1-5t+8t^2-7t^3+7t^4-7t^5+8t^6-5t^7+t^8
Seifert matrix of 12n_0509
-1 -1 -1 -1 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 1 0 0 0 0 0
0 -1 -1 -1 0 0 0 0
-1 -1 0 -1 -1 0 0 0
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 0 1 0
-1 0 0 0 -1 0 1 -1
2
49
First homology
of the double branched cover of 12n_0509
Z/7+Z/7
-4 4
12n_0510
2

detected by
the Nakanishi index
-1+11t-29t^2+39t^3-29t^4+11t^5-t^6
Seifert matrix of 12n_0510
0 -1 -1 -1 0 0
0 1 -1 1 1 0
0 0 1 0 0 0
0 0 -1 1 1 0
1 2 0 2 2 -1
0 0 0 0 0 1
2
121
First homology
of the double branched cover of 12n_0510
Z/11+Z/11
4 4
12n_0511
1

detected by
an unknotting move
-2+9t-19t^2+25t^3-19t^4+9t^5-2t^6
Seifert matrix of 12n_0511
0 0 1 0 1 -1
0 -1 0 0 0 0
0 -1 -1 -2 -1 0
-1 -1 -2 -1 -2 1
0 -1 -1 -1 0 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-1-2+t
85
First homology
of the double branched cover of 12n_0511
Z/85
0 0
12n_0512
1

detected by
an unknotting move
2-7t+15t^2-19t^3+15t^4-7t^5+2t^6
Seifert matrix of 12n_0512
-1 0 -1 1 -1 0
0 1 0 0 0 0
0 0 0 1 -1 0
0 1 1 1 1 1
0 0 -1 0 0 -1
0 1 1 1 0 2
1
Generator of the Alexander module
(-1-t+t^2,0,-3t+t^3,2+2t-t^3,0,0)
the Blanchfield form on it
-2t^-2+3t^-1-6+3t-2t^2
67
First homology
of the double branched cover of 12n_0512
Z/67
2 2
12n_0513
2

detected by
the signature
-2+13t-29t^2+37t^3-29t^4+13t^5-2t^6
Seifert matrix of 12n_0513
-1 0 -1 1 -1 0
0 -1 0 -1 0 -1
0 0 -2 1 -1 -1
0 0 1 -1 2 -1
0 0 -1 1 -2 0
0 0 0 -1 1 -2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
125
First homology
of the double branched cover of 12n_0513
Z/125
-4 4
12n_0514
1

detected by
an unknotting move
1-3t+8t^2-11t^3+8t^4-3t^5+t^6
Seifert matrix of 12n_0514
-1 1 -1 0 -1 0
0 1 1 1 1 1
0 1 0 0 -1 0
0 1 1 2 1 1
0 1 0 0 0 0
0 1 1 2 1 2
1
Generator of the Alexander module
(2t-3t^2+2t^3-t^4-t^5+t^6,0,-1+3t-2t^2-t^3+t^4,-2+t^2-t^3+2t^4-t^5,t-3t^2+2t^3+t^4-t^5,1-2t-t^2+3t^3-t^5)
the Blanchfield form on it
x
35
First homology
of the double branched cover of 12n_0514
Z/35
2 2
12n_0515
2

detected by
the signature
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 12n_0515
-1 1 -1 0 -1 0
0 -3 1 -1 1 -1
0 1 -1 -1 -2 -1
0 -1 0 -2 0 -2
0 1 -1 -1 -1 -1
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(27-120t+170t^2-123t^3+48t^4-12t^5+4t^6,8-71t+131t^2-146t^3+94t^4-28t^5-8t^6+8t^7,11+130t-235t^2+168t^3-52t^4-4t^5,-74+121t-80t^2+20t^3+4t^4,4-40t+59t^2-36t^3+4t^4+4t^5,166-274t+184t^2-48t^3-8t^4)
the Blanchfield form on it
x
89
First homology
of the double branched cover of 12n_0515
Z/89
-4 4
12n_0516
2

detected by
the signature
-2+11t-22t^2+27t^3-22t^4+11t^5-2t^6
Seifert matrix of 12n_0516
-1 1 -1 0 -1 0
0 -3 1 -1 1 -1
0 1 -2 -1 -2 -1
0 -1 0 -1 0 -2
0 1 -1 -1 -2 -1
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(-2+3t-16t^2+11t^3-2t^4,0,1+6t^2-2t^3,-12+7t+2t^2-t^3,1+6t^2-2t^3,-3+t)
the Blanchfield form on it
1507t^-3-8326t^-2+16805t^-1-20648+16805t-8326t^2+1507t^3
97
First homology
of the double branched cover of 12n_0516
Z/97
-4 4
12n_0517
1

detected by
an unknotting move
-1+4t-11t^2+21t^3-27t^4+21t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0517
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 1 1 0 1 0
-1 -1 0 0 1 1 1 1
0 0 0 0 0 0 1 0
-1 -1 0 0 1 0 1 1
1
Generator of the Alexander module
(0,-1-t+4t^2-7t^3+7t^4+15t^5-45t^6+54t^7-36t^8+13t^9-2t^10,3t^2-3t^3-5t^4+32t^5-59t^6+60t^7-37t^8+13t^9-2t^10,-2t-t^2+11t^3-17t^4+14t^5-6t^6+t^7,-3t+15t^2-7t^3-52t^4+187t^5-296t^6+277t^7-161t^8+54t^9-8t^10,6t^2-6t^3-10t^4+64t^5-118t^6+120t^7-74t^8+26t^9-4t^10,-3t+3t^2+5t^3-32t^4+59t^5-60t^6+37t^7-13
the Blanchfield form on it
x
101
First homology
of the double branched cover of 12n_0517
Z/101
0 0
12n_0518
3

detected by
the signature
-1+6t^2-16t^3+21t^4-16t^5+6t^6-t^8
Seifert matrix of 12n_0518
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 0 0 0 1 0
0 0 -1 -1 0 0 0 0
-1 -1 0 0 -1 0 1 0
0 0 0 0 -1 -1 0 0
0 0 0 0 0 0 -1 0
0 0 0 0 0 0 -1 -1
2
63
First homology
of the double branched cover of 12n_0518
Z/21+Z/3
-6 6
12n_0519
1

detected by
an unknotting move
2-3t+2t^2
Seifert matrix of 12n_0519
7 3
4 2
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
-1
7
First homology
of the double branched cover of 12n_0519
Z/7
2 2
12n_0520
1

detected by
an unknotting move
-4+18t-27t^2+18t^3-4t^4
Seifert matrix of 12n_0520
14 -3 2 -5
-4 3 0 2
-1 2 2 1
-5 2 0 2
1
Generator of the Alexander module
(1,0,1,0)
the Blanchfield form on it
-2t^-2+9t^-1-14+9t-2t^2
71
First homology
of the double branched cover of 12n_0520
Z/71
2 2
12n_0521
1

detected by
an unknotting move
1-6t+14t^2-18t^3+17t^4-18t^5+14t^6-6t^7+t^8
Seifert matrix of 12n_0521
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
0 0 1 0 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 -1 -1 0 -1 0
-1 0 0 -1 -1 -1 0 0
0 0 1 0 0 0 1 0
0 0 -1 -1 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,-1+t+9t^2+18t^3+5t^4-6t^5+6t^6,1+t+7t^2+15t^3+18t^4+5t^5-6t^6+6t^7,-1+t+4t^2+11t^3+14t^4-8t^5-6t^6+12t^7,-4t-5t^2-8t^3+5t^4+26t^5+24t^6+11t^7-6t^8+6t^9,0,-1-t+11t^2+36t^3+41t^4+4t^5-6t^6+12t^7)
the Blanchfield form on it
x
95
First homology
of the double branched cover of 12n_0521
Z/95
-2 2
12n_0522
1

detected by
an unknotting move
1-2t+5t^2-7t^3+5t^4-2t^5+t^6
Seifert matrix of 12n_0522
-1 1 -1 -1 -1 -1
0 1 1 1 1 1
0 1 0 -1 -1 -1
0 1 0 0 0 -1
0 1 0 -1 0 -1
0 1 0 0 0 0
1
Generator of the Alexander module
(1,0,0,1,0,0)
the Blanchfield form on it
t^-1-2+t
23
First homology
of the double branched cover of 12n_0522
Z/23
2 2
12n_0523
1

detected by
an unknotting move
2-3t+3t^2-3t^3+2t^4
Seifert matrix of 12n_0523
-1 1 -1 1
0 1 1 -1
0 1 0 1
0 -1 0 1
1
Generator of the Alexander module
(t^2-7t^3+3t^4-4t^5+4t^6,-2t-13t^2+33t^3-19t^4+20t^5-20t^6,11t^2-6t^3+4t^4-8t^5,1+6t-24t^2+14t^3-12t^4+16t^5)
the Blanchfield form on it
5867t^-3-14713t^-2+24009t^-1-27446+24009t-14713t^2+5867t^3
13
First homology
of the double branched cover of 12n_0523
Z/13
0 2
12n_0524
1

detected by
an unknotting move
2-11t+21t^2-23t^3+21t^4-11t^5+2t^6
Seifert matrix of 12n_0524
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 0 0 0
0 0 1 -1 -1 0
-1 1 1 0 -1 0
0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-2-13t^-1+23-13t+2t^2
91
First homology
of the double branched cover of 12n_0524
Z/91
-2 2
12n_0525
1

detected by
an unknotting move
-1+8t-28t^2+43t^3-28t^4+8t^5-t^6
Seifert matrix of 12n_0525
-1 0 0 0 1 1
0 -1 -1 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 -1 0 0 1 0
0 -1 -1 1 0 -1
1 or 2
117
First homology
of the double branched cover of 12n_0525
Z/117
0 0
12n_0526
2

detected by
the signature
1-4t+6t^2-3t^3+t^4-3t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0526
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 1 0 0 1 0 0 0
0 1 0 0 1 -1 -1 -1
-1 0 -1 0 0 0 -1 0
-1 0 -1 0 0 0 -1 -1
2
29
First homology
of the double branched cover of 12n_0526
Z/29
-4 4
12n_0527
2

detected by
the signature
-3+12t-20t^2+23t^3-20t^4+12t^5-3t^6
Seifert matrix of 12n_0527
1 0 0 0 0 0
-1 -1 1 -1 -1 1
0 0 -2 1 0 -1
0 0 0 -1 0 0
-1 0 0 -1 -1 1
0 0 -1 1 0 -2
1
Generator of the Alexander module
(0,-5+28t-45t^2+18t^3,5-13t+6t^2+10t^3-6t^4,-5+3t,-7+21t-19t^2-4t^3-4t^4+6t^5,-5t-2t^2+3t^3)
the Blanchfield form on it
9739t^-3-38956t^-2+64927t^-1-74666+64927t-38956t^2+9739t^3
93
First homology
of the double branched cover of 12n_0527
Z/93
-4 4
12n_0528
2

detected by
the signature
1+2t-10t^2+15t^3-10t^4+2t^5+t^6
Seifert matrix of 12n_0528
1 0 0 0 0 0
0 1 0 0 1 0
0 0 1 0 0 0
1 0 0 1 0 0
1 0 1 -1 1 0
1 0 1 0 0 1
1 or 2
37
First homology
of the double branched cover of 12n_0528
Z/37
4 4
12n_0529
1

detected by
an unknotting move
1-10t+28t^2-37t^3+28t^4-10t^5+t^6
Seifert matrix of 12n_0529
1 0 0 0 0 0
0 -1 0 0 0 0
0 0 1 0 0 0
1 0 0 -2 0 -1
1 -1 1 -1 -1 0
1 0 1 -1 0 -1
1 or 2
115
First homology
of the double branched cover of 12n_0529
Z/115
-2 2
12n_0530
1

detected by
an unknotting move
2-10t+19t^2-21t^3+19t^4-10t^5+2t^6
Seifert matrix of 12n_0530
0 1 1 0 1 0
0 -1 0 0 0 0
1 0 0 0 -1 0
1 0 -2 -2 -2 1
1 -1 -2 0 -1 0
-1 0 1 1 1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-2t^-2+5t^-1-4+5t-2t^2
83
First homology
of the double branched cover of 12n_0530
Z/83
-2 2
12n_0531
1

detected by
an unknotting move
-1+4t-11t^2+20t^3-25t^4+20t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0531
-1 0 0 0 0 0 0 0
-1 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 0 0 -1 0 0 0 0
0 0 0 1 1 0 1 0
-1 -1 0 0 1 1 1 1
0 0 0 0 0 0 1 0
0 0 0 1 1 0 1 1
1
Generator of the Alexander module
(0,0,1,1,1,-t,1,-t)
the Blanchfield form on it
t^-3-5t^-2+11t^-1-14+11t-5t^2+t^3
97
First homology
of the double branched cover of 12n_0531
Z/97
0 0
12n_0532
1

detected by
an unknotting move
-2+11t-29t^2+41t^3-29t^4+11t^5-2t^6
Seifert matrix of 12n_0532
-1 -1 0 0 0 0
0 -1 0 0 0 0
1 1 2 0 1 0
1 1 0 0 0 -1
1 0 0 0 1 0
1 1 1 -1 1 -1
1
Generator of the Alexander module
(0,0,3-2t,0,0,1-2t)
the Blanchfield form on it
-t^-2+3t^-1-6+3t-t^2
125
First homology
of the double branched cover of 12n_0532
Z/125
0 0
12n_0533
2

detected by
the Lickorish test
-1+4t-8t^2+12t^3-13t^4+12t^5-8t^6+4t^7-t^8
Seifert matrix of 12n_0533
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 1 0 0 1 1 0 0
0 0 0 0 0 1 0 0
-1 0 -1 0 0 0 -1 0
0 1 0 0 1 0 -1 -1
2
63
First homology
of the double branched cover of 12n_0533
Z/63
-2 2
12n_0534
1

detected by
an unknotting move
-2+11t-25t^2+33t^3-25t^4+11t^5-2t^6
Seifert matrix of 12n_0534
-1 0 0 -1 1 0
0 2 0 0 0 0
0 1 -1 0 0 0
0 -1 -1 -1 0 -1
0 1 0 0 1 1
0 1 0 0 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
2t^-1-3+2t
109
First homology
of the double branched cover of 12n_0534
Z/109
0 0
12n_0535
1

detected by
an unknotting move
-1+7t-11t^2+7t^3-t^4
Seifert matrix of 12n_0535
11 3 8 6
3 2 2 2
11 3 7 6
5 2 4 3
1
Generator of the Alexander module
(1-t+12t^2+225t^3-228t^4+36t^5,20-20t-245t^2+426t^3-777t^4+138t^5,41-41t-533t^2+615t^3-1353t^4+246t^5,-24+24t+307t^2-402t^3+831t^4-150t^5)
the Blanchfield form on it
-119561t^-1-749750-119561t
27
First homology
of the double branched cover of 12n_0535
Z/27
2 2
12n_0536
1

detected by
an unknotting move
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 12n_0536
-1 0 -1 1 -1 -1
0 -1 0 0 1 1
0 0 1 0 0 0
0 0 0 1 0 0
0 0 -1 0 0 1
0 0 -1 -1 1 2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-t^-1+3-t
81
First homology
of the double branched cover of 12n_0536
Z/81
0 0
12n_0537
1

detected by
an unknotting move
2-12t+27t^2-33t^3+27t^4-12t^5+2t^6
Seifert matrix of 12n_0537
0 1 1 0 0 -1
0 -1 0 0 0 0
0 -1 -1 0 0 0
0 0 0 -1 0 -1
0 -1 0 0 2 2
-1 0 0 0 1 0
1
Generator of the Alexander module
(2,0,0,2,-1-2t,0)
the Blanchfield form on it
5t^-3-30t^-2+67t^-1-82+67t-30t^2+5t^3
115
First homology
of the double branched cover of 12n_0537
Z/115
-2 2
12n_0538
2

detected by
the signature
1-5t+10t^2-11t^3+11t^4-11t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0538
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 1 0 0 1 0 0 0
0 1 0 0 1 -1 -1 -1
-1 0 -1 0 0 0 -1 0
0 0 0 0 1 0 -1 -1
1 or 2
65
First homology
of the double branched cover of 12n_0538
Z/65
-4 4
12n_0539
1

detected by
an unknotting move
-1+5t-14t^2+27t^3-33t^4+27t^5-14t^6+5t^7-t^8
Seifert matrix of 12n_0539
-1 0 0 0 0 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 1 0 0 1 1 0 0
-1 0 -1 0 0 1 1 1
0 0 0 0 1 1 0 1
1
Generator of the Alexander module
(0,0,t,1+t,0,0,1+t,0)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+11-8t+4t^2-t^3
127
First homology
of the double branched cover of 12n_0539
Z/127
-2 2
12n_0540
2

detected by
the Lickorish test
2-10t+21t^2-25t^3+21t^4-10t^5+2t^6
Seifert matrix of 12n_0540
-1 -1 0 0 -1 1
0 -1 0 0 -1 1
0 0 2 0 0 0
0 0 1 -1 0 0
0 0 -1 -1 -1 0
0 0 1 0 0 1
1
Generator of the Alexander module
(-1+t,0,0,0,-1,1)
the Blanchfield form on it
2t^-2-8t^-1+13-8t+2t^2
91
First homology
of the double branched cover of 12n_0540
Z/91
-2 2
12n_0541
1

detected by
an unknotting move
2-9t+19t^2-23t^3+19t^4-9t^5+2t^6
Seifert matrix of 12n_0541
1 0 0 0 0 0
1 1 0 1 0 1
1 1 2 1 0 1
1 1 1 0 0 1
0 1 0 0 -1 1
1 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,-t,t)
the Blanchfield form on it
2t^-2-5t^-1+6-5t+2t^2
83
First homology
of the double branched cover of 12n_0541
Z/83
2 2
12n_0542
1

detected by
an unknotting move
1-9t+28t^2-39t^3+28t^4-9t^5+t^6
Seifert matrix of 12n_0542
1 0 0 0 0 0
-1 -1 -1 1 -1 1
0 0 1 0 0 0
1 0 0 1 0 0
-1 0 -1 1 -1 1
1 0 1 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
t^-2-5t^-1+7-5t+t^2
115
First homology
of the double branched cover of 12n_0542
Z/115
2 2
12n_0543
2

detected by
the Lickorish test
1-5t+15t^2-21t^3+15t^4-5t^5+t^6
Seifert matrix of 12n_0543
-1 1 -1 0 0 -1
0 1 1 1 0 1
0 1 0 0 1 -1
0 1 1 2 1 1
0 0 0 0 1 0
0 1 0 0 1 0
1 or 2
63
First homology
of the double branched cover of 12n_0543
Z/63
2 2
12n_0544
1

detected by
an unknotting move
2-12t+28t^2-35t^3+28t^4-12t^5+2t^6
Seifert matrix of 12n_0544
-1 1 -1 0 0 -1
0 1 1 1 0 1
0 1 -2 -1 0 -2
0 1 0 1 0 0
0 0 -1 -1 -1 -1
0 1 -1 -1 0 -2
1
Generator of the Alexander module
(0,0,1,1,-t,1)
the Blanchfield form on it
-2t^-1+5-2t
119
First homology
of the double branched cover of 12n_0544
Z/119
-2 2
12n_0545
2

detected by
the signature
-2+10t-19t^2+23t^3-19t^4+10t^5-2t^6
Seifert matrix of 12n_0545
-1 1 -1 0 0 -1
0 -3 1 -1 0 1
0 1 -1 -1 0 -2
0 -1 0 -2 0 0
0 0 -1 -1 -1 -1
0 1 -1 -1 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
85
First homology
of the double branched cover of 12n_0545
Z/85
-4 4
12n_0546
2

detected by
the Nakanishi index
2-8t+14t^2-15t^3+14t^4-8t^5+2t^6
Seifert matrix of 12n_0546
1 1 1 1 0 1
0 1 0 1 0 0
0 1 2 1 0 0
0 1 1 0 0 0
0 0 -1 -1 -1 0
0 1 1 1 0 1
2
63
First homology
of the double branched cover of 12n_0546
Z/21+Z/3
2 2
12n_0547
1

detected by
an unknotting move
4-17t+27t^2-17t^3+4t^4
Seifert matrix of 12n_0547
-1 0 -1 -1
0 2 1 2
0 2 3 2
0 2 2 1
1
Generator of the Alexander module
(2-t,1,0,0)
the Blanchfield form on it
1
69
First homology
of the double branched cover of 12n_0547
Z/69
0 0
12n_0548
1

detected by
an unknotting move
-1+8t-20t^2+27t^3-20t^4+8t^5-t^6
Seifert matrix of 12n_0548
0 0 -1 1 -1 0
1 -1 0 1 0 -1
-1 -1 0 0 0 0
0 0 0 1 0 0
-1 0 -1 0 0 0
1 0 0 1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-t^-2+2t^-1-3+2t-t^2
85
First homology
of the double branched cover of 12n_0548
Z/85
0 0
12n_0549
2

detected by
the Nakanishi index
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 12n_0549
-1 0 0 0 0 -1
0 -1 0 -1 0 -1
0 0 0 0 0 -1
0 0 0 -1 -1 -1
0 0 -1 0 0 -1
0 0 -1 0 -1 -3
2
27
First homology
of the double branched cover of 12n_0549
Z/9+Z/3
-2 2
12n_0550
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 12n_0550
1 0 0 0
-2 -2 -2 -2
-1 -2 0 -1
-1 -1 0 -1
1
Generator of the Alexander module
(0,0,1,1)
the Blanchfield form on it
t^-1-2+t
33
First homology
of the double branched cover of 12n_0550
Z/33
0 0
12n_0551
2

detected by
the signature
-3+13t-23t^2+27t^3-23t^4+13t^5-3t^6
Seifert matrix of 12n_0551
1 0 0 0 0 0
-1 -1 1 0 1 0
1 0 -2 0 -1 -1
0 0 0 -1 0 -1
1 0 -1 -1 -2 -1
0 0 0 0 0 -1
1 or 2
105
First homology
of the double branched cover of 12n_0551
Z/105
-4 4
12n_0552
1

detected by
an unknotting move
-1+3t-t^2-t^3-t^4+3t^5-t^6
Seifert matrix of 12n_0552
1 0 0 0 0 0
-1 -1 1 0 1 0
1 0 0 -1 -1 -1
0 0 0 -1 0 -1
1 0 -1 -1 0 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,1,0,0)
the Blanchfield form on it
t^-1-2+t
9
First homology
of the double branched cover of 12n_0552
Z/9
0 2
12n_0553
3

detected by
the Nakanishi index
4-20t+33t^2-20t^3+4t^4
Seifert matrix of 12n_0553
-3 -4 0 -2
-5 -4 1 -2
0 0 -1 0
-1 -1 0 0
3
81
First homology
of the double branched cover of 12n_0553
Z/3+Z/9+Z/3
0 0
12n_0554
3

detected by
the Nakanishi index
-2+7t-9t^2+7t^3-2t^4
Seifert matrix of 12n_0554
-3 -4 0 -2
-5 -5 1 -2
0 0 1 0
-1 -1 0 0
3
27
First homology
of the double branched cover of 12n_0554
Z/3+Z/3+Z/3
2 2
12n_0555
3

detected by
the Nakanishi index
1-9t+33t^2-49t^3+33t^4-9t^5+t^6
Seifert matrix of 12n_0555
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
1 0 0 1 1 1
-1 -1 0 0 -1 -1
-1 0 -1 0 0 -1
3
135
First homology
of the double branched cover of 12n_0555
Z/15+Z/3+Z/3
2 2
12n_0556
3

detected by
the Nakanishi index
4-20t+33t^2-20t^3+4t^4
Seifert matrix of 12n_0556
1 0 0 0
1 1 -1 0
1 0 -2 0
1 -1 -1 -2
2
81
First homology
of the double branched cover of 12n_0556
Z/9+Z/3+Z/3
0 0
12n_0557
2

detected by
the signature
-3+12t-21t^2+25t^3-21t^4+12t^5-3t^6
Seifert matrix of 12n_0557
-1 -1 0 0 -1 0
0 -2 0 0 -1 0
0 1 -1 0 1 0
0 0 0 1 -1 0
0 -1 0 0 -2 0
0 0 -1 0 1 -1
1
Generator of the Alexander module
(-2+13t-7t^2-43t^3+46t^4+48t^5-76t^6+24t^7,-4-10t+34t^2-102t^3+92t^4+96t^5-152t^6+48t^7,7-24t+36t^2+28t^3-138t^4+108t^5+96t^6-152t^7+48t^8,-2+22t-19t^2-39t^3+46t^4+48t^5-76t^6+24t^7,-1-49t+48t^2+23t^3-156t^4+174t^5+64t^6-272t^7+200t^8-48t^9,-t+2t^2-30t^3+24t^4+82t^5-92t^6-96t^7+152t^8-48t^9)
the Blanchfield form on it
x
97
First homology
of the double branched cover of 12n_0557
Z/97
-4 4
12n_0558
2

detected by
the Lickorish test
1-3t+8t^2-11t^3+8t^4-3t^5+t^6
Seifert matrix of 12n_0558
-1 0 -1 0 0 0
0 -1 1 1 -1 1
0 0 -1 1 -1 1
0 0 0 1 0 1
0 0 0 0 -1 0
0 0 0 0 0 1
1 or 2
35
First homology
of the double branched cover of 12n_0558
Z/35
-2 2
12n_0559
2

detected by
the signature
-2+7t-11t^2+13t^3-11t^4+7t^5-2t^6
Seifert matrix of 12n_0559
-1 0 0 0 2 1
0 0 0 0 1 0
0 0 -1 -1 -2 -1
0 -1 0 -1 0 0
0 0 0 -2 -6 -4
0 -1 0 -1 -2 -1
1
Generator of the Alexander module
(0,0,1,2,0,2)
the Blanchfield form on it
t^-1-1+t
53
First homology
of the double branched cover of 12n_0559
Z/53
-4 4
12n_0560
1

detected by
an unknotting move
-3+14t-30t^2+39t^3-30t^4+14t^5-3t^6
Seifert matrix of 12n_0560
-1 -1 -1 -1 0 0
0 -1 -1 -1 -1 0
0 -2 -1 -1 -1 0
0 -2 -2 0 -1 0
0 0 0 -1 1 0
0 -1 -1 0 -1 -1
1
Generator of the Alexander module
(-t^2+t^3,0,0,1+t^2,0,t)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
133
First homology
of the double branched cover of 12n_0560
Z/133
0 0
12n_0561
2

detected by
the Lickorish test
-4+14t-19t^2+14t^3-4t^4
Seifert matrix of 12n_0561
-1 0 -1 0
0 -1 -1 -1
0 -1 -2 0
0 0 0 4
1
Generator of the Alexander module
(1,0,0,0)
the Blanchfield form on it
-4t^-1+9-4t
55
First homology
of the double branched cover of 12n_0561
Z/55
-2 2
12n_0562
2

detected by
the Lickorish test
-3+9t-11t^2+9t^3-3t^4
Seifert matrix of 12n_0562
-3 -5 -6 0
-6 -9 -9 0
-5 -6 -6 1
-1 -2 -1 -1
1 or 2
35
First homology
of the double branched cover of 12n_0562
Z/35
-2 2
12n_0563
1

detected by
an unknotting move
-5+18t-25t^2+18t^3-5t^4
Seifert matrix of 12n_0563
-4 -9 -10 -8
-10 -25 -25 -20
-9 -20 -20 -17
-7 -16 -17 -14
1
Generator of the Alexander module
(0,-22+40t-16t^2,-14+22t-8t^2,3-2t)
the Blanchfield form on it
1192t^-4-10696t^-3+40299t^-2-83934t^-1+106278-83934t+40299t^2-10696t^3+1192t^4
71
First homology
of the double branched cover of 12n_0563
Z/71
-2 2
12n_0564
1

detected by
an unknotting move
-2+10t-15t^2+10t^3-2t^4
Seifert matrix of 12n_0564
-3 0 -2 -2
0 1 0 0
-1 0 0 -1
0 1 0 1
1
Generator of the Alexander module
(-4+6t-2t^2,0,1,0)
the Blanchfield form on it
t^-1-2+t
39
First homology
of the double branched cover of 12n_0564
Z/39
2 2
12n_0565
2

detected by
the Nakanishi index
-2+7t-9t^2+9t^3-9t^4+7t^5-2t^6
Seifert matrix of 12n_0565
1 0 0 0 0 0
0 1 0 0 0 0
0 1 1 0 1 0
1 0 0 -2 0 -1
0 1 0 0 1 0
1 1 1 0 1 1
2
45
First homology
of the double branched cover of 12n_0565
Z/15+Z/3
4 4
12n_0566
1

detected by
an unknotting move
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 12n_0566
1 0 0 0
1 -2 0 -1
0 0 2 1
1 0 0 1
1 or 2
63
First homology
of the double branched cover of 12n_0566
Z/63
2 2
12n_0567
2

detected by
the Nakanishi index
-3+13t-26t^2+33t^3-26t^4+13t^5-3t^6
Seifert matrix of 12n_0567
-4 -2 -5 0 -7 -4
-3 -1 -3 0 -4 -2
-4 -2 -4 0 -7 -4
-2 -1 -1 -1 -2 -1
-6 -3 -6 0 -9 -6
-3 -1 -3 0 -5 -3
2
117
First homology
of the double branched cover of 12n_0567
Z/39+Z/3
0 0
12n_0568
1

detected by
an unknotting move
3-12t+24t^2-29t^3+24t^4-12t^5+3t^6
Seifert matrix of 12n_0568
-4 -2 0 0 -7 -4
-3 -1 0 0 -4 -2
-2 -1 -1 0 -2 -1
-1 -1 -1 -1 -2 -1
-6 -3 0 0 -9 -6
-3 -1 0 0 -5 -3
1
Generator of the Alexander module
(0,0,1-t-5t^2+t^3+3t^5-t^6,-1+3t^2-t^5,1+2t-t^4,0)
the Blanchfield form on it
107
First homology
of the double branched cover of 12n_0568
Z/107
-2 2
12n_0569
1

detected by
an unknotting move
3-10t+18t^2-21t^3+18t^4-10t^5+3t^6
Seifert matrix of 12n_0569
-9 -3 -6 3 -10 -6
-4 -1 -3 1 -4 -3
-7 -2 -4 2 -7 -4
1 0 0 -1 1 0
-9 -3 -6 3 -9 -6
-7 -2 -5 2 -7 -4
1
Generator of the Alexander module
(0,-1+t+t^2,0,0,0,2+t)
the Blanchfield form on it
-4t^-4+43t^-3-126t^-2+218t^-1-254+218t-126t^2+43t^3-4t^4
83
First homology
of the double branched cover of 12n_0569
Z/83
2 2
12n_0570
2

detected by
the Nakanishi index
1-3t+6t^2-8t^3+9t^4-8t^5+6t^6-3t^7+t^8
Seifert matrix of 12n_0570
-1 0 0 -1 -1 0 0 -1
0 1 0 0 0 1 0 0
0 1 1 0 0 1 1 0
0 0 0 0 -1 0 0 -1
0 1 1 -1 0 1 1 -1
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
0 0 0 0 -1 0 0 0
2
45
First homology
of the double branched cover of 12n_0570
Z/15+Z/3
4 4
12n_0571
2

detected by
the Nakanishi index
-1+3t-4t^2+4t^3-3t^4+4t^5-4t^6+3t^7-t^8
Seifert matrix of 12n_0571
-1 0 0 -1 -1 0 0 -1
0 1 0 0 0 1 0 0
0 1 1 0 0 1 1 0
0 0 0 -2 -1 0 0 -2
0 1 1 -1 0 1 1 -1
0 0 0 0 0 1 0 0
0 1 0 0 0 1 1 0
0 0 0 -1 -1 0 0 -2
2
27
First homology
of the double branched cover of 12n_0571
Z/9+Z/3
2 2
12n_0572
1

detected by
an unknotting move
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 12n_0572
-1 0 0 -1 -1 -1
0 2 0 0 0 0
0 -1 1 0 0 0
0 0 0 0 -1 -1
0 -1 1 -1 0 -1
0 0 0 0 -1 0
1
Generator of the Alexander module
(1-2t,0,-1,0,0,1)
the Blanchfield form on it
4t^-2-10t^-1+13-10t+4t^2
63
First homology
of the double branched cover of 12n_0572
Z/63
2 2
12n_0573
1

detected by
an unknotting move
-2+7t-12t^2+15t^3-12t^4+7t^5-2t^6
Seifert matrix of 12n_0573
-1 0 0 -1 -1 -1
0 2 0 0 0 0
0 -1 1 0 0 0
0 0 0 -2 -1 -2
0 -1 1 -1 0 -1
0 0 0 -1 -1 -2
1
Generator of the Alexander module
(t,0,1,0,0,0)
the Blanchfield form on it
-t^-1+2-t
57
First homology
of the double branched cover of 12n_0573
Z/57
0 2
12n_0574
4

detected by
the signature
-1+t-2t^3+3t^4-3t^5+3t^6-2t^7+t^9-t^10
Seifert matrix of 12n_0574
-1 0 0 0 0 0 0 0 0 0
0 -1 -1 0 -1 -1 0 -1 -1 -1
0 0 -1 0 -1 -1 0 0 -1 -1
-1 0 0 -1 0 0 0 0 0 0
-1 0 0 -1 -1 -1 0 0 0 -1
-1 0 0 -1 0 -1 0 0 0 0
0 -1 -1 0 -1 -1 -1 -1 -1 -1
0 0 -1 0 -1 -1 0 -1 -1 -1
0 0 0 0 -1 -1 0 0 -1 -1
-1 0 0 -1 0 -1 0 0 0 -1
2
9
First homology
of the double branched cover of 12n_0574
Z/3+Z/3
-8 8
12n_0575
3

detected by
the signature
2-3t+t^2+4t^3-7t^4+4t^5+t^6-3t^7+2t^8
Seifert matrix of 12n_0575
-1 0 0 0 0 0 0 0
0 -1 1 0 -1 -1 0 -1
0 0 -2 0 1 1 0 1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 -1 1 0 -1 -1 -1 -1
-1 0 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,1+2t,-t,-t,0,0,1+t,0)
the Blanchfield form on it
4t^-3-3t^-2-4t^-1+8-4t-3t^2+4t^3
3
First homology
of the double branched cover of 12n_0575
Z/3
-6 6
12n_0576
4

detected by
the signature
2-4t+5t^2-4t^3+3t^4-4t^5+5t^6-4t^7+2t^8
Seifert matrix of 12n_0576
-1 0 0 0 0 0 0 0
0 -2 -2 0 1 1 -2 1
0 -1 -2 0 1 1 -1 1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 -1 -2 0 1 1 -2 1
-1 0 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1+t+t^3-2t^4,t,0,0,0,0)
the Blanchfield form on it
10t^-3-14t^-2+7t^-1-2+7t-14t^2+10t^3
33
First homology
of the double branched cover of 12n_0576
Z/33
-8 8
12n_0577
1

detected by
an unknotting move
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 12n_0577
1 0 2 0 2 0
-1 -3 -1 -2 1 -3
1 0 1 0 2 0
0 -1 0 -1 1 -1
0 0 0 0 1 0
-1 -2 -1 -2 1 -3
1
Generator of the Alexander module
(0,0,0,t,0,1+2t)
the Blanchfield form on it
3t^-2-8t^-1+12-8t+3t^2
27
First homology
of the double branched cover of 12n_0577
Z/27
-2 2
12n_0578
1

detected by
an unknotting move
-3+11t-20t^2+25t^3-20t^4+11t^5-3t^6
Seifert matrix of 12n_0578
-2 -1 -1 -1 -1 -1
-1 1 0 -1 -1 0
-1 1 1 -1 -1 1
-2 -1 -1 -2 -1 -1
0 0 0 0 -1 0
-1 1 0 -1 -1 1
1
Generator of the Alexander module
(1,0,0,0,0,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
93
First homology
of the double branched cover of 12n_0578
Z/93
0 2
12n_0579
1

detected by
an unknotting move
1-2t-3t^2+9t^3-3t^4-2t^5+t^6
Seifert matrix of 12n_0579
1 0 0 0 0 0
1 0 1 -1 0 0
0 0 1 0 0 0
1 -1 0 -2 -1 -1
1 -1 1 -1 0 0
1 0 1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,-t,t)
the Blanchfield form on it
1
9
First homology
of the double branched cover of 12n_0579
Z/9
0 0
12n_0580
2

detected by
the Lickorish test
5-16t+23t^2-16t^3+5t^4
Seifert matrix of 12n_0580
0 -1 6 3
0 -1 1 1
5 0 30 15
2 0 14 7
1 or 2
65
First homology
of the double branched cover of 12n_0580
Z/65
0 0
12n_0581
3

detected by
the signature
3-5t+4t^2-3t^3+4t^4-5t^5+3t^6
Seifert matrix of 12n_0581
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 -1 -1 0 -1
-1 -1 0 -1 0 0
0 0 -1 -1 -3 -1
-1 -1 0 -1 0 -1
2
27
First homology
of the double branched cover of 12n_0581
Z/9+Z/3
-6 6
12n_0582
2

detected by
the Nakanishi index
1-2t+3t^2-2t^3+t^4
Seifert matrix of 12n_0582
-4 -3 -3 -3
-4 -4 -3 -3
-3 -3 -2 -3
-3 -3 -2 -2
2
9
First homology
of the double branched cover of 12n_0582
Z/3+Z/3
0 0
12n_0583
2

detected by
the Nakanishi index
-5+16t-21t^2+16t^3-5t^4
Seifert matrix of 12n_0583
-2 -1 -1 -1
-2 -2 -1 -1
0 0 -1 0
-1 -1 -1 2
2
63
First homology
of the double branched cover of 12n_0583
Z/21+Z/3
-2 2
12n_0584
1

detected by
an unknotting move
1-8t+22t^2-29t^3+22t^4-8t^5+t^6
Seifert matrix of 12n_0584
-1 -1 0 0 -1 0
0 -1 0 1 -1 1
0 0 1 0 0 0
0 0 0 1 0 1
0 0 -1 1 -1 0
0 0 1 0 0 -1
1
Generator of the Alexander module
(2-t-t^2,0,0,-t,1,1)
the Blanchfield form on it
t^-2-7t^-1+13-7t+t^2
91
First homology
of the double branched cover of 12n_0584
Z/91
-2 2
12n_0585
3

detected by
the signature
4-9t+10t^2-9t^3+10t^4-9t^5+4t^6
Seifert matrix of 12n_0585
-1 0 0 0 0 0
1 -2 1 1 -1 0
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
1 0 1 0 -2 0
0 -1 0 0 -1 -1
1 or 2
55
First homology
of the double branched cover of 12n_0585
Z/55
-6 6
12n_0586
1

detected by
an unknotting move
-1+8t-24t^2+35t^3-24t^4+8t^5-t^6
Seifert matrix of 12n_0586
-1 0 0 0 0 0
1 1 1 0 -1 0
-1 0 -1 0 0 0
-1 -1 -1 1 0 0
1 0 1 0 1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,-t,0,1,0,0)
the Blanchfield form on it
2t^-2-9t^-1+15-9t+2t^2
101
First homology
of the double branched cover of 12n_0586
Z/101
0 0
12n_0587
1

detected by
an unknotting move
-1+10t-28t^2+39t^3-28t^4+10t^5-t^6
Seifert matrix of 12n_0587
-1 0 0 0 0 0
1 1 1 1 1 1
0 1 2 0 0 1
-1 0 0 -1 0 0
1 1 1 1 2 1
1 2 1 1 1 1
1
Generator of the Alexander module
(0,0,0,-2t+t^2,0,1+5t-5t^2+t^3)
the Blanchfield form on it
-1
117
First homology
of the double branched cover of 12n_0587
Z/117
0 0
12n_0588
1

detected by
an unknotting move
-2+9t-19t^2+25t^3-19t^4+9t^5-2t^6
Seifert matrix of 12n_0588
0 0 -1 1 -1 1
1 -2 1 -2 1 -1
0 0 0 0 -1 1
1 -1 1 -2 1 -1
0 0 0 0 0 1
1 0 1 0 1 0
1
Generator of the Alexander module
(0,1-t,1,0,0,0)
the Blanchfield form on it
-t^-4+7t^-3-22t^-2+42t^-1-52+42t-22t^2+7t^3-t^4
85
First homology
of the double branched cover of 12n_0588
Z/85
0 0
12n_0589
2

detected by
the signature
-2+12t-26t^2+33t^3-26t^4+12t^5-2t^6
Seifert matrix of 12n_0589
-1 0 -1 -1 0 -1
0 -1 -1 0 -1 -1
0 0 -2 -1 0 -2
0 0 -2 -1 -1 -2
0 0 0 -1 0 0
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(-2t^2+2t^3,1+4t^2-t^3,0,0,0,-t)
the Blanchfield form on it
-2t^-2+6t^-1-8+6t-2t^2
113
First homology
of the double branched cover of 12n_0589
Z/113
-4 4
12n_0590
3

detected by
the signature
-1+4t-4t^2+2t^3-t^4+2t^5-4t^6+4t^7-t^8
Seifert matrix of 12n_0590
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 1 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
-1 1 0 -1 -1 -1 -1 -1
-1 0 0 -1 0 -1 0 -1
1 or 2
23
First homology
of the double branched cover of 12n_0590
Z/23
-6 6
12n_0591
3

detected by
the signature
1-2t^2+2t^3-t^4+2t^5-2t^6+t^8
Seifert matrix of 12n_0591
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
-1 1 0 -1 -1 -1 -1 -1
-1 0 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
t^-3-2t^-1+3-2t+t^3
7
First homology
of the double branched cover of 12n_0591
Z/7
-6 6
12n_0592
2

detected by
the Nakanishi index
1-4t+8t^2-8t^3+7t^4-8t^5+8t^6-4t^7+t^8
Seifert matrix of 12n_0592
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 1 1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 1 0
-1 0 0 -1 1 1 1 1
-1 1 0 -1 0 0 1 0
-1 0 0 -1 1 0 1 1
2
49
First homology
of the double branched cover of 12n_0592
Z/7+Z/7
4 4
12n_0593
2

detected by
the signature
-2+9t-13t^2+13t^3-13t^4+9t^5-2t^6
Seifert matrix of 12n_0593
-1 0 0 0 0 0
0 1 0 0 0 0
-1 1 -1 -1 0 0
-1 0 0 -1 0 0
-1 1 0 -1 -1 1
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
2t^-1-3+2t
61
First homology
of the double branched cover of 12n_0593
Z/61
-4 4
12n_0594
2

detected by
the signature
2-t-5t^2+9t^3-5t^4-t^5+2t^6
Seifert matrix of 12n_0594
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 1 -1 -1 0 0
-1 0 0 -1 0 0
-1 1 0 -1 -1 1
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,0,1,0,-1,0)
the Blanchfield form on it
t^-2+t^-1-2+t+t^2
13
First homology
of the double branched cover of 12n_0594
Z/13
-4 4
12n_0595
1

detected by
an unknotting move
2-9t+21t^2-27t^3+21t^4-9t^5+2t^6
Seifert matrix of 12n_0595
-1 0 0 0 0 0
0 1 0 0 0 0
-1 1 1 -1 0 0
-1 0 0 -1 0 0
-1 1 0 -1 1 0
1 0 0 1 -1 2
1
Generator of the Alexander module
(0,0,0,0,1,-1)
the Blanchfield form on it
-t^-1+1-t
91
First homology
of the double branched cover of 12n_0595
Z/91
2 2
12n_0596
2

detected by
the Lickorish test
3-11t+21t^2-25t^3+21t^4-11t^5+3t^6
Seifert matrix of 12n_0596
-1 0 0 0 0 0
1 2 1 1 0 1
0 1 2 0 -1 1
-1 0 0 -1 0 0
0 0 0 0 1 0
1 2 1 1 -1 2
1
Generator of the Alexander module
(0,1,0,0,4,-2)
the Blanchfield form on it
-42t^-2+143t^-1-215+143t-42t^2
95
First homology
of the double branched cover of 12n_0596
Z/95
2 2
12n_0597
1

detected by
an unknotting move
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 12n_0597
0 0 1 0 -1 1
1 -2 -2 -2 1 -1
1 -1 -2 -1 1 -1
1 -1 -2 -2 1 -1
0 0 0 0 0 1
1 0 0 0 1 0
1
Generator of the Alexander module
(0,0,1-t^2,-t+t^3,-t,-t^2)
the Blanchfield form on it
1
75
First homology
of the double branched cover of 12n_0597
Z/75
-2 2
12n_0598
2

detected by
the Nakanishi index
1-8t+24t^2-33t^3+24t^4-8t^5+t^6
Seifert matrix of 12n_0598
-1 0 1 0 0 0
0 -1 0 -1 0 0
0 1 -1 1 -1 1
0 0 0 -1 0 0
0 -1 0 -1 1 0
0 1 0 0 0 1
2
99
First homology
of the double branched cover of 12n_0598
Z/33+Z/3
-2 2
12n_0599
1

detected by
an unknotting move
-1+4t-7t^2+10t^3-11t^4+10t^5-7t^6+4t^7-t^8
Seifert matrix of 12n_0599
-1 0 0 0 0 0 0 0
0 1 0 0 1 0 1 0
-1 1 -1 -1 1 0 1 0
-1 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
-1 1 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,1+t+t^2,t+2t^2-2t^3,-2t+t^2-t^3,1+t,-t-t^2-t^3,0,-t-t^2)
the Blanchfield form on it
t^-2-2t^-1+3-2t+t^2
55
First homology
of the double branched cover of 12n_0599
Z/55
-2 2
12n_0600
3

detected by
the signature
4-9t+12t^2-13t^3+12t^4-9t^5+4t^6
Seifert matrix of 12n_0600
-1 0 0 0 0 0
1 -2 1 0 -1 0
-1 0 -1 0 0 0
0 -1 0 -1 -1 0
1 0 1 0 -2 0
0 -1 0 -1 -1 -1
2
63
First homology
of the double branched cover of 12n_0600
Z/21+Z/3
-6 6
12n_0601
2

detected by
the Nakanishi index
1-3t+6t^2-7t^3+6t^4-3t^5+t^6
Seifert matrix of 12n_0601
-1 0 0 0 0 0
1 -1 1 1 0 1
-1 0 -1 0 0 0
0 0 0 1 0 1
1 1 1 1 -1 1
0 0 0 0 0 1
2
27
First homology
of the double branched cover of 12n_0601
Z/9+Z/3
-2 2
12n_0602
2

detected by
the Nakanishi index
1-9t+24t^2-31t^3+24t^4-9t^5+t^6
Seifert matrix of 12n_0602
-1 0 0 0 0 0
1 1 1 0 -1 0
-1 0 -1 0 0 0
0 -1 0 -1 -1 0
1 0 1 0 1 0
0 -1 0 -1 -1 -1
2
99
First homology
of the double branched cover of 12n_0602
Z/33+Z/3
-2 2
12n_0603
3

detected by
the signature
-1+4t-4t^2+3t^4-4t^6+4t^7-t^8
Seifert matrix of 12n_0603
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 1 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 0 -1 0
-1 0 0 -1 0 -1 0 0
-1 0 -1 -1 0 0 -1 0
-1 1 0 -1 0 -1 0 -1
1 or 2
15
First homology
of the double branched cover of 12n_0603
Z/15
-6 6
12n_0604
2

detected by
the Nakanishi index
1-4t+10t^2-16t^3+19t^4-16t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0604
-1 0 -1 -1 -1 -1 0 -1
0 1 0 0 0 0 1 0
0 1 0 -1 0 -1 1 -1
0 0 -1 0 -1 -1 0 -1
0 1 -1 -1 0 -1 1 -1
0 1 0 -1 0 0 1 -1
0 0 0 0 0 0 1 0
0 0 -1 0 -1 -1 0 0
2
81
First homology
of the double branched cover of 12n_0604
Z/27+Z/3
4 4
12n_0605
2

detected by
the Nakanishi index
-1+2t-4t^3+7t^4-4t^5+2t^7-t^8
Seifert matrix of 12n_0605
-1 0 -1 -1 -1 -1 0 -1
0 1 0 0 0 0 1 0
0 1 0 -1 0 -1 1 -1
0 0 -1 -2 -1 -1 0 -2
0 1 -1 -1 0 -1 1 -1
0 1 0 -1 0 0 1 -1
0 0 0 0 0 0 1 0
0 0 -1 -1 -1 -1 0 -2
2
9
First homology
of the double branched cover of 12n_0605
Z/3+Z/3
0 0
12n_0606
1

detected by
an unknotting move
2-8t+18t^2-23t^3+18t^4-8t^5+2t^6
Seifert matrix of 12n_0606
-1 1 -1 -1 -1 0
0 1 1 1 1 1
0 0 0 -1 -1 -1
0 1 -1 0 -1 0
0 0 0 -1 0 -1
0 1 0 1 0 2
1
Generator of the Alexander module
(1-t,0,0,0,1,0)
the Blanchfield form on it
2t^-2-6t^-1+8-6t+2t^2
79
First homology
of the double branched cover of 12n_0606
Z/79
2 2
12n_0607
1

detected by
an unknotting move
2-7t+13t^2-15t^3+13t^4-7t^5+2t^6
Seifert matrix of 12n_0607
0 1 -1 -1 -1 1
1 -2 1 1 1 -1
0 0 0 0 -1 1
0 0 -1 0 -1 1
0 0 0 0 0 1
1 0 1 1 1 0
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-2t^-2+6t^-1-9+6t-2t^2
59
First homology
of the double branched cover of 12n_0607
Z/59
2 2
12n_0608
1

detected by
an unknotting move
3-10t+15t^2-10t^3+3t^4
Seifert matrix of 12n_0608
0 1 1 1
1 -2 -1 -1
0 0 1 -1
1 0 -1 0
1
Generator of the Alexander module
(0,1,0,1)
the Blanchfield form on it
-t^-1+2-t
41
First homology
of the double branched cover of 12n_0608
Z/41
0 0
12n_0609
2

detected by
the signature
1-4t+7t^2-6t^3+5t^4-6t^5+7t^6-4t^7+t^8
Seifert matrix of 12n_0609
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
-1 1 -1 -1 0 0 1 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 -1 -1 0 -1
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
-1 0 0 -1 0 -1 0 -1
1
Generator of the Alexander module
(0,t-t^2+2t^3-t^4-3t^5+3t^6-t^7,2+3t-2t^2-t^3-t^4-t^5+2t^6-t^7,0,1+t^2+t^3-4t^4+2t^6-t^7,0,-1+t-2t^2+t^3+3t^4-3t^5+t^6,-t^2+t^3-2t^4+t^5+3t^6-3t^7+t^8)
the Blanchfield form on it
x
41
First homology
of the double branched cover of 12n_0609
Z/41
-4 4
12n_0610
1

detected by
an unknotting move
1-4t+8t^2-12t^3+15t^4-12t^5+8t^6-4t^7+t^8
Seifert matrix of 12n_0610
-1 0 0 0 0 0 0 0
0 1 0 0 1 0 1 1
-1 1 -1 -1 1 0 1 1
-1 0 0 -1 0 0 0 0
0 0 0 0 1 0 1 0
-1 1 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 1 0 1 1
1
Generator of the Alexander module
(0,-1,-1,1,0,0,0,0)
the Blanchfield form on it
1
65
First homology
of the double branched cover of 12n_0610
Z/65
0 0
12n_0611
2

detected by
the Nakanishi index
2-9t+17t^2-19t^3+17t^4-9t^5+2t^6
Seifert matrix of 12n_0611
-1 0 0 0 0 0
0 1 0 0 -1 0
-1 1 -1 -1 -1 0
-1 0 0 -1 0 0
0 0 0 0 2 0
-1 1 0 -1 0 -1
2
75
First homology
of the double branched cover of 12n_0611
Z/15+Z/5
-2 2
12n_0612
2

detected by
the Lickorish test
1-9t+23t^2-29t^3+23t^4-9t^5+t^6
Seifert matrix of 12n_0612
-1 1 0 1 -1 0
0 -2 -1 -1 0 0
0 0 1 0 0 0
0 -1 0 -2 1 0
0 1 0 1 0 0
0 -1 0 -1 0 -1
1 or 2
95
First homology
of the double branched cover of 12n_0612
Z/95
-2 2
12n_0613
1

detected by
an unknotting move
1-6t+15t^2-23t^3+27t^4-23t^5+15t^6-6t^7+t^8
Seifert matrix of 12n_0613
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
0 -1 -1 0 -1 0 0 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 0 1 0
0 0 0 0 0 1 0 0
0 0 0 0 0 1 1 0
0 -1 -1 0 0 0 0 -1
1
Generator of the Alexander module
(18-58t-129t^2+269t^3-48t^4-131t^5+9t^6,-19-28t+12t^2-68t^3+16t^4+90t^5-6t^6,-3-5t+5t^2-t^3,-2t-3t^2-3t^3+t^4-t^5,4-11t-26t^2+63t^3-12t^4-28t^5+2t^6,0,7+10t-t^2+33t^3-8t^4-45t^5+3t^6,2t+4t^2)
the Blanchfield form on it
x
117
First homology
of the double branched cover of 12n_0613
Z/117
0 2
12n_0614
1

detected by
an unknotting move
-1+6t-17t^2+25t^3-17t^4+6t^5-t^6
Seifert matrix of 12n_0614
0 -1 -1 0 0 0
-1 -2 -2 -1 0 -1
-1 -1 0 -1 0 -1
0 0 0 -1 0 0
1 0 0 0 -1 1
-1 -1 -1 -1 0 0
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
-1
73
First homology
of the double branched cover of 12n_0614
Z/73
0 0
12n_0615
2

detected by
the Lickorish test
-1+6t-15t^2+19t^3-17t^4+19t^5-15t^6+6t^7-t^8
Seifert matrix of 12n_0615
-1 -1 -1 -1 1 0 -1 1
0 -1 -1 -1 0 0 0 1
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 -1 0 0 0 -1 -1 0
0 -1 -1 -1 1 0 -1 1
0 0 0 0 1 0 0 1
1
Generator of the Alexander module
(2t^2+2t^3-t^4+2t^6+2t^7-6t^8+12t^9-11t^10+5t^11-2t^12,0,-1-3t-t^2+2t^3-t^4+2t^5-t^6+t^8+5t^9-4t^11+3t^12-2t^13,-1-3t-2t^2-t^3-3t^4+t^5-4t^6+t^7-3t^8+6t^9-3t^10+2t^11,2t+4t^2+2t^3+5t^4+3t^6+t^7+6t^8-6t^9-t^10+t^11-2t^12,t+t^3+3t^4-t^5-2t^6+4t^7-t^8-5t^9+5t^10-2t^11,1+t+t^2+t^3-t^4+4t^5-6t^6+9t^7-9t^
the Blanchfield form on it
x
99
First homology
of the double branched cover of 12n_0615
Z/99
-2 2
12n_0616
1

detected by
an unknotting move
-1+6t-15t^2+21t^3-15t^4+6t^5-t^6
Seifert matrix of 12n_0616
0 -1 -1 0 0 -1
0 1 0 0 0 0
-2 -1 -1 -1 -1 -1
-1 -1 -1 -1 0 0
-1 -1 -1 -1 -1 0
0 1 0 0 0 1
1
Generator of the Alexander module
(0,1,6-4t+t^2,-t+t^2,0,0)
the Blanchfield form on it
-1
65
First homology
of the double branched cover of 12n_0616
Z/65
0 0
12n_0617
2

detected by
the signature
-1+3t-3t^3+3t^5-t^6
Seifert matrix of 12n_0617
0 -1 -1 0 0 -1
0 1 0 0 0 0
-2 -1 -1 -1 -1 -1
-1 -1 -1 0 0 0
-1 -1 -1 -1 0 0
0 1 0 0 0 1
2
5
First homology
of the double branched cover of 12n_0617
Z/5
4 4
12n_0618
1

detected by
an unknotting move
1-6t+15t^2-21t^3+21t^4-21t^5+15t^6-6t^7+t^8
Seifert matrix of 12n_0618
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
0 0 1 0 0 0 0 0
-1 0 0 -1 -1 -1 0 0
0 0 0 0 -1 0 -1 0
0 0 0 0 -1 -1 -1 0
0 0 1 0 0 0 1 0
0 0 -1 0 -1 -1 -1 -1
1
Generator of the Alexander module
(0,-4t+3t^2+2t^3-t^4,t-t^2,-1-3t+2t^2+2t^3-t^4,1-2t-t^2+3t^3-t^4,-t+2t^3-t^4,1+t-3t^2+t^3,1-2t-t^2+3t^3-t^4)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-9+8t-4t^2+t^3
107
First homology
of the double branched cover of 12n_0618
Z/107
-2 2
12n_0619
2

detected by
the signature
-1+6t-14t^2+15t^3-13t^4+15t^5-14t^6+6t^7-t^8
Seifert matrix of 12n_0619
1 0 0 0 0 0 0 0
-1 -1 0 -1 -1 -1 0 -1
0 0 1 0 0 0 0 0
-1 0 0 -1 -1 -1 0 0
0 0 0 0 1 1 -1 1
0 0 0 0 0 1 -1 1
0 0 1 0 0 0 1 0
0 0 -1 0 0 0 -1 1
1 or 2
85
First homology
of the double branched cover of 12n_0619
Z/85
4 4
12n_0620
1

detected by
an unknotting move
2-13t+34t^2-45t^3+34t^4-13t^5+2t^6
Seifert matrix of 12n_0620
2 0 1 1 2 0
0 -1 0 0 1 1
0 0 -1 0 0 1
0 0 1 0 1 0
1 0 2 1 2 0
1 0 1 1 2 -1
1
Generator of the Alexander module
(0,3-3t+t^2,0,0,1,0)
the Blanchfield form on it
1
143
First homology
of the double branched cover of 12n_0620
Z/143
-2 2
12n_0621
2

detected by
the Lickorish test
1-7t+23t^2-33t^3+23t^4-7t^5+t^6
Seifert matrix of 12n_0621
0 1 0 1 -1 1
1 0 1 -1 1 -2
-1 1 -1 0 -1 2
0 0 0 1 0 0
0 0 0 0 1 0
1 -1 0 -2 2 -2
1 or 2
95
First homology
of the double branched cover of 12n_0621
Z/95
2 2
12n_0622
2

detected by
the Nakanishi index
-1+6t-14t^2+19t^3-19t^4+19t^5-14t^6+6t^7-t^8
Seifert matrix of 12n_0622
-1 0 0 1 -1 0 -1 0
-1 1 -1 0 0 -1 -1 1
-1 0 -1 0 -1 -1 -1 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
-1 0 0 1 -1 -1 -1 0
0 0 0 1 -1 0 -1 0
0 0 -1 0 0 -1 0 1
2
99
First homology
of the double branched cover of 12n_0622
Z/33+Z/3
-2 2
12n_0623
2

detected by
the signature
1-5t+10t^2-8t^3+5t^4-8t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0623
-1 0 0 0 0 0 0 0
0 -1 -1 0 -1 1 0 0
-1 0 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 0 1 0 0
0 -1 -1 0 -1 1 -1 0
0 -1 0 0 -1 0 0 1
1 or 2
53
First homology
of the double branched cover of 12n_0623
Z/53
-4 4
12n_0624
2

detected by
the signature
-1+3t-6t^3+9t^4-6t^5+3t^7-t^8
Seifert matrix of 12n_0624
-1 0 0 0 0 0 0 0
0 -1 -1 0 -1 1 0 0
-1 0 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 0 -1 0 0
0 -1 -1 0 -1 1 -1 0
0 -1 0 0 -1 0 0 1
1
Generator of the Alexander module
(0,1,0,0,1,0,0,t)
the Blanchfield form on it
-t^-3+2t^-1-3+2t-t^3
13
First homology
of the double branched cover of 12n_0624
Z/13
-4 4
12n_0625
1

detected by
an unknotting move
-1+5t-12t^2+18t^3-19t^4+18t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0625
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
-1 1 1 -1 1 0 1 0
-1 0 0 -1 0 0 0 0
-1 1 0 -1 1 0 1 0
0 0 0 0 0 1 0 0
0 0 0 0 0 1 1 0
0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,1+2t-t^2,0,0,-1-2t-t^2+t^3)
the Blanchfield form on it
t^-3-3t^-2+5t^-1-5+5t-3t^2+t^3
91
First homology
of the double branched cover of 12n_0625
Z/91
2 2
12n_0626
3

detected by
the new u==2 criterion
-2+15t-36t^2+47t^3-36t^4+15t^5-2t^6
Seifert matrix of 12n_0626
0 1 1 1 -1 1
1 0 -2 -1 1 -1
1 -1 -2 -2 2 -2
0 0 0 1 0 1
0 0 0 0 1 0
0 0 0 -1 1 1
2
153
First homology
of the double branched cover of 12n_0626
Z/51+Z/3
4 4
12n_0627
1

detected by
an unknotting move
1-4t+12t^2-25t^3+33t^4-25t^5+12t^6-4t^7+t^8
Seifert matrix of 12n_0627
-1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0
-1 1 1 -1 0 0 1 1
-1 0 0 -1 0 0 0 0
-1 0 0 -1 -1 -1 0 0
0 0 0 0 0 -1 0 0
0 0 0 0 0 1 1 0
-1 1 0 -1 0 0 1 1
1
Generator of the Alexander module
(0,2-t-t^2+t^3,-2t-t^2+4t^3-t^4-2t^5+t^6,-2t+t^2+t^3-t^4,1-2t-t^2+3t^3+t^4-3t^5+t^6,-t-t^2+t^3+t^4-t^5,1-3t^2+2t^3+t^4-t^5,2-t-t^2+t^3)
the Blanchfield form on it
x
117
First homology
of the double branched cover of 12n_0627
Z/117
0 0
12n_0628
1

detected by
an unknotting move
-1+8t-25t^2+37t^3-25t^4+8t^5-t^6
Seifert matrix of 12n_0628
0 -1 0 -1 -1 -1
-1 0 0 0 -1 -1
-1 -1 -1 -1 -1 0
0 0 0 -1 0 -1
-2 -1 -1 -1 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,1,0)
the Blanchfield form on it
1
105
First homology
of the double branched cover of 12n_0628
Z/105
0 0
12n_0629
1

detected by
an unknotting move
1-4t+6t^2-5t^3+6t^4-4t^5+t^6
Seifert matrix of 12n_0629
1 0 1 0 0 -1
0 1 1 1 0 -1
0 0 1 0 0 0
1 1 1 0 1 -1
-1 0 0 0 -1 -1
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
27
First homology
of the double branched cover of 12n_0629
Z/27
2 2
12n_0630
2

detected by
the Lickorish test
1-4t+3t^2+t^3+3t^4-4t^5+t^6
Seifert matrix of 12n_0630
0 -1 0 -1 -1 -1
-1 0 0 0 -1 -1
-1 -1 -1 -1 -1 0
0 0 0 -1 0 -1
-2 -1 -1 -1 -1 -1
0 0 0 0 0 -1
2
15
First homology
of the double branched cover of 12n_0630
Z/15
-2 2
12n_0631
1

detected by
an unknotting move
-1+6t-19t^2+29t^3-19t^4+6t^5-t^6
Seifert matrix of 12n_0631
1 0 1 0 0 -1
0 0 1 1 0 -1
0 0 1 0 0 0
1 1 1 0 1 -1
-1 0 0 0 -1 -1
0 0 0 0 0 -1
1
Generator of the Alexander module
(0,1+t-t^2,0,-3-4t+3t^2,0,0)
the Blanchfield form on it
t^-2-4t^-1+10-4t+t^2
81
First homology
of the double branched cover of 12n_0631
Z/81
0 0
12n_0632
1

detected by
an unknotting move
1-7t+19t^2-30t^3+33t^4-30t^5+19t^6-7t^7+t^8
Seifert matrix of 12n_0632
1 0 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 0 -1
-1 0 -1 -1 0 -1 0 -1
0 0 0 1 1 0 -1 1
0 0 0 0 1 0 0 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 1 0 -1 1
1
Generator of the Alexander module
(12t^2-9t^3+79t^4-113t^5+21t^6+35t^7-29t^8+6t^9,-54t+6t^2+136t^3-146t^4+70t^5-12t^6,7-118t-108t^2+539t^3-157t^4-512t^5+559t^6-247t^7+39t^8,27t-57t^2+46t^3-19t^4+3t^5,-6+9t-34t^2+33t^3+11t^4-27t^5+16t^6-3t^7,-54t^2+33t^3+187t^4-328t^5+235t^6-85t^7+12t^8,9+11t-47t^2+43t^3-19t^4+3t^5,0)
the Blanchfield form on it
x
147
First homology
of the double branched cover of 12n_0632
Z/147
2 2
12n_0633
1

detected by
an unknotting move
-2+10t-22t^2+29t^3-22t^4+10t^5-2t^6
Seifert matrix of 12n_0633
-1 -1 -1 -1 -1 0
0 1 0 1 0 0
0 1 2 1 0 0
0 1 1 0 0 0
0 0 -1 -1 -1 0
0 1 1 1 0 1
1
Generator of the Alexander module
(1,0,0,0,0,0)
the Blanchfield form on it
1
97
First homology
of the double branched cover of 12n_0633
Z/97
0 0
12n_0634
1

detected by
an unknotting move
1-5t+11t^2-13t^3+11t^4-5t^5+t^6
Seifert matrix of 12n_0634
0 -1 0 -1 0 -1
-2 -1 -1 -1 -1 -1
-1 -1 -1 -1 0 0
0 0 0 -1 0 -1
-1 -1 -1 -1 -1 0
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-9t^-1+15-9t+2t^2
47
First homology
of the double branched cover of 12n_0634
Z/47
-2 2
12n_0635
1

detected by
an unknotting move
1-7t+19t^2-32t^3+39t^4-32t^5+19t^6-7t^7+t^8
Seifert matrix of 12n_0635
-1 0 0 1 -1 0 -1 0
-1 1 -1 0 0 1 -1 1
-1 0 -1 0 -1 0 -1 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 -1 0 0 1 0 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 1 0 1
1
Generator of the Alexander module
(0,0,-1,0,0,1,0,-2t+t^2)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
157
First homology
of the double branched cover of 12n_0635
Z/157
0 0
12n_0636
2

detected by
the Nakanishi index
-1+7t-19t^2+27t^3-19t^4+7t^5-t^6
Seifert matrix of 12n_0636
-1 0 0 0 0 -1
0 1 1 -1 0 -1
-1 0 0 -1 0 -2
-1 0 0 -2 -1 -2
0 0 0 0 1 0
-1 0 -1 0 0 -1
2
81
First homology
of the double branched cover of 12n_0636
Z/9+Z/9
0 0
12n_0637
2

detected by
the Nakanishi index
2-13t+32t^2-41t^3+32t^4-13t^5+2t^6
Seifert matrix of 12n_0637
-1 0 -1 0 0 0
0 -2 -1 -2 1 0
0 -1 -2 -1 1 -1
0 -1 -1 -2 1 0
0 0 0 0 1 0
0 -1 -1 0 0 0
2
135
First homology
of the double branched cover of 12n_0637
Z/45+Z/3
-2 2
12n_0638
3

detected by
the signature
2-3t+2t^2-t^3+2t^4-3t^5+2t^6
Seifert matrix of 12n_0638
-1 0 0 0 1 0
0 -2 0 -1 0 -1
0 -1 -1 -1 -1 -1
0 -1 0 -1 0 0
0 -1 0 0 -2 0
0 -1 0 -1 0 -1
1 or 2
15
First homology
of the double branched cover of 12n_0638
Z/15
-6 6
12n_0639
3

detected by
the signature
-1+4t-5t^2+5t^3-5t^4+5t^5-5t^6+4t^7-t^8
Seifert matrix of 12n_0639
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 1 -1 -1 -1 0 -1 0
-1 1 0 -1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 0 0
-1 1 0 -1 -1 0 -1 0
-1 1 0 0 -1 -1 0 -1
1 or 2
35
First homology
of the double branched cover of 12n_0639
Z/35
-6 6
12n_0640
3

detected by
the signature
1-3t^2+7t^3-9t^4+7t^5-3t^6+t^8
Seifert matrix of 12n_0640
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 1 -1 -1 -1 0 -1 0
-1 1 0 -1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 0 0
-1 1 0 -1 -1 0 -1 0
-1 1 0 0 -1 -1 0 -1
1 or 2
27
First homology
of the double branched cover of 12n_0640
Z/27
-6 6
12n_0641
2

detected by
the signature
1-4t+9t^2-13t^3+15t^4-13t^5+9t^6-4t^7+t^8
Seifert matrix of 12n_0641
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
-1 1 1 0 -1 0 0 0
-1 1 1 1 -1 0 1 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 1 0 1
-1 1 1 0 -1 0 1 0
-1 1 0 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-8t^-1+9-8t+4t^2-t^3
69
First homology
of the double branched cover of 12n_0641
Z/69
4 4
12n_0642
3

detected by
the Nakanishi index
1+7t-15t^2+7t^3+t^4
Seifert matrix of 12n_0642
1 0 0 0
1 1 0 -1
1 -1 1 -1
1 0 0 1
3
27
First homology
of the double branched cover of 12n_0642
Z/3+Z/3+Z/3
2 2
12n_0643
2

detected by
the Nakanishi index
-2+8t-10t^2+9t^3-10t^4+8t^5-2t^6
Seifert matrix of 12n_0643
-1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
1 -1 1 0 -2 0
-1 1 -1 -1 0 -1
2
49
First homology
of the double branched cover of 12n_0643
Z/7+Z/7
-4 4
12n_0644
3

detected by
the signature
2-2t+t^3-2t^5+2t^6
Seifert matrix of 12n_0644
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
1 -1 1 0 -2 0
-1 1 -1 -1 0 -1
1 or 2
7
First homology
of the double branched cover of 12n_0644
Z/7
-6 6
12n_0645
1

detected by
an unknotting move
2-8t+16t^2-19t^3+16t^4-8t^5+2t^6
Seifert matrix of 12n_0645
-1 0 0 0 0 0
0 1 0 0 0 0
-1 0 -1 0 0 0
-1 0 -1 1 0 1
1 -1 1 0 2 0
-1 1 -1 0 0 1
1
Generator of the Alexander module
(0,0,1,2,-1,1)
the Blanchfield form on it
-1
71
First homology
of the double branched cover of 12n_0645
Z/71
2 2
12n_0646
1

detected by
an unknotting move
-1+5t-12t^2+21t^3-25t^4+21t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0646
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 1 1 0 0 0 0 1
-1 1 1 -1 -1 0 0 1
-1 0 0 0 -1 0 0 0
-1 0 1 0 -1 -1 0 1
-1 1 1 0 -1 -1 -1 1
0 1 0 0 0 0 0 1
1
Generator of the Alexander module
(0,1+3t,0,-1+t+3t^2,t^2,2+t-2t^2,-1-t-2t^2,0)
the Blanchfield form on it
-t^-3+3t^-2-5t^-1+8-5t+3t^2-t^3
103
First homology
of the double branched cover of 12n_0646
Z/103
-2 2
12n_0647
3

detected by
the signature
1-3t^2+6t^3-7t^4+6t^5-3t^6+t^8
Seifert matrix of 12n_0647
-1 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 -1
0 0 -1 0 0 0 0 0
-1 1 1 -1 -1 0 0 1
-1 0 0 0 -1 0 0 0
-1 0 1 0 -1 -1 0 1
-1 1 1 0 -1 -1 -1 1
0 0 -1 0 0 0 0 -1
1 or 2
23
First homology
of the double branched cover of 12n_0647
Z/23
-6 6
12n_0648
3

detected by
the signature
-1+4t-3t^2-t^3+3t^4-t^5-3t^6+4t^7-t^8
Seifert matrix of 12n_0648
-1 0 0 0 0 0 0 0
0 -1 0 0 0 -1 0 -1
0 0 1 0 0 0 0 0
-1 0 1 -1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 0 0
0 -1 0 0 0 -1 -1 -1
-1 0 1 0 -1 -1 0 -1
1 or 2
11
First homology
of the double branched cover of 12n_0648
Z/11
-6 6
12n_0649
2

detected by
the signature
1-5t+11t^2-14t^3+15t^4-14t^5+11t^6-5t^7+t^8
Seifert matrix of 12n_0649
-1 0 0 0 0 0 0 0
0 -1 -1 -1 0 0 0 -1
-1 0 -1 -1 -1 0 -1 0
0 0 0 1 0 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 -1 0
0 0 0 1 0 0 1 0
-1 0 -1 -1 -1 0 -1 -1
1
Generator of the Alexander module
(0,-2+2t^2,-t,0,1-t^2,t-t^2,0,-2t)
the Blanchfield form on it
11t^-3-59t^-2+109t^-1-135+109t-59t^2+11t^3
77
First homology
of the double branched cover of 12n_0649
Z/77
-4 4
12n_0650
1

detected by
an unknotting move
1-4t+7t^2-4t^3+t^4
Seifert matrix of 12n_0650
0 1 1 0
1 0 0 0
0 0 1 0
0 -1 0 -1
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
1
17
First homology
of the double branched cover of 12n_0650
Z/17
0 0
12n_0651
2

detected by
the Lickorish test
2-11t+28t^2-37t^3+28t^4-11t^5+2t^6
Seifert matrix of 12n_0651
-2 -1 -1 -1 0 -1
-1 0 0 -1 0 -1
-1 -1 -2 -1 0 -2
-2 -1 -1 -2 0 -1
1 0 0 1 1 1
-1 -1 -1 -1 0 -2
2
119
First homology
of the double branched cover of 12n_0651
Z/119
-2 2
12n_0652
2

detected by
A(F_3)
-1+5t-15t^2+30t^3-37t^4+30t^5-15t^6+5t^7-t^8
Seifert matrix of 12n_0652
-1 0 0 0 0 0 0 0
0 1 0 -1 0 0 0 0
-1 1 1 -1 -1 0 -1 1
0 0 0 -1 0 0 -1 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 -1 0
0 0 0 0 0 0 -1 0
-1 1 0 -1 -1 0 -1 1
2
139
First homology
of the double branched cover of 12n_0652
Z/139
-2 2
12n_0653
3

detected by
the signature
-1+4t-5t^2+6t^3-7t^4+6t^5-5t^6+4t^7-t^8
Seifert matrix of 12n_0653
-1 0 0 0 0 0 0 0
-1 -1 1 0 -1 -1 0 -1
0 0 1 0 0 0 0 0
-1 0 1 -1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 0 0 -1 -1 0 0
-1 -1 1 0 -1 -1 -1 -1
-1 0 1 0 -1 -1 0 -1
1 or 2
39
First homology
of the double branched cover of 12n_0653
Z/39
-6 6
12n_0654
3

detected by
the new u==2 criterion
-2+8t-9t^2+7t^3-9t^4+8t^5-2t^6
Seifert matrix of 12n_0654
-1 0 0 0 0 0
1 -2 -1 0 1 1
0 0 1 0 0 0
-1 0 1 -1 -1 0
-1 0 0 0 -1 0
-1 0 0 0 -1 -1
2
45
First homology
of the double branched cover of 12n_0654
Z/15+Z/3
-4 4
12n_0655
3

detected by
the signature
2-2t-t^2+3t^3-t^4-2t^5+2t^6
Seifert matrix of 12n_0655
-1 0 0 0 0 0
1 -2 -1 0 1 1
0 0 -1 0 0 0
-1 0 1 -1 -1 0
-1 0 0 0 -1 0
-1 0 0 0 -1 -1
1
Generator of the Alexander module
(0,1-2t+2t^2,-t,-t,-1,-1)
the Blanchfield form on it
7t^-4-18t^-3+15t^-2+9t^-1-24+9t+15t^2-18t^3+7t^4
3
First homology
of the double branched cover of 12n_0655
Z/3
-6 6
12n_0656
1

detected by
an unknotting move
2-10t+23t^2-29t^3+23t^4-10t^5+2t^6
Seifert matrix of 12n_0656
-1 0 0 0 0 0
1 2 -1 0 1 0
0 0 1 0 0 0
-1 0 1 1 -1 0
-1 0 0 0 -1 0
-1 -1 0 0 -1 1
1
Generator of the Alexander module
(0,-2t,-1+t,t,0,1)
the Blanchfield form on it
-3t^-4+22t^-3-73t^-2+141t^-1-174+141t-73t^2+22t^3-3t^4
99
First homology
of the double branched cover of 12n_0656
Z/99
2 2
12n_0657 1 or 2
1-4t+9t^2-16t^3+21t^4-16t^5+9t^6-4t^7+t^8
Seifert matrix of 12n_0657
-1 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0
0 1 1 0 0 0 1 1
-1 1 1 -1 -1 0 1 1
-1 0 0 0 -1 0 0 0
-1 1 1 0 -1 -1 0 1
0 0 0 0 0 0 1 0
0 1 0 0 0 0 1 1
1 or 2
81
First homology
of the double branched cover of 12n_0657
Z/81
0 0
12n_0658
2

detected by
the signature
1-5t+12t^2-17t^3+19t^4-17t^5+12t^6-5t^7+t^8
Seifert matrix of 12n_0658
-1 0 0 0 0 0 0 0
-1 -1 1 0 -1 -1 0 1
0 0 1 0 0 0 0 1
-1 0 1 -1 -1 0 0 1
-1 0 0 0 -1 0 0 0
-1 0 1 0 -1 -1 0 0
-1 -1 1 0 -1 -1 -1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+8t^-1-9+8t-4t^2+t^3
89
First homology
of the double branched cover of 12n_0658
Z/89
-4 4
12n_0659
2

detected by
the signature
-2+10t-16t^2+17t^3-16t^4+10t^5-2t^6
Seifert matrix of 12n_0659
-1 0 0 0 0 0
0 1 0 0 0 0
0 1 -1 0 0 -1
-1 0 0 -1 0 0
-1 1 0 -1 -1 0
1 0 0 1 0 -2
1
Generator of the Alexander module
(0,0,3-3t+t^2,-1+t,0,0)
the Blanchfield form on it
41t^-3-206t^-2+333t^-1-356+333t-206t^2+41t^3
73
First homology
of the double branched cover of 12n_0659
Z/73
-4 4
12n_0660
2

detected by
the signature
1+3t-12t^2+17t^3-12t^4+3t^5+t^6
Seifert matrix of 12n_0660
1 0 0 0 0 0
0 1 1 0 1 0
1 0 1 1 0 0
0 0 0 1 0 0
1 0 0 0 1 -1
1 0 0 1 0 1
2
45
First homology
of the double branched cover of 12n_0660
Z/45
4 4
12n_0661
2

detected by
the signature
-2+6t-5t^2+3t^3-5t^4+6t^5-2t^6
Seifert matrix of 12n_0661
-1 0 0 0 0 0
-1 -1 -1 0 0 -1
-1 0 -1 0 0 0
-1 -1 -1 -1 0 0
-1 0 -1 0 -1 -1
0 0 0 0 0 2
1
Generator of the Alexander module
(0,0,0,t,1,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
29
First homology
of the double branched cover of 12n_0661
Z/29
-4 4
12n_0662
1

detected by
an unknotting move
2-8t+13t^2-13t^3+13t^4-8t^5+2t^6
Seifert matrix of 12n_0662
-1 0 0 0 0 0
-1 -1 -1 0 1 -1
-1 0 -1 0 0 0
-1 0 -1 -1 0 -1
0 0 0 0 1 0
0 0 0 0 -1 2
1
Generator of the Alexander module
(0,-6t^2+3t^3,0,2t^2-t^3,-2t+t^2,1-4t^2+2t^3)
the Blanchfield form on it
35t^-2-199t^-1+327-199t+35t^2
59
First homology
of the double branched cover of 12n_0662
Z/59
-2 2
12n_0663
1

detected by
an unknotting move
-1+6t-15t^2+23t^3-25t^4+23t^5-15t^6+6t^7-t^8
Seifert matrix of 12n_0663
-1 0 0 0 0 0 0 0
0 -1 -1 -1 0 -1 0 0
-1 0 -1 -1 -1 0 -1 0
0 0 0 1 0 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 -1 -1 -1 -1 -1 0
0 0 0 1 0 0 1 0
0 -1 0 0 0 -1 0 1
1
Generator of the Alexander module
(0,-4-t+9t^2-26t^3+31t^4-16t^5+3t^6,4-10t+16t^2-14t^3+6t^4-t^5,4-10t+16t^2-14t^3+6t^4-t^5,1-2t+t^2,-4+2t+4t^2-18t^3+22t^4-11t^5+2t^6,0,4-14t+18t^2-10t^3-12t^4+21t^5-11t^6+2t^7)
the Blanchfield form on it
x
115
First homology
of the double branched cover of 12n_0663
Z/115
-2 2
12n_0664
1

detected by
an unknotting move
1-7t+20t^2-34t^3+41t^4-34t^5+20t^6-7t^7+t^8
Seifert matrix of 12n_0664
1 0 0 0 0 0 -1 0
0 -1 -1 0 0 0 0 0
0 0 -1 -1 0 0 0 0
0 0 0 1 0 0 0 0
0 -1 -1 0 -1 0 0 0
1 -1 0 0 -1 1 -1 1
0 -1 0 0 -1 0 -1 0
1 0 0 0 -1 0 -1 1
1
Generator of the Alexander module
(0,7-4t+15t^2-28t^3+27t^4-23t^5+6t^6,-10t+9t^2-10t^3+3t^4,0,7-4t+25t^2-37t^3+37t^4-26t^5+6t^6,7t-4t^2+15t^3-28t^4+27t^5-23t^6+6t^7,10+4t-t^2-10t^3+14t^4-20t^5+6t^6,-7-3t-8t^2+t^3-7t^4+3t^5)
the Blanchfield form on it
x
165
First homology
of the double branched cover of 12n_0664
Z/165
0 2
12n_0665
2

detected by
the Lickorish test
-2+10t-15t^2+10t^3-2t^4
Seifert matrix of 12n_0665
1 -1 -1 0
-2 4 3 0
-2 4 2 -1
0 0 0 1
1
Generator of the Alexander module
(1,-2,-2,0)
the Blanchfield form on it
t^-1-3+t
39
First homology
of the double branched cover of 12n_0665
Z/39
2 2
12n_0666
2

detected by
the Nakanishi index
1-4t+10t^2-16t^3+19t^4-16t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0666
0 -1 -1 -1 -1 0 -1 -1
-1 -2 -1 -1 -1 -1 -1 -1
-1 -2 -2 -1 -1 -1 -1 -1
0 0 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 0
-1 -2 -2 -1 -1 -2 -1 -1
0 -1 0 -1 -1 0 0 -1
0 0 0 0 -1 0 0 -1
2
81
First homology
of the double branched cover of 12n_0666
Z/27+Z/3
-4 4
12n_0667
1

detected by
an unknotting move
2-8t+17t^2-21t^3+17t^4-8t^5+2t^6
Seifert matrix of 12n_0667
1 1 0 1 1 1
0 0 0 1 1 0
0 0 -1 1 1 0
0 1 0 0 0 0
0 1 0 1 -1 0
0 0 -1 1 1 -1
1
Generator of the Alexander module
(-t,0,-1,1,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
75
First homology
of the double branched cover of 12n_0667
Z/75
-2 2
12n_0668
2

detected by
the signature
1-5t+13t^2-21t^3+25t^4-21t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0668
1 0 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 0 0 -1 0 0 -1 0
0 -1 -1 0 -1 0 0 0
1 0 -1 0 -1 1 0 0
-1 1 1 0 1 -1 -1 0
0 0 0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,-1,0,1+t)
the Blanchfield form on it
3t^-3-14t^-2+31t^-1-38+31t-14t^2+3t^3
105
First homology
of the double branched cover of 12n_0668
Z/105
-4 4
12n_0669
2

detected by
the Nakanishi index
2-10t+23t^2-29t^3+23t^4-10t^5+2t^6
Seifert matrix of 12n_0669
1 0 0 0 -1 0
0 -1 0 0 0 0
0 -1 -1 0 0 0
1 -1 -1 -2 -1 1
0 -1 -1 0 -1 0
1 0 -1 0 -1 1
2
99
First homology
of the double branched cover of 12n_0669
Z/33+Z/3
-2 2
12n_0670
1

detected by
an unknotting move
1-2t+3t^2-4t^3+5t^4-4t^5+3t^6-2t^7+t^8
Seifert matrix of 12n_0670
-1 0 0 1 1 0 1 0
0 -1 0 -1 -1 0 -1 0
-1 0 -1 1 1 0 1 0
0 0 0 0 -1 1 -1 1
0 0 0 -1 0 0 -1 0
0 0 0 0 0 1 0 1
0 0 0 0 -1 1 0 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,1-t-t^2,1+t^3,3t^2-3t^3-2t^4,1+t,0,1+3t,-1)
the Blanchfield form on it
8t^-3-50t^-2+109t^-1-141+109t-50t^2+8t^3
25
First homology
of the double branched cover of 12n_0670
Z/25
0 0
12n_0671
3

detected by
the signature
-1+6t-13t^2+18t^3-19t^4+18t^5-13t^6+6t^7-t^8
Seifert matrix of 12n_0671
-1 0 0 1 1 0 1 0
0 -1 0 -1 -1 0 -1 0
-1 0 -1 1 1 0 1 0
0 0 0 -2 -1 0 -2 0
0 0 0 -1 0 0 -1 0
0 0 0 -1 0 -1 -1 0
0 0 0 -1 -1 0 -2 0
0 0 0 -1 0 -1 -1 -1
1
Generator of the Alexander module
(0,1,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-7t^-1+8-7t+5t^2-t^3
95
First homology
of the double branched cover of 12n_0671
Z/95
-6 6
12n_0672
2

detected by
the Lickorish test
1-4t+12t^2-17t^3+12t^4-4t^5+t^6
Seifert matrix of 12n_0672
-1 0 0 1 1 1
0 1 0 0 0 0
-1 0 -1 1 1 1
0 1 0 1 0 -1
0 1 0 0 1 0
0 1 0 0 0 1
1 or 2
51
First homology
of the double branched cover of 12n_0672
Z/51
2 2
12n_0673
1

detected by
an unknotting move
1-t+t^4-t^7+t^8
Seifert matrix of 12n_0673
-1 0 0 1 1 1 1 1
0 -1 0 -1 -1 -1 -1 -1
-1 0 -1 1 1 1 1 1
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,t,0,0,1,0,0)
the Blanchfield form on it
t^-1-2+t
5
First homology
of the double branched cover of 12n_0673
Z/5
0 2
12n_0674
3

detected by
the signature
-1+5t-10t^2+14t^3-15t^4+14t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0674
-1 0 0 1 1 1 1 1
0 -1 0 -1 -1 -1 -1 -1
-1 0 -1 1 1 1 1 1
0 0 0 -2 -2 -1 -2 -2
0 0 0 -1 -2 -1 -1 -2
0 0 0 -1 -1 0 -1 -1
0 0 0 -1 -2 -1 -2 -2
0 0 0 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-9t^-1+11-9t+5t^2-t^3
75
First homology
of the double branched cover of 12n_0674
Z/75
-6 6
12n_0675
1

detected by
an unknotting move
1-3t+6t^2-8t^3+9t^4-8t^5+6t^6-3t^7+t^8
Seifert matrix of 12n_0675
-1 0 0 1 1 1 1 1
0 -1 0 -1 -1 -1 -1 -1
-1 0 -1 1 1 1 1 1
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
0 0 0 -1 -1 -2 -1 -1
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
1
Generator of the Alexander module
(-2-2t+2t^2,1+t-t^2,t-t^2,0,0,0,0,0)
the Blanchfield form on it
27t^-3-54t^-2+55t^-1-34+55t-54t^2+27t^3
45
First homology
of the double branched cover of 12n_0675
Z/45
0 2
12n_0676
1

detected by
an unknotting move
2-2t-4t^2+9t^3-4t^4-2t^5+2t^6
Seifert matrix of 12n_0676
-1 0 0 1 -1 1
0 -1 0 -1 1 -1
-1 0 -1 1 -1 1
0 0 0 0 1 -1
0 0 0 0 1 1
0 0 0 -1 1 0
1
Generator of the Alexander module
(0,-t,-1,1,-1,1)
the Blanchfield form on it
2t^-2-2+2t^2
9
First homology
of the double branched cover of 12n_0676
Z/9
0 0
12n_0677
2

detected by
the signature
-2+10t-20t^2+25t^3-20t^4+10t^5-2t^6
Seifert matrix of 12n_0677
-1 0 0 1 -1 1
0 -1 0 -1 1 -1
-1 0 -1 1 -1 1
0 0 0 -2 2 -1
0 0 0 1 -3 1
0 0 0 -1 1 0
1
Generator of the Alexander module
(0,-1+t-2t^2,1-2t+2t^2-2t^3,0,1-t+2t^2,0)
the Blanchfield form on it
-35t^-4+223t^-3-625t^-2+1097t^-1-1304+1097t-625t^2+223t^3-35t^4
89
First homology
of the double branched cover of 12n_0677
Z/89
-4 4
12n_0678
1

detected by
an unknotting move
2-8t+18t^2-23t^3+18t^4-8t^5+2t^6
Seifert matrix of 12n_0678
-1 0 0 1 -1 1
0 -1 0 -1 1 -1
-1 0 -1 1 -1 1
0 0 0 0 1 -1
0 0 0 0 1 1
0 0 0 -1 1 -2
1
Generator of the Alexander module
(0,1,1,0,0,0)
the Blanchfield form on it
2t^-2-6t^-1+10-6t+2t^2
79
First homology
of the double branched cover of 12n_0678
Z/79
-2 2
12n_0679
4

detected by
the signature
1-t-t^2+4t^3-6t^4+7t^5-6t^6+4t^7-t^8-t^9+t^10
Seifert matrix of 12n_0679
-1 -1 0 -1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0 0 0
0 -1 0 -1 0 0 0 0 0 0
0 -1 0 -1 -1 -1 -1 0 -1 -1
0 -1 0 -1 0 -1 -1 0 0 -1
0 -1 0 -1 0 0 -1 0 0 0
0 0 0 0 -1 -1 -1 -1 -1 -1
0 -1 0 -1 0 -1 -1 0 -1 -1
0 -1 0 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0,0,0)
the Blanchfield form on it
t^-4-t^-3-t^-2+4t^-1-5+4t-t^2-t^3+t^4
25
First homology
of the double branched cover of 12n_0679
Z/25
-8 8
12n_0680
3

detected by
the signature
2-3t-t^2+8t^3-11t^4+8t^5-t^6-3t^7+2t^8
Seifert matrix of 12n_0680
-1 -1 0 -1 0 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0
0 -1 0 -1 0 0 0 0
0 -1 0 -1 -1 1 -1 0
0 1 0 1 0 -2 1 0
0 -1 0 -1 0 0 -1 0
0 0 0 0 -1 1 -1 -1
1
Generator of the Alexander module
(0,0,0,0,0,1,-2,0)
the Blanchfield form on it
-7t^-4+20t^-3-18t^-2-4t^-1+18-4t-18t^2+20t^3-7t^4
19
First homology
of the double branched cover of 12n_0680
Z/19
-6 6
12n_0681
1

detected by
an unknotting move
1-2t+3t^2-4t^3+5t^4-4t^5+3t^6-2t^7+t^8
Seifert matrix of 12n_0681
-1 0 0 1 1 0 1 1
0 -1 0 -1 -1 0 -1 -1
-1 0 -1 1 1 0 1 1
0 0 0 0 -1 1 -1 -1
0 0 0 0 0 1 0 -1
0 0 0 0 0 1 0 0
0 0 0 0 -1 1 0 -1
0 0 0 -1 -1 0 -1 0
1
Generator of the Alexander module
(0,-t+t^2-t^3-t^4+t^5,1+t-2t^2+5t^3-2t^5+t^6-t^7,2t^2-4t^3+4t^4-t^5-2t^6+2t^7-t^8,0,-2t+2t^2-t^4+t^5,0,0)
the Blanchfield form on it
x
25
First homology
of the double branched cover of 12n_0681
Z/25
0 0
12n_0682
3

detected by
the signature
-1+6t-13t^2+18t^3-19t^4+18t^5-13t^6+6t^7-t^8
Seifert matrix of 12n_0682
-1 0 0 1 1 0 1 1
0 -1 0 -1 -1 0 -1 -1
-1 0 -1 1 1 0 1 1
0 0 0 -2 -2 0 -2 -1
0 0 0 -1 -2 0 -1 -1
0 0 0 -1 -1 -1 -1 0
0 0 0 -1 -2 0 -2 -1
0 0 0 -1 -1 0 -1 0
1
Generator of the Alexander module
(0,1,1,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-7t^-1+8-7t+5t^2-t^3
95
First homology
of the double branched cover of 12n_0682
Z/95
-6 6
12n_0683
2

detected by
the signature
-1+4t-11t^2+18t^3-21t^4+18t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0683
1 0 0 0 0 0 -1 0
1 1 -1 -1 0 0 -1 -1
0 0 0 -1 1 0 0 -1
0 0 0 0 1 0 0 0
-1 0 1 1 0 0 1 1
1 1 -1 -1 0 1 -1 -1
0 0 -1 -1 1 0 -1 -1
0 0 0 -1 1 0 0 0
1
Generator of the Alexander module
(0,0,-1,0,0,0,0,0)
the Blanchfield form on it
t^-3-3t^-2+6t^-1-7+6t-3t^2+t^3
89
First homology
of the double branched cover of 12n_0683
Z/89
4 4
12n_0684
2

detected by
the signature
1-4t+10t^2-15t^3+17t^4-15t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0684
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 0 0 0 0 -1 0
1 -1 -1 1 1 0 -2 0
1 -1 -1 0 1 0 -2 0
1 -1 -1 1 1 1 -2 0
0 -2 -1 0 0 0 -2 0
0 0 0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-3+4t^-2-9t^-1+11-9t+4t^2-t^3
77
First homology
of the double branched cover of 12n_0684
Z/77
4 4
12n_0685
1

detected by
an unknotting move
2-8t+18t^2-23t^3+18t^4-8t^5+2t^6
Seifert matrix of 12n_0685
1 0 0 0 -1 0
0 -1 0 0 0 0
0 -1 0 0 -1 0
-1 1 1 2 2 0
0 -2 -1 0 -2 0
0 0 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-4t^-2+9t^-1-12+9t-4t^2+t^3
79
First homology
of the double branched cover of 12n_0685
Z/79
2 2
12n_0686
2

detected by
the signature
1-5t+13t^2-19t^3+21t^4-19t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0686
1 0 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
0 -1 -1 -1 0 -1 0 0
0 -1 0 -1 0 0 0 0
0 -1 -1 -1 -1 -1 0 0
0 -1 0 -1 0 -1 0 0
1 0 -1 -1 -1 -1 1 0
-1 1 1 1 1 1 -1 -1
1
Generator of the Alexander module
(0,2t+t^3,2t+2t^2-t^3+t^4-t^5,0,1+2t-2t^2-t^3-t^4-t^5,0,-2t^3-t^5,4t^2+2t^4)
the Blanchfield form on it
x
97
First homology
of the double branched cover of 12n_0686
Z/97
-4 4
12n_0687
1

detected by
an unknotting move
2-10t+25t^2-33t^3+25t^4-10t^5+2t^6
Seifert matrix of 12n_0687
1 0 -1 0 0 0
0 -1 0 0 0 0
0 -1 -1 1 0 0
0 1 0 1 0 0
1 0 -1 1 1 0
-1 1 1 -1 -1 2
1
Generator of the Alexander module
(0,1,1-t,-t,0,1)
the Blanchfield form on it
-2t^-2+7t^-1-12+7t-2t^2
107
First homology
of the double branched cover of 12n_0687
Z/107
2 2
12n_0688
4

detected by
the signature
-1+t+t^2-5t^3+9t^4-11t^5+9t^6-5t^7+t^8+t^9-t^10
Seifert matrix of 12n_0688
-1 -1 0 0 -1 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0 0 0
0 0 0 -1 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 0 0 0 0
0 -1 0 0 -1 -1 -1 0 0 -1
0 -1 0 0 -1 0 -1 0 0 0
0 0 0 -1 0 -1 -1 -1 -1 -1
0 0 0 0 0 -1 -1 0 -1 -1
0 -1 0 0 -1 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,-t,0,0)
the Blanchfield form on it
-t^-4-t^-3+8t^-2-16t^-1+19-16t+8t^2-t^3-t^4
37
First homology
of the double branched cover of 12n_0688
Z/37
-8 8
12n_0689
3

detected by
the signature
2-3t+5t^3-7t^4+5t^5-3t^7+2t^8
Seifert matrix of 12n_0689
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 -2 0 1 1 1
0 -1 0 0 -1 0 0 0
0 -1 0 0 -1 -1 -1 -1
0 -1 0 0 -1 0 -1 0
0 -1 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(0,0,-1-t,-1,0,0,0,0)
the Blanchfield form on it
4t^-3-2t^-2-4t^-1+7-4t-2t^2+4t^3
7
First homology
of the double branched cover of 12n_0689
Z/7
-6 6
12n_0690
1

detected by
an unknotting move
1+2t-12t^2+19t^3-12t^4+2t^5+t^6
Seifert matrix of 12n_0690
-1 0 0 -1 1 0
0 -1 0 1 -1 0
-1 0 -1 -1 1 0
0 0 0 1 1 1
0 0 0 1 0 0
0 0 0 1 1 2
1
Generator of the Alexander module
(0,0,t,0,1,1)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
45
First homology
of the double branched cover of 12n_0690
Z/45
0 0
12n_0691
3

detected by
the signature
2-3t-2t^2+12t^3-17t^4+12t^5-2t^6-3t^7+2t^8
Seifert matrix of 12n_0691
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 -2 0 0 1 0
0 -1 0 0 -1 0 0 0
0 -1 0 -1 -1 -1 0 -1
0 -1 0 0 -1 0 -1 0
0 -1 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-4+2t^-3+t^-2-8t^-1+12-8t+t^2+2t^3-t^4
35
First homology
of the double branched cover of 12n_0691
Z/35
-6 6
12n_0692
3

detected by
the signature
2-3t-2t^2+12t^3-17t^4+12t^5-2t^6-3t^7+2t^8
Seifert matrix of 12n_0692
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 -1 0 0 0
0 0 0 -2 0 0 1 1
0 -1 0 0 -1 0 0 0
0 -1 0 -1 -1 -1 0 0
0 -1 0 0 -1 0 -1 0
0 -1 0 0 -1 0 -1 -1
1
Generator of the Alexander module
(2t-6t^2-8t^3-3t^4+6t^5+8t^7+8t^8+2t^9,9t+3t^2+6t^3+6t^4,t^3,3t+2t^3+2t^4,-6t-2t^2-4t^3-4t^4,1+t^3+6t^4+2t^5+4t^6+4t^7+t^8,-t^4-2t^5,-t^4-2t^5)
the Blanchfield form on it
x
35
First homology
of the double branched cover of 12n_0692
Z/35
-6 6
12n_0693
2

detected by
the signature
-1+4t-2t^2-7t^3+13t^4-7t^5-2t^6+4t^7-t^8
Seifert matrix of 12n_0693
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 0 0 0
0 -1 0 1 -1 -1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 0
0 -1 0 1 0 -1 -1 -1
1
Generator of the Alexander module
(0,1+2t,-1-t^2,-2,-2t,2,0,0)
the Blanchfield form on it
-2t^-3+4t^-2+4t^-1-11+4t+4t^2-2t^3
13
First homology
of the double branched cover of 12n_0693
Z/13
-4 4
12n_0694
3

detected by
the signature
1-4t^2+9t^3-11t^4+9t^5-4t^6+t^8
Seifert matrix of 12n_0694
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 -1 0 0 0 0
0 -1 0 1 -1 -1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 0
0 -1 0 1 0 -1 -1 -1
1 or 2
35
First homology
of the double branched cover of 12n_0694
Z/35
-6 6
12n_0695
1

detected by
an unknotting move
1-4t+10t^2-17t^3+21t^4-17t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0695
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 0 0 0
0 -1 0 1 1 -1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 1 1
0 -1 0 1 0 -1 0 1
1
Generator of the Alexander module
(0,0,0,0,1,0,0,0)
the Blanchfield form on it
-t^-2+2t^-1-3+2t-t^2
85
First homology
of the double branched cover of 12n_0695
Z/85
0 0
12n_0696
2

detected by
the signature
-1+4t-2t^2-7t^3+13t^4-7t^5-2t^6+4t^7-t^8
Seifert matrix of 12n_0696
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 0 0 0
0 -1 0 1 -1 -1 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 -1 -1 -1 0
0 -1 0 1 0 -1 0 -1
1
Generator of the Alexander module
(0,-t,1+t^2,0,t,-1,1+t,t)
the Blanchfield form on it
-t^-3+3t^-2-1+3t^2-t^3
13
First homology
of the double branched cover of 12n_0696
Z/13
-4 4
12n_0697
2

detected by
the signature
1-4t+6t^2-t^3-3t^4-t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0697
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
0 0 0 1 0 0 0 1
0 -1 0 1 -1 -1 0 1
0 -1 0 0 0 -1 0 0
0 -1 0 1 0 -1 -1 0
0 0 0 0 0 0 0 1
1 or 2
21
First homology
of the double branched cover of 12n_0697
Z/21
-4 4
12n_0698
2

detected by
the signature
-2+12t-25t^2+31t^3-25t^4+12t^5-2t^6
Seifert matrix of 12n_0698
0 1 0 0 -1 0
0 2 1 0 0 1
-1 2 1 -1 -1 1
-1 1 0 0 -1 0
0 1 0 0 0 0
0 1 0 0 0 2
1
Generator of the Alexander module
(0,0,1,-t,0,0)
the Blanchfield form on it
2t^-2-6t^-1+7-6t+2t^2
109
First homology
of the double branched cover of 12n_0698
Z/109
4 4
12n_0699
1

detected by
an unknotting move
-2+12t-19t^2+12t^3-2t^4
Seifert matrix of 12n_0699
2 1 2 -6
1 2 2 -6
1 2 2 -7
-3 -5 -6 22
1
Generator of the Alexander module
(4-8t-8t^2+22t^3-15t^4+3t^5,-185+403t+370t^2-1067t^3+735t^4-147t^5,-15+33t+30t^2-87t^3+60t^4-12t^5,112-244t-224t^2+646t^3-445t^4+89t^5)
the Blanchfield form on it
72031t^-7-734919t^-6+3018749t^-5-6013758t^-4+3690534t^-3+10321431t^-2-30790852t^-1+40873568-30790852t+10321431t^2+3690534t^3-6013758t^4+3018749t^5-734919t^6+72031t^7
47
First homology
of the double branched cover of 12n_0699
Z/47
2 2
12n_0700
2

detected by
the signature
-2+11t-21t^2+25t^3-21t^4+11t^5-2t^6
Seifert matrix of 12n_0700
1 0 0 0 0 0
0 2 1 0 0 1
0 2 1 0 -1 1
1 0 0 1 0 0
0 1 0 0 0 0
-1 1 0 -1 0 2
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-5t^-1+6-5t+2t^2
93
First homology
of the double branched cover of 12n_0700
Z/93
4 4
12n_0701
2

detected by
the Nakanishi index
-3+16t-25t^2+16t^3-3t^4
Seifert matrix of 12n_0701
0 1 0 0
0 2 1 1
-1 2 1 1
0 1 0 3
2
63
First homology
of the double branched cover of 12n_0701
Z/21+Z/3
2 2
12n_0702
1

detected by
an unknotting move
-2+12t-28t^2+37t^3-28t^4+12t^5-2t^6
Seifert matrix of 12n_0702
-1 0 -1 0 0 -1
0 2 0 0 0 0
0 1 0 1 1 0
0 0 1 0 0 1
0 1 0 0 1 0
0 0 0 0 1 -1
1
Generator of the Alexander module
(1,0,-t,0,0,1)
the Blanchfield form on it
2t^-1-3+2t
121
First homology
of the double branched cover of 12n_0702
Z/121
0 0
12n_0703
2

detected by
the signature
1-5t+11t^2-13t^3+13t^4-13t^5+11t^6-5t^7+t^8
Seifert matrix of 12n_0703
1 0 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
0 -1 -1 -1 0 0 -1 0
0 0 0 -1 -1 1 0 0
1 0 0 1 0 -1 0 1
0 -1 -1 0 0 0 -1 0
1 0 -1 0 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,1-t,-1-t+2t^3-t^4,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+7t^-1-6+7t-4t^2+t^3
73
First homology
of the double branched cover of 12n_0703
Z/73
-4 4
12n_0704
1

detected by
an unknotting move
4-15t+23t^2-15t^3+4t^4
Seifert matrix of 12n_0704
-1 1 1 1
0 7 5 2
0 3 3 1
0 2 2 0
1
Generator of the Alexander module
(-6+8t-2t^2,0,1-t,3-2t)
the Blanchfield form on it
1
61
First homology
of the double branched cover of 12n_0704
Z/61
0 0
12n_0705
1

detected by
an unknotting move
-1+9t-26t^2+37t^3-26t^4+9t^5-t^6
Seifert matrix of 12n_0705
1 0 0 0 0 -1
0 -1 0 0 0 0
0 1 0 0 -1 -1
1 -1 1 1 1 0
0 1 -1 0 -2 -1
0 0 0 0 -1 -2
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-1
109
First homology
of the double branched cover of 12n_0705
Z/109
0 0
12n_0706
2

detected by
the Nakanishi index
1-4t+6t^2-8t^3+11t^4-8t^5+6t^6-4t^7+t^8
Seifert matrix of 12n_0706
1 0 0 0 0 0 0 0
1 1 0 1 1 0 1 0
-1 0 -1 -1 -1 -1 0 -1
0 0 0 -1 0 0 0 0
1 0 0 0 1 0 0 0
-1 0 0 -1 -1 -1 0 0
1 0 0 1 0 0 1 0
0 0 0 -1 0 0 0 -1
2
49
First homology
of the double branched cover of 12n_0706
Z/7+Z/7
0 0
12n_0707
2

detected by
the signature
-1+4t-11t^2+17t^3-19t^4+17t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0707
0 0 1 0 0 0 1 -1
1 1 1 -1 0 0 1 -1
0 0 1 0 0 0 1 0
0 0 0 0 1 0 0 0
-1 0 -1 1 0 0 -1 1
1 1 1 -1 0 1 1 -1
0 0 0 0 0 0 1 0
0 0 0 -1 1 0 0 0
1 or 2
85
First homology
of the double branched cover of 12n_0707
Z/85
4 4
12n_0708
1

detected by
an unknotting move
1-3t+6t^2-9t^3+11t^4-9t^5+6t^6-3t^7+t^8
Seifert matrix of 12n_0708
0 -1 0 1 0 -1 0 -1
0 -1 0 0 0 0 0 0
-1 0 -1 1 -1 -1 0 0
1 1 0 -2 1 1 0 1
-1 -1 0 1 0 -1 0 -1
0 -1 0 1 0 0 0 -1
-1 0 -1 1 -1 -1 -1 0
0 -1 0 1 0 0 0 0
1
Generator of the Alexander module
(0,0,t+t^2,0,0,1,0,0)
the Blanchfield form on it
t^-3-2t^-2+4t^-1-4+4t-2t^2+t^3
49
First homology
of the double branched cover of 12n_0708
Z/49
0 0
12n_0709
1

detected by
an unknotting move
1-4t+8t^2-11t^3+13t^4-11t^5+8t^6-4t^7+t^8
Seifert matrix of 12n_0709
0 -1 -1 0 -1 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
-1 -1 -1 0 -1 0 -1 0
0 -1 -1 0 0 0 -1 0
-1 0 0 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 0 -2 -1
-1 0 -1 -1 -1 0 -1 0
1
Generator of the Alexander module
(0,2,1,0,0,0,0,0)
the Blanchfield form on it
2t^-3-4t^-2-2t^-1+11-2t-4t^2+2t^3
61
First homology
of the double branched cover of 12n_0709
Z/61
0 2
12n_0710
1

detected by
an unknotting move
2-10t+22t^2-27t^3+22t^4-10t^5+2t^6
Seifert matrix of 12n_0710
1 1 1 0 1 0
0 -1 0 0 0 0
0 -1 -1 0 0 0
1 0 0 -1 -1 -1
1 -1 -1 0 -2 -1
1 0 -1 0 -1 0
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
1
95
First homology
of the double branched cover of 12n_0710
Z/95
-2 2
12n_0711
1

detected by
an unknotting move
1-5t+13t^2-23t^3+29t^4-23t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0711
1 0 1 0 1 -1 0 0
0 -1 0 0 0 0 0 0
0 0 1 0 1 0 0 0
0 -1 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
0 -1 0 -1 0 -1 0 0
1 0 1 -1 1 -1 1 0
-1 1 -1 1 -1 1 -1 -1
1 or 2
113
First homology
of the double branched cover of 12n_0711
Z/113
0 0
12n_0712
2

detected by
the Lickorish test
3-13t+27t^2-33t^3+27t^4-13t^5+3t^6
Seifert matrix of 12n_0712
3 0 3 0 0 0
-1 -3 0 -2 0 0
1 0 2 0 0 0
0 -1 1 -1 0 0
2 1 1 1 1 1
2 1 1 1 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
-3t^-2+11t^-1-17+11t-3t^2
119
First homology
of the double branched cover of 12n_0712
Z/119
2 2
12n_0713
2

detected by
the Lickorish test
3-11t+20t^2-23t^3+20t^4-11t^5+3t^6
Seifert matrix of 12n_0713
1 3 3 0 0 2
0 -3 -4 -2 0 -4
0 -6 -6 -3 0 -6
0 -5 -5 -1 0 -4
1 3 3 0 1 2
0 -5 -5 -2 0 -5
1
Generator of the Alexander module
(0,2,0,0,1,1)
the Blanchfield form on it
-3t^-2+8t^-1-12+8t-3t^2
91
First homology
of the double branched cover of 12n_0713
Z/91
2 2
12n_0714
2

detected by
the linking form on L_4
3-14t+30t^2-37t^3+30t^4-14t^5+3t^6
Seifert matrix of 12n_0714
-2 -1 -1 -1 -1 0
-1 1 -1 -1 0 -1
-2 -1 -2 -1 -1 0
0 0 0 -1 0 0
-2 -1 -2 -1 -2 0
0 0 1 0 0 1
2
131
First homology
of the double branched cover of 12n_0714
Z/131
-2 2
12n_0715
1

detected by
an unknotting move
6-22t+33t^2-22t^3+6t^4
Seifert matrix of 12n_0715
-17 -21 -21 -12
-20 -24 -25 -14
-24 -30 -30 -18
-16 -20 -21 -13
1 or 2
89
First homology
of the double branched cover of 12n_0715
Z/89
0 0
12n_0716
1

detected by
an unknotting move
2-9t+18t^2-21t^3+18t^4-9t^5+2t^6
Seifert matrix of 12n_0716
-1 0 0 0 0 0
0 2 0 1 1 0
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
0 0 -1 0 1 0
1 1 1 1 0 -1
1
Generator of the Alexander module
(0,1,0,0,1,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
79
First homology
of the double branched cover of 12n_0716
Z/79
-2 2
12n_0717
2

detected by
the Lickorish test
1-4t+12t^2-17t^3+12t^4-4t^5+t^6
Seifert matrix of 12n_0717
0 -1 -1 1 0 0
0 1 0 0 0 1
0 0 0 1 0 0
1 1 1 -1 0 0
0 -1 -1 1 1 -1
0 0 -1 1 0 0
2
51
First homology
of the double branched cover of 12n_0717
Z/51
2 2
12n_0718
1

detected by
an unknotting move
2-7t+12t^2-13t^3+12t^4-7t^5+2t^6
Seifert matrix of 12n_0718
0 -1 -1 1 0 0
0 1 0 0 0 1
0 0 0 1 0 0
1 1 1 -2 0 0
0 -1 -1 1 1 -1
0 0 -1 1 0 -1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
-1
55
First homology
of the double branched cover of 12n_0718
Z/55
2 2
12n_0719
1

detected by
an unknotting move
1-5t+13t^2-17t^3+13t^4-5t^5+t^6
Seifert matrix of 12n_0719
0 -1 0 1 -1 1
-1 -1 -1 -1 0 -1
0 0 -1 0 0 0
0 -1 0 0 -1 1
0 0 -1 0 -1 0
0 0 1 0 0 1
1
Generator of the Alexander module
(0,t,0,0,-1,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
55
First homology
of the double branched cover of 12n_0719
Z/55
-2 2
12n_0720
2

detected by
the signature
-2+11t-23t^2+29t^3-23t^4+11t^5-2t^6
Seifert matrix of 12n_0720
-1 0 -1 0 0 0
0 1 1 0 0 0
0 0 -1 0 0 0
0 1 1 -1 0 -1
1 0 1 -1 -2 -1
1 0 1 -1 -1 -2
1
Generator of the Alexander module
(0,-t-3t^2,1+3t,-7t+6t^2,6t-9t^2,1-12t+9t^2)
the Blanchfield form on it
-6t^-2+19t^-1-22+19t-6t^2
101
First homology
of the double branched cover of 12n_0720
Z/101
-4 4
12n_0721
1

detected by
an unknotting move
1-2t+3t^2-4t^3+5t^4-4t^5+3t^6-2t^7+t^8
Seifert matrix of 12n_0721
-1 -1 -1 -1 -1 -1 -1 -1
0 -1 0 -1 -1 -1 -1 -1
0 -1 -1 -1 -1 -1 -1 -1
0 0 0 0 -1 -1 -1 -1
0 0 0 0 0 -1 0 -1
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,0,1,0,0,0,0)
the Blanchfield form on it
-t^-3+2t^-2-2t^-1+1-2t+2t^2-t^3
25
First homology
of the double branched cover of 12n_0721
Z/25
0 0
12n_0722
3

detected by
the signature
-1+4t-7t^2+10t^3-11t^4+10t^5-7t^6+4t^7-t^8
Seifert matrix of 12n_0722
-1 -1 -1 -1 -1 -1 -1 -1
0 -1 0 -1 -1 -1 -1 -1
0 -1 -1 -1 -1 -1 -1 -1
0 0 0 -2 -2 -1 -2 -2
0 0 0 -1 -2 -1 -1 -2
0 0 0 -1 -1 0 -1 -1
0 0 0 -1 -2 -1 -2 -2
0 0 0 -1 -1 -1 -1 -2
1
Generator of the Alexander module
(0,0,0,0,0,0,0,1)
the Blanchfield form on it
-t^-3+4t^-2-6t^-1+7-6t+4t^2-t^3
55
First homology
of the double branched cover of 12n_0722
Z/55
-6 6
12n_0723
1

detected by
an unknotting move
2-4t+3t^2-t^3+3t^4-4t^5+2t^6
Seifert matrix of 12n_0723
-1 -1 -1 -1 1 -1
0 -1 0 -1 1 -1
0 -1 -1 -1 1 -1
0 0 0 0 1 -1
0 0 0 0 1 1
0 0 0 -1 1 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-2t^-2+t^-1+t-2t^2+t^3
19
First homology
of the double branched cover of 12n_0723
Z/19
-2 2
12n_0724
2

detected by
the signature
-2+8t-13t^2+15t^3-13t^4+8t^5-2t^6
Seifert matrix of 12n_0724
-1 -1 -1 -1 1 -1
0 -1 0 -1 1 -1
0 -1 -1 -1 1 -1
0 0 0 -2 2 -1
0 0 0 1 -3 1
0 0 0 -1 1 0
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
t^-3-4t^-2+7t^-1-8+7t-4t^2+t^3
61
First homology
of the double branched cover of 12n_0724
Z/61
-4 4
12n_0725
4

detected by
the signature
1-t+t^3-2t^4+3t^5-2t^6+t^7-t^9+t^10
Seifert matrix of 12n_0725
-1 -1 0 -1 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0
-1 -1 -1 -1 0 0 0 0 0 0
0 -1 0 -1 0 0 0 0 0 0
-1 -1 -1 -1 -1 -1 -1 0 -1 -1
-1 -1 -1 -1 0 -1 -1 0 0 -1
-1 -1 -1 -1 0 0 -1 0 0 0
0 0 0 0 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 0 -1 -1 0 -1 -1
-1 -1 -1 -1 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,1,0,0,0,0,0,0,0)
the Blanchfield form on it
t^-4-t^-3+t^-1-1+t-t^3+t^4
5
First homology
of the double branched cover of 12n_0725
Z/5
-8 8
12n_0726
2

detected by
the Lickorish test
-4+16t-23t^2+16t^3-4t^4
Seifert matrix of 12n_0726
-2 0 0 0
-1 -2 2 -1
1 1 -3 1
-1 -1 1 0
1
Generator of the Alexander module
(0,t,1,t)
the Blanchfield form on it
-2t^-1+4-2t
63
First homology
of the double branched cover of 12n_0726
Z/63
-2 2
12n_0727
1

detected by
an unknotting move
2-10t+21t^2-25t^3+21t^4-10t^5+2t^6
Seifert matrix of 12n_0727
-1 0 0 0 0 0
0 -1 0 1 1 -1
-1 0 -1 0 0 0
-1 0 -1 -1 0 0
0 0 -1 0 1 0
1 0 1 0 -1 2
1
Generator of the Alexander module
(0,-t,0,-1,-1,1)
the Blanchfield form on it
1
91
First homology
of the double branched cover of 12n_0727
Z/91
-2 2
12n_0728
1

detected by
an unknotting move
-1+5t-13t^2+22t^3-25t^4+22t^5-13t^6+5t^7-t^8
Seifert matrix of 12n_0728
-1 0 0 0 -1 0 0 0
1 1 0 1 1 1 0 1
-1 0 -1 0 -1 0 -1 0
0 0 0 -1 0 0 0 0
0 0 0 0 -1 0 0 0
1 0 0 1 0 1 0 1
-1 0 0 -1 -1 0 -1 0
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,1,0,0)
the Blanchfield form on it
-t^-1+1-t
107
First homology
of the double branched cover of 12n_0728
Z/107
-2 2
12n_0729
2

detected by
the signature
-2+9t-16t^2+19t^3-16t^4+9t^5-2t^6
Seifert matrix of 12n_0729
-1 0 0 0 -1 -1
0 0 0 0 1 1
-1 0 -1 -1 -1 -1
0 0 0 -2 -1 -1
0 0 0 0 -1 0
0 1 0 -1 -1 -2
1
Generator of the Alexander module
(0,1,-t,0,0,1)
the Blanchfield form on it
-2t^-2+5t^-1-6+5t-2t^2
73
First homology
of the double branched cover of 12n_0729
Z/73
-4 4
12n_0730
1

detected by
an unknotting move
1-4t+11t^2-15t^3+11t^4-4t^5+t^6
Seifert matrix of 12n_0730
0 0 1 0 1 0
-1 -1 0 -1 0 -1
1 0 0 1 1 0
1 0 1 1 1 0
1 0 1 0 0 0
-1 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,0,0,0,0,1)
the Blanchfield form on it
2t^-2-4t^-1+5-4t+2t^2
47
First homology
of the double branched cover of 12n_0730
Z/47
-2 2
12n_0731
1

detected by
an unknotting move
-2+11t-28t^2+39t^3-28t^4+11t^5-2t^6
Seifert matrix of 12n_0731
2 0 1 1 1 0
-1 -1 0 -1 0 -1
1 0 2 1 1 0
2 0 1 2 1 0
1 0 1 0 0 0
-1 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,2+4t+11t^2+6t^3,-3-3t-14t^2-24t^3-t^4+6t^5,1+4t^2+3t^3,-3t-3t^2+4t^3+3t^4,3t+7t^2-2t^3+16t^4+4t^5-6t^6)
the Blanchfield form on it
x
121
First homology
of the double branched cover of 12n_0731
Z/121
0 0
12n_0732
1

detected by
an unknotting move
1-9t+28t^2-39t^3+28t^4-9t^5+t^6
Seifert matrix of 12n_0732
-2 0 -2 0 0 -1
0 -1 0 0 0 0
-1 1 -1 0 0 -1
-1 -1 0 1 -1 0
-1 0 -1 0 -1 -1
-1 1 -2 0 0 -2
1
Generator of the Alexander module
(0,2+46t-127t^2+156t^3-92t^4+26t^5,-2-46t+127t^2-156t^3+92t^4-26t^5,1+7t-16t^2-8t^3+42t^4-36t^5+13t^6,0,-2-70t+191t^2-234t^3+138t^4-39t^5)
the Blanchfield form on it
x
115
First homology
of the double branched cover of 12n_0732
Z/115
-2 2
12n_0733
1

detected by
an unknotting move
2-12t+31t^2-41t^3+31t^4-12t^5+2t^6
Seifert matrix of 12n_0733
1 0 1 0 0 0
-1 -1 -1 0 0 -1
0 0 1 0 0 0
0 -1 -1 -1 1 0
1 1 1 0 -2 0
1 0 1 0 0 -1
1
Generator of the Alexander module
(0,t,0,0,1-t,0)
the Blanchfield form on it
2t^-2-9t^-1+16-9t+2t^2
131
First homology
of the double branched cover of 12n_0733
Z/131
-2 2
12n_0734
2

detected by
the signature
-2+10t-19t^2+23t^3-19t^4+10t^5-2t^6
Seifert matrix of 12n_0734
-2 0 0 -1 -1 -1
1 -2 1 0 1 1
-1 1 0 0 -1 -1
-1 -1 0 -2 -1 -1
-2 0 0 -1 -2 -1
-2 0 0 -1 -2 -2
1
Generator of the Alexander module
(0,-2+8t-7t^2+2t^3,1-t,0,0,1+t-3t^2+t^3)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
85
First homology
of the double branched cover of 12n_0734
Z/85
-4 4
12n_0735
1

detected by
an unknotting move
-4+18t-27t^2+18t^3-4t^4
Seifert matrix of 12n_0735
-3 0 0 1
-1 -2 1 0
1 1 0 0
1 -1 0 -2
1
Generator of the Alexander module
(0,3,-2,2)
the Blanchfield form on it
-8t^-1+20-8t
71
First homology
of the double branched cover of 12n_0735
Z/71
-2 2
12n_0736
1

detected by
an unknotting move
2-13t+36t^2-49t^3+36t^4-13t^5+2t^6
Seifert matrix of 12n_0736
2 0 1 1 1 0
-1 -1 -1 -1 0 -1
1 0 2 1 1 1
2 0 1 2 1 0
1 0 1 0 0 0
0 0 0 0 0 1
1
Generator of the Alexander module
(22t-24t^2+20t^3-4t^4,-t,4-4t+5t^2-t^3,t,-1,1+t^2+2t^3)
the Blanchfield form on it
-231t^-6+2610t^-5-13905t^-4+44429t^-3-96297t^-2+150435t^-1-174110+150435t-96297t^2+44429t^3-13905t^4+2610t^5-231t^6
151
First homology
of the double branched cover of 12n_0736
Z/151
2 2
12n_0737
2

detected by
the Nakanishi index
-2+7t-9t^2+9t^3-9t^4+7t^5-2t^6
Seifert matrix of 12n_0737
-2 0 0 0 -1 0
0 0 -1 1 -1 0
-1 0 0 1 -1 0
1 1 1 -2 1 1
-2 0 0 0 -2 0
0 -1 -1 1 0 0
2
45
First homology
of the double branched cover of 12n_0737
Z/15+Z/3
0 2
12n_0738
2

detected by
the signature
-2+13t-30t^2+39t^3-30t^4+13t^5-2t^6
Seifert matrix of 12n_0738
-2 -2 0 -1 1 -1
0 2 0 1 -1 1
1 2 -1 1 -1 1
-1 0 0 -1 0 -1
0 -1 0 -1 0 -1
-1 -1 0 -1 1 -2
1
Generator of the Alexander module
(0,3,t,0,-2,0)
the Blanchfield form on it
-t^-2+5t^-1-7+5t-t^2
129
First homology
of the double branched cover of 12n_0738
Z/129
-4 4
12n_0739
2

detected by
the signature
1-4t+5t^2+t^3-5t^4+t^5+5t^6-4t^7+t^8
Seifert matrix of 12n_0739
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 0 -1 0 0 1
0 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0
1 0 0 1 1 1 1 0
1 0 0 1 1 0 1 0
1 1 0 1 1 1 1 -1
1
Generator of the Alexander module
(4t-2t^2,-6t-15t^2-5t^3-19t^4+25t^5-6t^6,-6t-17t^2-8t^3-15t^4+24t^5-6t^6,8t+6t^2+t^3+17t^4-13t^6+4t^7,-2t+t^2,1-2t+9t^2-4t^3-32t^4-4t^6-18t^7+24t^8-6t^9,12t+34t^2+16t^3+26t^4-54t^5+20t^6-2t^7,-1-14t^2-21t^3-10t^4-48t^5+22t^6-46t^7+49t^8-12t^9)
the Blanchfield form on it
x
13
First homology
of the double branched cover of 12n_0739
Z/13
4 4
12n_0740
1

detected by
an unknotting move
-2+10t-24t^2+33t^3-24t^4+10t^5-2t^6
Seifert matrix of 12n_0740
-2 1 0 -1 0 0
0 1 0 -1 0 0
1 -1 -1 1 0 0
-1 0 0 0 1 -1
0 0 0 0 1 0
-1 0 0 -1 0 0
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
1
105
First homology
of the double branched cover of 12n_0740
Z/105
0 0
12n_0741
1

detected by
an unknotting move
3-11t+21t^2-25t^3+21t^4-11t^5+3t^6
Seifert matrix of 12n_0741
3 0 3 3 0 3
-1 -3 0 0 -2 0
1 0 2 1 0 1
1 0 2 2 0 2
0 -1 1 1 -1 1
1 0 2 1 0 2
1 or 2
95
First homology
of the double branched cover of 12n_0741
Z/95
2 2
12n_0742
2

detected by
the Lickorish test
2-9t+21t^2-27t^3+21t^4-9t^5+2t^6
Seifert matrix of 12n_0742
-1 0 0 0 0 0
0 2 0 0 0 1
-1 0 0 0 0 -1
0 0 0 1 0 0
-1 -1 -1 0 1 -2
-2 0 -1 1 0 -2
2
91
First homology
of the double branched cover of 12n_0742
Z/91
2 2
12n_0743
2

detected by
the Lickorish test
6-21t+31t^2-21t^3+6t^4
Seifert matrix of 12n_0743
3 0 0 3
-1 -3 -2 0
0 -1 -1 1
1 0 0 3
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
2t^-1-3+2t
85
First homology
of the double branched cover of 12n_0743
Z/85
0 0
12n_0744
2

detected by
the signature
-2+9t-15t^2+17t^3-15t^4+9t^5-2t^6
Seifert matrix of 12n_0744
-1 0 0 0 0 0
0 -1 0 1 0 0
-1 -1 1 -1 1 0
-1 0 0 -1 1 0
1 0 0 0 -2 0
0 -1 0 0 1 -1
1
Generator of the Alexander module
(0,2-4t+3t^2+t^3-t^4,4t-4t^2+t^3,0,1+t-4t^2+t^4,-2t+4t^2-3t^3-t^4+t^5)
the Blanchfield form on it
6t^-2-9t^-1+10-9t+6t^2
69
First homology
of the double branched cover of 12n_0744
Z/69
-4 4
12n_0745
2

detected by
the Nakanishi index
-1+10t-30t^2+43t^3-30t^4+10t^5-t^6
Seifert matrix of 12n_0745
-1 0 0 0 0 0
0 1 0 1 0 0
-1 -1 1 -1 1 0
-1 0 0 -1 1 0
1 0 0 0 1 0
0 -1 0 0 1 -1
2
125
First homology
of the double branched cover of 12n_0745
Z/25+Z/5
0 0
12n_0746
2

detected by
the Lickorish test
2-11t+28t^2-37t^3+28t^4-11t^5+2t^6
Seifert matrix of 12n_0746
-1 0 0 0 0 0
0 2 0 1 0 1
-1 -1 1 -1 1 0
-1 0 0 -1 1 0
1 0 0 0 1 0
0 0 0 0 1 1
2
119
First homology
of the double branched cover of 12n_0746
Z/119
2 2
12n_0747
2

detected by
the signature
-1+5t-13t^2+20t^3-23t^4+20t^5-13t^6+5t^7-t^8
Seifert matrix of 12n_0747
0 0 0 0 0 1 0 0
-1 1 -1 1 0 0 0 1
-1 0 0 0 0 1 0 0
-1 0 -1 0 0 0 0 1
0 0 0 0 1 1 0 0
1 0 1 -1 0 0 0 -1
-1 1 -1 1 0 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-3-4t^-2+9t^-1-11+9t-4t^2+t^3
101
First homology
of the double branched cover of 12n_0747
Z/101
4 4
12n_0748
1

detected by
an unknotting move
1-4t+9t^2-16t^3+19t^4-16t^5+9t^6-4t^7+t^8
Seifert matrix of 12n_0748
-2 -2 -1 -1 -2 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1
-2 -2 -2 -1 -2 -1 -1 -1
0 -1 0 -1 -1 -1 0 -1
-1 -2 -1 -1 -1 -1 -1 -1
0 0 0 0 0 -1 0 0
-1 -1 -1 -1 -1 -1 0 -1
0 -1 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(1,0,0,0,0,0,0,0)
the Blanchfield form on it
-t^-1+1-t
79
First homology
of the double branched cover of 12n_0748
Z/79
-2 2
12n_0749
2

detected by
the Lickorish test
1-t+t^2-t^3+t^4-t^5+t^6
Seifert matrix of 12n_0749
-1 0 0 0 0 1
-1 0 -1 0 0 1
0 1 0 0 0 0
-1 -1 0 -1 1 1
1 1 1 0 -1 -1
1 1 0 0 0 -2
1
Generator of the Alexander module
?
the Blanchfield form on it
?
7
First homology
of the double branched cover of 12n_0749
Z/7
-2 4
12n_0750
2

detected by
the signature
2-5t+7t^2-5t^3+2t^4
Seifert matrix of 12n_0750
-2 -1 -4 -1
-1 -1 -3 -1
-4 -2 -11 -3
0 0 -1 -1
1
Generator of the Alexander module
(0,1,0,0)
the Blanchfield form on it
3t^-1-4+3t
21
First homology
of the double branched cover of 12n_0750
Z/21
-4 4
12n_0751
1

detected by
an unknotting move
1-4t+9t^2-13t^3+15t^4-13t^5+9t^6-4t^7+t^8
Seifert matrix of 12n_0751
-1 0 0 0 0 1 0 0
-1 1 -1 1 0 0 0 1
-1 0 -1 0 0 1 0 0
-1 0 -1 0 0 0 0 1
0 0 0 0 -1 0 0 0
1 0 1 -1 -1 -1 0 -1
-1 1 -1 1 0 0 1 1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,t-t^2,0,0,0,1,0,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
69
First homology
of the double branched cover of 12n_0751
Z/69
0 2
12n_0752
2

detected by
the Lickorish test
2-9t+20t^2-25t^3+20t^4-9t^5+2t^6
Seifert matrix of 12n_0752
0 1 1 1 1 1
1 -1 1 1 0 1
0 1 0 1 1 1
2 0 2 1 0 2
1 -1 1 1 -1 1
1 0 1 1 0 2
2
87
First homology
of the double branched cover of 12n_0752
Z/87
-2 2
12n_0753
2

detected by
the signature
-2+11t-24t^2+31t^3-24t^4+11t^5-2t^6
Seifert matrix of 12n_0753
-1 0 0 -1 1 -1
0 -1 -1 0 -1 0
0 0 -2 0 -1 -1
0 0 -1 0 0 -1
0 0 0 1 -2 1
0 0 -1 -1 0 -2
1
Generator of the Alexander module
(0,4-4t+2t^2,0,0,1,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
105
First homology
of the double branched cover of 12n_0753
Z/105
-4 4
12n_0754
1

detected by
an unknotting move
1-5t+13t^2-21t^3+25t^4-21t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0754
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
0 1 -1 -1 0 0 0 0
-1 0 0 -1 0 0 0 0
-1 0 0 -1 1 0 1 0
-1 0 0 -1 1 1 1 1
0 1 0 -1 0 0 1 0
-1 0 0 -1 1 0 1 1
1
Generator of the Alexander module
(0,0,-1+2t^3,-1-3t^2,0,-t,1+3t^2,0)
the Blanchfield form on it
t^-3-5t^-2+9t^-1-11+9t-5t^2+t^3
105
First homology
of the double branched cover of 12n_0754
Z/105
0 2
12n_0755
2

detected by
the Lickorish test
1-10t+29t^2-39t^3+29t^4-10t^5+t^6
Seifert matrix of 12n_0755
-2 0 0 -1 -1 -1
0 -1 0 0 0 0
0 1 1 1 0 0
-2 0 0 -2 -1 -1
0 0 0 0 -1 0
-1 1 0 0 -1 0
1
Generator of the Alexander module
(0,0,1,0,0,0)
the Blanchfield form on it
2t^-2-8t^-1+11-8t+2t^2
119
First homology
of the double branched cover of 12n_0755
Z/119
-2 2
12n_0756
2

detected by
the Nakanishi index
2-10t+23t^2-29t^3+23t^4-10t^5+2t^6
Seifert matrix of 12n_0756
-1 0 0 0 0 0
0 -1 0 0 0 0
0 1 -1 -1 0 0
-1 0 0 -1 0 0
0 1 0 -1 1 0
1 0 0 1 -1 2
2
99
First homology
of the double branched cover of 12n_0756
Z/33+Z/3
-2 2
12n_0757
2

detected by
the Lickorish test
1-9t+28t^2-39t^3+28t^4-9t^5+t^6
Seifert matrix of 12n_0757
1 0 0 0 0 0
0 1 0 0 0 0
1 0 -1 1 -1 0
0 -1 0 -1 0 0
0 1 -1 1 -2 0
1 0 0 1 -1 -1
2
115
First homology
of the double branched cover of 12n_0757
Z/115
-2 2
12n_0758
3

detected by
the signature
5-14t+21t^2-23t^3+21t^4-14t^5+5t^6
Seifert matrix of 12n_0758
-1 0 -1 0 0 -1
0 -1 0 0 0 0
0 0 -2 1 -1 -1
0 -1 0 -1 0 0
0 1 -1 1 -2 0
0 0 -1 1 -1 -2
1 or 2
103
First homology
of the double branched cover of 12n_0758
Z/103
-6 6
12n_0759
2

detected by
the Lickorish test
-7+28t-41t^2+28t^3-7t^4
Seifert matrix of 12n_0759
-2 0 -1 0
1 -2 0 -1
-1 -1 -2 0
1 -1 0 1
1 or 2
111
First homology
of the double branched cover of 12n_0759
Z/111
-2 2
12n_0760
2

detected by
the Nakanishi index
-2+11t-29t^2+41t^3-29t^4+11t^5-2t^6
Seifert matrix of 12n_0760
-1 0 -1 0 0 -1
-1 1 -1 1 1 0
0 0 -2 0 0 -2
1 0 1 1 0 1
0 0 0 1 1 0
0 0 -1 0 0 -2
2
125
First homology
of the double branched cover of 12n_0760
Z/25+Z/5
0 0
12n_0761
2

detected by
the signature
-1+5t-10t^2+10t^3-9t^4+10t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0761
-1 0 -1 0 0 -1 -1 0
-1 -1 -1 0 0 -1 -1 0
0 0 -1 0 -1 -1 -1 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 0
0 0 0 1 -1 -1 -1 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 -1 0 1
1
Generator of the Alexander module
(0,-2t+3t^3+t^4-6t^5+16t^6-17t^7+13t^8-6t^9+t^10,0,-2-t+t^2-2t^3+10t^4-11t^5+13t^6-7t^7+t^8,2+2t+t^3-8t^4+10t^5-13t^6+7t^7-t^8,-1+t+10t^2-8t^3-19t^4+21t^5-15t^6-t^7+10t^8+4t^9-4t^10,-1-t-3t^2+4t^3+17t^4-18t^5+18t^6-6t^7-4t^8-2t^9+2t^10,-3t+t^2+7t^3-3t^4-4t^5+16t^6-19t^7+12t^8-5t^9+t^10)
the Blanchfield form on it
x
61
First homology
of the double branched cover of 12n_0761
Z/61
-4 4
12n_0762
2

detected by
the signature
-1+5t-10t^2+12t^3-13t^4+12t^5-10t^6+5t^7-t^8
Seifert matrix of 12n_0762
-1 0 -1 0 0 -1 -1 0
-1 -1 -1 0 0 -1 -1 0
0 0 -1 0 -1 -1 -1 0
0 0 0 -1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 1 -1 -1 -1 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 -1 0 1
1 or 2
69
First homology
of the double branched cover of 12n_0762
Z/69
-4 4
12n_0763
1

detected by
an unknotting move
-1+12t-36t^2+51t^3-36t^4+12t^5-t^6
Seifert matrix of 12n_0763
-1 0 0 0 0 0
0 1 0 1 0 0
0 -1 -1 0 -1 0
-1 0 0 -1 0 0
0 0 0 1 1 1
1 1 0 1 1 2
1 or 2
149
First homology
of the double branched cover of 12n_0763
Z/149
0 0
12n_0764
3

detected by
the signature
3-5t+3t^2-t^3+3t^4-5t^5+3t^6
Seifert matrix of 12n_0764
-1 0 0 0 0 0
0 -1 0 0 0 0
1 0 -2 1 -1 0
0 -1 0 -1 0 0
1 0 -1 1 -2 0
1 -1 0 0 -1 -1
2
23
First homology
of the double branched cover of 12n_0764
Z/23
-6 6
12n_0765
2

detected by
the signature
-3+15t-31t^2+39t^3-31t^4+15t^5-3t^6
Seifert matrix of 12n_0765
-1 0 0 0 0 0
0 1 0 0 0 0
1 0 -2 1 -1 0
0 -1 0 -1 0 0
1 0 -1 1 -2 0
1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,-1-t,3-t,-1,1-t,t+t^2)
the Blanchfield form on it
-4t^-2+17t^-1-25+17t-4t^2
137
First homology
of the double branched cover of 12n_0765
Z/137
-4 4
12n_0766
2

detected by
the signature
-3+13t-21t^2+23t^3-21t^4+13t^5-3t^6
Seifert matrix of 12n_0766
1 0 0 0 0 0
0 -1 0 0 0 0
1 0 -2 1 -1 0
0 -1 0 -1 0 0
1 0 -1 1 -2 0
1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,0,11-7t-2t^2+t^3+2t^4,0,-1,-1+t+t^2)
the Blanchfield form on it
44t^-7-206t^-6+291t^-5-226t^-4+851t^-3-2513t^-2+3927t^-1-4336+3927t-2513t^2+851t^3-226t^4+291t^5-206t^6+44t^7
97
First homology
of the double branched cover of 12n_0766
Z/97
-4 4
12n_0767
1

detected by
an unknotting move
-1+4t-9t^2+15t^3-17t^4+15t^5-9t^6+4t^7-t^8
Seifert matrix of 12n_0767
0 -1 0 0 0 0 -1 0
0 1 0 -1 0 0 0 0
-1 -1 -1 0 0 -1 -1 -1
-1 -1 0 1 1 -1 -1 0
0 0 0 0 1 0 0 0
-1 -1 0 0 0 0 -1 0
0 -1 0 0 0 0 0 0
-1 -1 0 0 0 -1 -1 -1
1
Generator of the Alexander module
(0,2+t-t^2+t^3,1-t-t^2+t^3-t^4,0,0,0,0,0)
the Blanchfield form on it
-t^-3+5t^-2-10t^-1+12-10t+5t^2-t^3
75
First homology
of the double branched cover of 12n_0767
Z/75
2 2
12n_0768
1

detected by
an unknotting move
-1+3t-5t^2+7t^3-5t^4+3t^5-t^6
Seifert matrix of 12n_0768
-1 -1 0 0 0 -1
0 1 0 -1 0 3
-1 -1 -1 0 0 -1
0 -1 0 1 1 -4
0 0 0 0 1 0
0 2 0 -3 -3 13
1
Generator of the Alexander module
(14t-13t^2-25t^3+12t^4-2t^5+t^6,t+2t^2-t^3,-7t-8t^2+24t^3+19t^4-12t^5+2t^6-t^7,1-14t+13t^2+25t^3-12t^4+2t^5-t^6,1+3t+2t^3-t^4,-3+3t+3t^2-2t^3)
the Blanchfield form on it
x
25
First homology
of the double branched cover of 12n_0768
Z/25
0 0
12n_0769
2

detected by
the Lickorish test
2-8t+20t^2-27t^3+20t^4-8t^5+2t^6
Seifert matrix of 12n_0769
1 1 1 0 1 1
0 0 0 0 -1 -1
0 0 1 0 0 0
0 -1 0 -1 -1 -1
1 0 1 0 2 0
0 -1 0 0 0 0
1
Generator of the Alexander module
(2t,0,0,-2t,1+2t-2t^2,0)
the Blanchfield form on it
9t^-3-36t^-2+90t^-1-122+90t-36t^2+9t^3
87
First homology
of the double branched cover of 12n_0769
Z/87
2 2
12n_0770
2

detected by
the signature
-3+16t-35t^2+45t^3-35t^4+16t^5-3t^6
Seifert matrix of 12n_0770
-6 -9 3 -6 0 -3
-5 -5 2 -4 -1 -2
0 1 -1 0 0 0
-4 -6 2 -5 0 -1
-1 -3 1 -2 0 -1
-5 -5 1 -4 -1 -4
1
Generator of the Alexander module
(0,-1+t-5t^2+4t^3-3t^4,1-t+5t^2-4t^3+3t^4,1-t+5t^2-4t^3+3t^4,0,-2+3t-9t^2+9t^3-7t^4+3t^5)
the Blanchfield form on it
896t^-3-4780t^-2+10459t^-1-13448+10459t-4780t^2+896t^3
153
First homology
of the double branched cover of 12n_0770
Z/153
-4 4
12n_0771
1

detected by
an unknotting move
2-10t+24t^2-31t^3+24t^4-10t^5+2t^6
Seifert matrix of 12n_0771
4 1 2 0 1 0
2 0 1 0 1 0
1 0 1 0 0 0
1 1 0 2 1 1
2 0 1 0 0 0
0 1 0 0 1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-3-6t^-2+15t^-1-20+15t-6t^2+t^3
103
First homology
of the double branched cover of 12n_0771
Z/103
2 2
12n_0772
1

detected by
an unknotting move
3-13t+29t^2-37t^3+29t^4-13t^5+3t^6
Seifert matrix of 12n_0772
1 -1 0 0 0 -1
0 -1 0 0 0 0
0 0 -1 0 0 0
0 1 -1 -2 -1 1
1 0 0 -1 1 0
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-3+5t^-2-12t^-1+16-12t+5t^2-t^3
127
First homology
of the double branched cover of 12n_0772
Z/127
-2 2
12n_0773
2

detected by
the signature
-3+11t-19t^2+23t^3-19t^4+11t^5-3t^6
Seifert matrix of 12n_0773
1 1 0 0 1 0
-1 2 -1 0 1 0
1 1 1 0 1 0
1 1 1 1 1 1
0 0 0 0 1 0
-1 1 -1 0 1 -1
1 or 2
89
First homology
of the double branched cover of 12n_0773
Z/89
4 4
12n_0774
1

detected by
an unknotting move
-4+13t-17t^2+13t^3-4t^4
Seifert matrix of 12n_0774
0 1 0 0
0 3 1 4
0 0 1 0
-1 3 2 5
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
t^-1-2+t
51
First homology
of the double branched cover of 12n_0774
Z/51
2 2
12n_0775
1

detected by
an unknotting move
1-6t+17t^2-27t^3+29t^4-27t^5+17t^6-6t^7+t^8
Seifert matrix of 12n_0775
-1 -1 0 -1 0 0 0 -1
0 1 0 0 0 0 0 0
-1 0 1 0 0 0 -1 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
-1 0 1 0 0 1 -1 -1
-1 0 0 -1 0 0 -1 -1
0 -1 0 -1 -1 0 0 -1
1 or 2
131
First homology
of the double branched cover of 12n_0775
Z/131
-2 2
12n_0776
1

detected by
an unknotting move
-1+6t-15t^2+21t^3-21t^4+21t^5-15t^6+6t^7-t^8
Seifert matrix of 12n_0776
-1 -1 0 -1 0 0 0 -1
0 -1 0 0 0 0 0 0
-1 0 1 0 0 0 -1 0
0 -1 0 -1 -1 0 0 0
0 0 0 0 1 0 0 0
-1 0 1 0 0 1 -1 -1
-1 0 0 -1 0 0 -1 -1
0 -1 0 -1 -1 0 0 -1
1
Generator of the Alexander module
(0,0,-1-2t-2t^2+2t^3+2t^4,0,0,2t-6t^2+4t^4,-1-2t-2t^2+2t^3+2t^4,0)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
107
First homology
of the double branched cover of 12n_0776
Z/107
-2 2
12n_0777
1

detected by
an unknotting move
-2+8t-14t^2+17t^3-14t^4+8t^5-2t^6
Seifert matrix of 12n_0777
-1 1 0 0 -1 0
0 2 0 1 0 1
-1 1 -1 0 -1 0
0 2 0 1 -1 1
0 1 0 0 0 0
0 1 0 0 0 2
1
Generator of the Alexander module
(0,0,1-t+t^2,0,0,-3+3t-2t^2)
the Blanchfield form on it
-1
65
First homology
of the double branched cover of 12n_0777
Z/65
0 2
12n_0778
2

detected by
the signature
-3+11t-18t^2+21t^3-18t^4+11t^5-3t^6
Seifert matrix of 12n_0778
-1 0 -1 -1 0 -1
0 1 0 -1 0 0
0 -1 -1 -1 0 -1
0 -1 0 -2 0 0
0 -1 0 -1 -1 0
0 -1 0 -1 0 -1
1
Generator of the Alexander module
(-7-216t+340t^2+273t^3-548t^4+260t^5,-11-124t+555t^2-352t^3-718t^4+954t^5-380t^6,25+173t-317t^2-260t^3+525t^4-250t^5,6-24t+366t^2-508t^3-403t^4+804t^5-380t^6,-8+32t-90t^2-142t^3+305t^4+216t^5-374t^6+462t^7-374t^8+180t^9,-9+70t-84t^2-65t^3+128t^4-60t^5)
the Blanchfield form on it
x
85
First homology
of the double branched cover of 12n_0778
Z/85
-4 4
12n_0779
2

detected by
the Lickorish test
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 12n_0779
-1 0 0 1 -1 0
0 1 0 0 0 0
0 -1 -1 0 0 0
0 1 0 1 1 0
0 0 1 0 -2 1
0 -1 -1 0 0 -1
2
111
First homology
of the double branched cover of 12n_0779
Z/111
-2 2
12n_0780
1

detected by
an unknotting move
-1+8t-19t^2+25t^3-19t^4+8t^5-t^6
Seifert matrix of 12n_0780
-2 0 -1 -1 -1 0
0 -1 0 0 0 0
-2 0 -1 -1 -2 0
-1 0 -1 0 -1 0
-1 1 -1 -1 -2 0
-1 -1 -1 -1 0 1
1
Generator of the Alexander module
(0,-2+t,0,-2+t,0,3-3t+t^2)
the Blanchfield form on it
-t^-1+2-t
81
First homology
of the double branched cover of 12n_0780
Z/81
0 2
12n_0781
2

detected by
A(F_5)
1-4t+10t^2-19t^3+25t^4-19t^5+10t^6-4t^7+t^8
Seifert matrix of 12n_0781
1 0 1 0 1 -1 0 -1
0 -1 0 0 0 0 0 0
0 0 1 0 1 0 0 -1
1 0 1 1 1 -1 0 -1
0 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
0 -1 0 0 0 -1 -1 -1
0 0 0 0 0 0 0 -1
2
93
First homology
of the double branched cover of 12n_0781
Z/93
0 0
12n_0782
1

detected by
an unknotting move
-2+8t-18t^2+25t^3-18t^4+8t^5-2t^6
Seifert matrix of 12n_0782
1 0 0 0 0 0
-1 0 -1 0 -1 0
1 0 1 0 0 0
1 -1 1 -1 -1 0
0 -2 0 0 -1 0
1 0 1 -1 0 -1
1 or 2
81
First homology
of the double branched cover of 12n_0782
Z/81
0 0
12n_0783
1

detected by
an unknotting move
2-11t+30t^2-41t^3+30t^4-11t^5+2t^6
Seifert matrix of 12n_0783
1 0 1 1 1 0
0 -1 1 1 1 -1
0 0 -2 -1 -1 1
0 0 -1 -2 -1 1
0 0 -2 -1 -2 1
0 0 1 1 0 0
1
Generator of the Alexander module
(24+15t+25t^2-28t^3-18t^4-25t^5+20t^6+4t^7,49+42t+30t^2-42t^3-54t^4-30t^5+56t^6-7t^7,142+117t+125t^2-170t^3-169t^4-127t^5+139t^6+83t^7-39t^8-3t^9,43t+116t^2+58t^3-29t^4-191t^5-61t^6+2t^7+196t^8-76t^9-6t^10,90+81t+74t^2-114t^3-128t^4-76t^5+91t^6+79t^7-39t^8-3t^9,21+18t+13t^2-18t^3-23t^4-13t^5+24t^6-3
the Blanchfield form on it
x
127
First homology
of the double branched cover of 12n_0783
Z/127
-2 2
12n_0784
1

detected by
an unknotting move
1-6t+15t^2-25t^3+29t^4-25t^5+15t^6-6t^7+t^8
Seifert matrix of 12n_0784
-1 0 -1 0 0 0 -1 0
-1 -1 -1 0 0 0 -1 0
0 0 -1 1 -1 1 -1 0
0 0 0 1 0 1 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 1 -1 0 -1 0
-1 0 -1 0 0 0 0 1
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
t^-3-6t^-2+14t^-1-19+14t-6t^2+t^3
123
First homology
of the double branched cover of 12n_0784
Z/123
-2 2
12n_0785
1

detected by
an unknotting move
-6+23t-33t^2+23t^3-6t^4
Seifert matrix of 12n_0785
1 -1 -1 0
0 -1 -2 0
0 -2 -1 0
1 0 -1 2
1
Generator of the Alexander module
(0,0,8t^2-4t^3,1+4t-18t^2+24t^3-8t^4)
the Blanchfield form on it
-3t^-1+4-3t
91
First homology
of the double branched cover of 12n_0785
Z/91
2 2
12n_0786
1

detected by
an unknotting move
2-12t+33t^2-45t^3+33t^4-12t^5+2t^6
Seifert matrix of 12n_0786
-1 0 0 1 0 0
0 -1 0 -1 0 0
1 -1 1 -1 1 0
0 0 0 -2 0 0
1 -1 0 -1 1 0
1 0 1 -1 1 -1
1
Generator of the Alexander module
(0,0,0,0,2-t,-1+t)
the Blanchfield form on it
3t^-3-18t^-2+51t^-1-70+51t-18t^2+3t^3
139
First homology
of the double branched cover of 12n_0786
Z/139
-2 2
12n_0787
1

detected by
an unknotting move
-1+4t-9t^2+14t^3-15t^4+14t^5-9t^6+4t^7-t^8
Seifert matrix of 12n_0787
1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
1 -1 1 0 0 0 0 0
1 0 1 -1 1 1 1 1
0 -1 0 0 -1 -1 0 -1
0 -1 0 0 0 -1 0 0
1 -1 1 0 0 0 1 0
0 -1 0 0 0 -1 0 -1
1
Generator of the Alexander module
(0,0,1+t,-1,0,-t-t^2,0,0)
the Blanchfield form on it
1
71
First homology
of the double branched cover of 12n_0787
Z/71
-2 2
12n_0788
1

detected by
an unknotting move
-2+10t-25t^2+35t^3-25t^4+10t^5-2t^6
Seifert matrix of 12n_0788
1 0 0 0 0 0
0 -1 0 0 0 0
1 -1 1 0 0 0
1 0 1 -1 1 -1
1 -1 1 0 1 0
0 1 0 0 0 -2
1
Generator of the Alexander module
(0,7-7t+2t^2,-5+2t,14t-14t^2+4t^3,7t-7t^2+2t^3,-7+7t-2t^2)
the Blanchfield form on it
121t^-3-607t^-2+1518t^-1-2128+1518t-607t^2+121t^3
109
First homology
of the double branched cover of 12n_0788
Z/109
0 0
12n_0789
1

detected by
an unknotting move
-2+9t-20t^2+27t^3-20t^4+9t^5-2t^6
Seifert matrix of 12n_0789
-6 0 -4 -2 -4 -3
-2 1 -1 -1 -1 0
-4 0 -2 -1 -2 -2
-2 0 -1 0 -1 -1
-6 0 -4 -2 -5 -2
0 0 0 0 0 -1
1
Generator of the Alexander module
(3+21t-30t^2+32t^3-64t^4+69t^5-64t^6+128t^7-142t^8+80t^9-16t^10,-5-34t+60t^2-130t^3+244t^4-315t^5+371t^6-557t^7+685t^8-695t^9+646t^10-540t^11+318t^12-112t^13+16t^14,-2t^2-13t^3+37t^4-45t^5+55t^6-82t^7+105t^8-128t^9+146t^10-126t^11+64t^12-16t^13,2t^2+13t^3-37t^4+45t^5-55t^6+82t^7-105t^8+128t^9-146t^1
the Blanchfield form on it
x
89
First homology
of the double branched cover of 12n_0789
Z/89
0 0
12n_0790
1

detected by
an unknotting move
1-5t+15t^2-28t^3+35t^4-28t^5+15t^6-5t^7+t^8
Seifert matrix of 12n_0790
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 1 -1 0 0 0
0 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 -1 0 -1 -1 1 1
-1 0 -1 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,-1-t-t^3,-1-t-2t^3,-1-t,0,-2t-t^3,1-t-t^2)
the Blanchfield form on it
t^-2-3t^-1+4-3t+t^2
133
First homology
of the double branched cover of 12n_0790
Z/133
0 0
12n_0791
2

detected by
the signature
1-5t+13t^2-18t^3+19t^4-18t^5+13t^6-5t^7+t^8
Seifert matrix of 12n_0791
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 -1 -1 0 0 0
0 0 0 0 -1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 -1 0 -1 -1 1 1
-1 0 -1 0 -1 0 0 1
1
Generator of the Alexander module
(0,0,t-t^2,1,0,0,2,0)
the Blanchfield form on it
-t^-3+3t^-2-4t^-1+4-4t+3t^2-t^3
93
First homology
of the double branched cover of 12n_0791
Z/93
-4 4
12n_0792
1

detected by
an unknotting move
-1+4t-10t^2+16t^3-17t^4+16t^5-10t^6+4t^7-t^8
Seifert matrix of 12n_0792
1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
1 -1 1 0 0 0 0 0
1 -1 1 1 0 0 1 0
1 0 1 1 -1 1 1 1
0 -1 0 0 0 -1 0 0
1 -1 1 0 0 0 1 0
1 -1 1 1 0 0 1 1
1
Generator of the Alexander module
(0,2t,1+2t^2-2t^3+2t^4+2t^6,2t-2t^3-2t^5,-3t+3t^2+2t^4-t^5,2t+t^2+t^5,2t,2t+t^3)
the Blanchfield form on it
x
79
First homology
of the double branched cover of 12n_0792
Z/79
2 2
12n_0793
2

detected by
the signature
-3+9t-12t^2+13t^3-12t^4+9t^5-3t^6
Seifert matrix of 12n_0793
-1 -1 -1 -1 1 0
0 -1 0 -1 0 -1
0 -1 -1 -1 0 -1
0 0 0 -1 0 -1
0 0 0 0 1 2
0 0 0 0 2 1
1
Generator of the Alexander module
(-2+6t-2t^2+6t^3+11t^4+2t^5,2-4t+3t^2,-1+2t-2t^2,t,1-2t-2t^3-9t^4-2t^5,-1+4t-2t^3)
the Blanchfield form on it
-22t^-8+27t^-7+313t^-6-850t^-5+1249t^-4-380t^-3-2333t^-2+5311t^-1-6630+5311t-2333t^2-380t^3+1249t^4-850t^5+313t^6+27t^7-22t^8
61
First homology
of the double branched cover of 12n_0793
Z/61
-4 4
12n_0794
1

detected by
an unknotting move
-2+9t-23t^2+33t^3-23t^4+9t^5-2t^6
Seifert matrix of 12n_0794
1 0 0 0 0 0
0 -1 0 0 0 0
1 -1 1 0 0 0
-1 1 -1 2 0 0
1 0 1 -1 -1 1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(0,-2t+2t^3-2t^4+2t^6,t-5t^2+3t^3+2t^4-4t^5+2t^6+2t^7,1+4t+4t^2-12t^3+11t^4-4t^5-4t^6-2t^7,2t-6t^2+6t^4-6t^5+4t^7,-2t-3t^2+8t^3-6t^4+t^5+4t^6)
the Blanchfield form on it
x
101
First homology
of the double branched cover of 12n_0794
Z/101
0 0
12n_0795
1

detected by
an unknotting move
-6+20t-27t^2+20t^3-6t^4
Seifert matrix of 12n_0795
-1 2 2 1
0 -1 -4 -2
0 -3 -5 -2
0 -2 -3 -2
1
Generator of the Alexander module
(-3+5t-3t^2,-5+3t,0,0)
the Blanchfield form on it
2t^-1-2+2t
79
First homology
of the double branched cover of 12n_0795
Z/79
-2 2
12n_0796
2

detected by
the signature
-2+11t-22t^2+27t^3-22t^4+11t^5-2t^6
Seifert matrix of 12n_0796
-4 -4 0 0 -6 0
-7 -5 -1 0 -9 0
1 0 0 0 0 0
1 0 1 -1 1 0
-9 -8 -1 0 -14 0
1 0 1 -1 1 -1
1 or 2
97
First homology
of the double branched cover of 12n_0796
Z/97
-4 4
12n_0797
1

detected by
an unknotting move
-3+15t-23t^2+15t^3-3t^4
Seifert matrix of 12n_0797
3 0 0 0
2 -5 -2 -5
2 -1 -1 0
1 -5 -1 -7
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
3
59
First homology
of the double branched cover of 12n_0797
Z/59
-2 2
12n_0798
2

detected by
A(F_2)
1-7t+22t^2-31t^3+22t^4-7t^5+t^6
Seifert matrix of 12n_0798
-1 0 0 0 1 0
0 1 0 0 0 0
1 0 1 1 -1 1
0 -1 0 -1 0 0
0 1 0 0 1 0
1 -1 0 0 -1 1
2
91
First homology
of the double branched cover of 12n_0798
Z/91
2 2
12n_0799
1

detected by
an unknotting move
2-13t+32t^2-41t^3+32t^4-13t^5+2t^6
Seifert matrix of 12n_0799
-2 -4 0 -2 0 2
-2 -1 0 -1 -1 1
1 2 -1 2 0 -1
-2 -4 0 -1 0 2
0 -2 0 -1 0 1
0 1 0 0 0 -1
1
Generator of the Alexander module
(2t+16t^2-72t^3+64t^4-46t^5+12t^6,-12-24t+44t^2+126t^3-73t^4-92t^5+116t^6-92t^7+24t^8,1+8t-36t^2+32t^3-23t^4+6t^5,-6-13t+46t^2+18t^3-32t^4+23t^5-6t^6,-3-8t+11t^2+63t^3-64t^4+46t^5-12t^6,-6-13t+46t^2+18t^3-32t^4+23t^5-6t^6)
the Blanchfield form on it
x
135
First homology
of the double branched cover of 12n_0799
Z/135
-2 2
12n_0800
1

detected by
an unknotting move
-1+5t-13t^2+24t^3-29t^4+24t^5-13t^6+5t^7-t^8
Seifert matrix of 12n_0800
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
-1 -1 -1 0 -1 -1 -1 0
0 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0
0 -1 0 0 0 -1 0 0
-1 -1 0 -1 -1 -1 -1 0
1 0 0 1 1 0 0 1
1
Generator of the Alexander module
(0,0,0,-t,0,0,1+t,-1-t)
the Blanchfield form on it
t^-2-3t^-1+3-3t+t^2
115
First homology
of the double branched cover of 12n_0800
Z/115
2 2
12n_0801
1

detected by
an unknotting move
-1+5t-7t^2+5t^3-t^4
Seifert matrix of 12n_0801
1 2 0 2
1 1 0 1
-1 -2 -2 -3
1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-1-1+t
19
First homology
of the double branched cover of 12n_0801
Z/19
-2 2
12n_0802
1

detected by
an unknotting move
1-5t+14t^2-25t^3+31t^4-25t^5+14t^6-5t^7+t^8
Seifert matrix of 12n_0802
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 1 0 0 0 -1
-1 -1 -1 0 1 -1 0 -1
0 -1 0 0 0 -1 0 0
-1 -1 -1 1 0 -1 1 -1
0 0 0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,0,0,0,0,1,0)
the Blanchfield form on it
-t^-1+1-t
121
First homology
of the double branched cover of 12n_0802
Z/121
0 0
12n_0803
2

detected by
the signature
1-5t+14t^2-21t^3+23t^4-21t^5+14t^6-5t^7+t^8
Seifert matrix of 12n_0803
-1 -1 0 0 0 -1 0 0
0 -1 0 0 0 0 0 0
-1 -1 -1 0 0 -1 0 0
-1 0 -1 1 0 0 0 -1
-1 -1 -1 0 -1 -1 0 -1
0 -1 0 0 0 -1 0 0
-1 -1 -1 1 0 -1 1 -1
0 0 0 0 0 0 0 -1
1 or 2
105
First homology
of the double branched cover of 12n_0803
Z/105
-4 4
12n_0804
1

detected by
an unknotting move
1-4t+11t^2-20t^3+23t^4-20t^5+11t^6-4t^7+t^8
Seifert matrix of 12n_0804
-1 0 0 0 0 0 0 0
1 1 0 1 1 1 1 1
-1 0 -1 0 -1 -1 0 -1
0 0 0 1 1 1 0 1
0 0 0 0 -1 -1 0 -1
0 0 0 0 0 -1 0 0
1 0 0 1 1 1 1 1
0 0 0 0 0 -1 0 -1
1
Generator of the Alexander module
(192-396t-458t^2+570t^3-96t^4+668t^5+960t^6,-141+377t+468t^2-1091t^3-541t^4-262t^5-1043t^6+698t^7+960t^8,7-86t-54t^2+475t^3+380t^4+49t^5+307t^6-349t^7-480t^8,76-128t-198t^2+128t^3-104t^4+144t^5+288t^6,62-106t-160t^2+111t^3-80t^4+125t^5+240t^6,12-6t-39t^2-27t^3-48t^4-36t^5,-3+36t+129t^2-39t^3-973t^4-
the Blanchfield form on it
x
95
First homology
of the double branched cover of 12n_0804
Z/95
-2 2
12n_0805
2

detected by
the Lickorish test
-2+8t-19t^2+27t^3-19t^4+8t^5-2t^6
Seifert matrix of 12n_0805
-1 0 0 0 0 0
1 1 0 1 1 -1
-1 0 -1 0 0 1
0 0 0 1 0 -1
1 0 0 1 1 -1
0 0 0 0 0 -2
1
Generator of the Alexander module
(0,0,1,t-t^2,-t,0)
the Blanchfield form on it
2t^-2-6t^-1+7-6t+2t^2
85
First homology
of the double branched cover of 12n_0805
Z/85
0 0
12n_0806
3

detected by
the signature
4-10t+12t^2-11t^3+12t^4-10t^5+4t^6
Seifert matrix of 12n_0806
-1 1 -1 1 -1 1
0 -2 0 -1 0 -1
0 0 -1 1 -1 1
0 -1 0 -2 0 -1
0 0 0 0 -1 1
0 -1 0 -1 0 -2
2
63
First homology
of the double branched cover of 12n_0806
Z/21+Z/3
-6 6
12n_0807
2

detected by
the signature
-2+8t-12t^2+13t^3-12t^4+8t^5-2t^6
Seifert matrix of 12n_0807
-1 1 -1 1 -1 1
0 -2 0 -1 0 -1
0 0 -1 1 -1 1
0 -1 0 0 0 -1
0 0 0 0 -1 1
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(1,0,0,0,0,2t)
the Blanchfield form on it
-t^-2+3t^-1-3+3t-t^2
57
First homology
of the double branched cover of 12n_0807
Z/57
-4 4
12n_0808
1

detected by
an unknotting move
-2+8t-11t^2+8t^3-2t^4
Seifert matrix of 12n_0808
-1 -1 -1 -1
-1 -1 -2 -3
-1 -1 -3 -3
-2 -3 -4 -4
1
Generator of the Alexander module
(0,0,0,1)
the Blanchfield form on it
-t^-1+2-t
31
First homology
of the double branched cover of 12n_0808
Z/31
-2 2
12n_0809
1

detected by
an unknotting move
-2+4t-3t^2+4t^3-2t^4
Seifert matrix of 12n_0809
-1 -1 1 -1
-1 -1 0 -1
-1 -1 -1 1
0 -1 0 -2
1
Generator of the Alexander module
(1,0,1-2t,0)
the Blanchfield form on it
-t^-1+2-t
15
First homology
of the double branched cover of 12n_0809
Z/15
-2 2
12n_0810
2

detected by
the Lickorish test
2-8t+12t^2-11t^3+12t^4-8t^5+2t^6
Seifert matrix of 12n_0810
-1 1 -1 1 -1 1
0 0 0 -1 0 -1
0 0 -1 1 -1 1
0 -1 0 0 0 -1
0 0 0 0 -1 1
0 -1 0 -1 0 0
1
Generator of the Alexander module
(0,0,-t^2,0,1+t^2-t^3,0)
the Blanchfield form on it
-3t^-5+18t^-4-52t^-3+99t^-2-140t^-1+154-140t+99t^2-52t^3+18t^4-3t^5
55
First homology
of the double branched cover of 12n_0810
Z/55
-2 2
12n_0811
1

detected by
an unknotting move
2-7t+14t^2-17t^3+14t^4-7t^5+2t^6
Seifert matrix of 12n_0811
-1 1 -1 1 0 1
0 -2 0 -1 0 -1
0 0 -1 0 -1 1
0 -1 0 0 1 -1
0 0 0 0 1 0
0 -1 0 -1 0 -2
1
Generator of the Alexander module
(t,0,-2,1,0,0)
the Blanchfield form on it
2t^-2-5t^-1+8-5t+2t^2
63
First homology
of the double branched cover of 12n_0811
Z/63
-2 2
12n_0812
1

detected by
an unknotting move
1-2t+3t^2-2t^3+t^4
Seifert matrix of 12n_0812
-3 -3 -4 -3
-4 -4 -6 -5
-4 -4 -5 -4
-4 -5 -5 -4
1
Generator of the Alexander module
(0,t,1,-t)
the Blanchfield form on it
-3t^-1+4-3t
9
First homology
of the double branched cover of 12n_0812
Z/9
0 0
12n_0813
2

detected by
the Nakanishi index
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0813
-1 1 -1 1 0 1
0 0 0 -1 0 -1
0 0 -1 0 -1 1
0 -1 0 0 1 -1
0 0 0 0 1 0
0 -1 0 -1 0 0
2
81
First homology
of the double branched cover of 12n_0813
Z/9+Z/9
0 0
12n_0814
2

detected by
the Lickorish test
-6+24t-35t^2+24t^3-6t^4
Seifert matrix of 12n_0814
0 -1 -1 0
-2 0 1 -1
-2 1 0 -1
-1 0 -1 -2
1
Generator of the Alexander module
(0,2,2,1)
the Blanchfield form on it
-2t^-1+4-2t
95
First homology
of the double branched cover of 12n_0814
Z/95
-2 2
12n_0815
1

detected by
an unknotting move
-1+2t-t^2+2t^3-t^4
Seifert matrix of 12n_0815
-1 1 -2 1
0 0 0 1
0 0 -1 0
0 1 -1 2
1
Generator of the Alexander module
(1,0,0,1)
the Blanchfield form on it
-t^-1+2-t
7
First homology
of the double branched cover of 12n_0815
Z/7
-2 2
12n_0816
1

detected by
an unknotting move
-2+11t-26t^2+35t^3-26t^4+11t^5-2t^6
Seifert matrix of 12n_0816
-1 1 -1 1 0 1
0 2 0 1 0 1
0 0 -1 0 -1 1
0 1 0 2 1 1
0 0 0 0 1 0
0 1 0 1 0 0
1
Generator of the Alexander module
(2+2t-6t^2+4t^3,0,2t-5t^2+2t^3,0,1-2t,-1+t+2t^2)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
113
First homology
of the double branched cover of 12n_0816
Z/113
0 0
12n_0817
2

detected by
the Nakanishi index
-2+6t-10t^2+13t^3-10t^4+6t^5-2t^6
Seifert matrix of 12n_0817
1 0 0 0 -1 0
0 1 2 0 2 0
0 2 1 0 2 0
0 -1 0 -1 0 -1
0 1 1 0 2 0
0 0 1 0 1 -1
2
49
First homology
of the double branched cover of 12n_0817
Z/7+Z/7
0 0
12n_0818
1

detected by
an unknotting move
1-9t+22t^2-27t^3+22t^4-9t^5+t^6
Seifert matrix of 12n_0818
1 0 0 0 0 0
1 -1 0 0 1 0
-1 0 -1 0 -1 0
0 -1 0 -1 1 -1
-1 0 0 0 1 0
1 -1 0 0 1 -1
1 or 2
91
First homology
of the double branched cover of 12n_0818
Z/91
-2 2
12n_0819
1

detected by
an unknotting move
3-12t+24t^2-29t^3+24t^4-12t^5+3t^6
Seifert matrix of 12n_0819
3 3 4 2 4 3
2 1 2 1 2 2
3 3 3 2 4 3
3 3 3 1 2 3
4 4 4 1 3 4
2 1 2 1 2 1
1 or 2
107
First homology
of the double branched cover of 12n_0819
Z/107
-2 2
12n_0820
3

detected by
the signature
1-6t+12t^2-17t^3+19t^4-17t^5+12t^6-6t^7+t^8
Seifert matrix of 12n_0820
0 0 0 -1 0 0 0 0
-1 1 -1 0 1 0 1 0
-1 0 0 -1 0 0 0 0
-1 0 -1 0 0 0 1 0
-1 0 -1 0 1 0 1 0
-1 1 -1 0 1 1 1 0
0 0 0 0 0 0 1 0
0 0 0 1 0 0 0 1
1 or 2
91
First homology
of the double branched cover of 12n_0820
Z/91
6 6
12n_0821
1

detected by
an unknotting move
-1+3t-5t^2+6t^3-5t^4+6t^5-5t^6+3t^7-t^8
Seifert matrix of 12n_0821
0 0 0 -1 0 0 0 0
-1 0 -1 -1 0 -1 0 0
-1 0 0 -1 0 0 0 0
-1 -1 -1 -2 -1 -1 0 -1
-1 -1 -1 -1 0 -1 0 0
-1 0 -1 -1 0 0 0 0
0 -1 0 -1 -1 -1 -1 0
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,-t,0,1,1,0,-t,0)
the Blanchfield form on it
-t^-2+4t^-1-6+4t-t^2
35
First homology
of the double branched cover of 12n_0821
Z/35
2 2
12n_0822
1

detected by
an unknotting move
1-3t+6t^2-11t^3+13t^4-11t^5+6t^6-3t^7+t^8
Seifert matrix of 12n_0822
-2 -2 -1 -1 -1 -1 -2 -1
-1 -1 -1 -1 -1 -1 -1 -1
-2 -2 -2 -1 -1 -1 -2 -1
0 -1 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 0
-1 -1 -1 -1 -1 0 -1 -1
-1 -2 -1 -1 -1 -1 -1 -1
0 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(-t,0,0,0,0,1,0,0)
the Blanchfield form on it
t^-1-2+t
55
First homology
of the double branched cover of 12n_0822
Z/55
-2 2
12n_0823
2

detected by
the signature
-2+12t-24t^2+29t^3-24t^4+12t^5-2t^6
Seifert matrix of 12n_0823
0 0 0 -1 3 0
0 1 0 0 0 0
-1 0 0 -1 3 0
-1 1 -1 0 0 1
2 -3 2 0 2 -2
0 0 0 0 0 1
1
Generator of the Alexander module
(0,0,t-t^2,1,-2-4t+2t^2,0)
the Blanchfield form on it
-27t^-3+163t^-2-329t^-1+398-329t+163t^2-27t^3
105
First homology
of the double branched cover of 12n_0823
Z/105
4 4
12n_0824
1

detected by
an unknotting move
-2+7t-14t^2+19t^3-14t^4+7t^5-2t^6
Seifert matrix of 12n_0824
0 0 0 -1 3 0
0 -1 0 -1 3 0
-1 0 0 -1 3 0
-1 0 -1 -2 5 0
2 0 2 5 -11 0
0 0 0 -1 2 -1
1
Generator of the Alexander module
(0,-2+t-t^2+t^3,2-2t+2t^2-t^3,0,1,0)
the Blanchfield form on it
t^-1-2+t
65
First homology
of the double branched cover of 12n_0824
Z/65
0 0
12n_0825
1

detected by
an unknotting move
-2+6t-9t^2+11t^3-9t^4+6t^5-2t^6
Seifert matrix of 12n_0825
0 1 1 1 1 1
0 1 0 0 0 0
0 1 0 1 1 1
1 1 1 0 0 1
0 1 0 0 -2 0
0 1 0 0 0 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-t^-1+2-t
45
First homology
of the double branched cover of 12n_0825
Z/45
0 2
12n_0826
1

detected by
an unknotting move
1-9t+24t^2-31t^3+24t^4-9t^5+t^6
Seifert matrix of 12n_0826
-1 0 -1 0 -1 -1
0 1 0 0 0 0
0 -1 -1 0 -1 -1
0 1 0 -2 0 -1
0 0 0 -1 0 -1
0 0 0 -1 -1 -2
1
Generator of the Alexander module
(-1-t+t^2,0,1-3t^2+t^3,-1-t+t^2,0,0)
the Blanchfield form on it
t^-2-7t^-1+9-7t+t^2
99
First homology
of the double branched cover of 12n_0826
Z/99
-2 2
12n_0827
2

detected by
the Lickorish test
-1+5t-14t^2+25t^3-29t^4+25t^5-14t^6+5t^7-t^8
Seifert matrix of 12n_0827
-1 0 0 0 -1 0 0 -1
1 1 0 1 1 1 1 1
-1 0 -1 0 -1 -1 0 -1
0 0 0 1 0 1 0 0
0 0 0 0 -1 0 0 -1
0 0 0 0 0 -1 0 0
1 0 0 1 0 1 1 0
0 0 0 0 0 0 0 -1
1
Generator of the Alexander module
(0,-t,t,1,0,0,1,0)
the Blanchfield form on it
t^-3-5t^-2+10t^-1-12+10t-5t^2+t^3
119
First homology
of the double branched cover of 12n_0827
Z/119
-2 2
12n_0828
1

detected by
an unknotting move
-3+12t-24t^2+31t^3-24t^4+12t^5-3t^6
Seifert matrix of 12n_0828
1 1 1 0 0 0
0 1 2 0 0 0
0 2 1 0 0 0
0 -1 0 -1 0 -1
1 1 1 0 1 0
-1 -1 0 0 0 -1
1
Generator of the Alexander module
(0,1-t,0,-t+t^2,t,1-t)
the Blanchfield form on it
-3t^-1+6-3t
109
First homology
of the double branched cover of 12n_0828
Z/109
0 0
12n_0829
1

detected by
an unknotting move
1-5t+11t^2-18t^3+21t^4-18t^5+11t^6-5t^7+t^8
Seifert matrix of 12n_0829
0 0 0 0 -1 0 0 0
0 1 0 0 0 0 0 0
-1 0 0 0 -1 0 0 0
-1 0 -1 0 0 0 1 0
-1 1 -1 1 0 0 1 1
-1 0 -1 1 0 1 1 1
0 0 0 0 0 0 1 0
-1 0 -1 1 0 0 1 0
1
Generator of the Alexander module
(0,0,0,0,1+t+t^2,1+t^2,0,0)
the Blanchfield form on it
-t^-3+4t^-2-5t^-1+5-5t+4t^2-t^3
91
First homology
of the double branched cover of 12n_0829
Z/91
2 2
12n_0830
2

detected by
the signature
2-4t+5t^2-4t^3+2t^4
Seifert matrix of 12n_0830
-2 -3 0 -1
-3 -6 -1 -2
-1 -3 -2 -1
0 -1 0 -1
1
Generator of the Alexander module
(0,1,2,0)
the Blanchfield form on it
2t^-1-2+2t
17
First homology
of the double branched cover of 12n_0830
Z/17
-4 4
12n_0831
1

detected by
an unknotting move
-1+5t-12t^2+20t^3-23t^4+20t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0831
-1 0 0 0 -1 0 0 0
0 -1 0 0 -1 0 0 0
-1 0 -1 0 -1 0 0 0
-1 0 -1 0 0 0 1 0
-1 0 -1 1 -1 0 1 1
-1 0 -1 1 0 1 1 1
0 0 0 0 0 0 1 0
-1 0 -1 1 0 0 1 0
1
Generator of the Alexander module
(0,1,0,0,0,0,0,0)
the Blanchfield form on it
1
99
First homology
of the double branched cover of 12n_0831
Z/99
-2 2
12n_0832
2

detected by
the signature
-3+13t-23t^2+27t^3-23t^4+13t^5-3t^6
Seifert matrix of 12n_0832
2 1 0 0 0 1
3 3 0 0 0 3
1 0 -1 0 0 0
-1 -2 -1 1 0 -2
1 1 0 0 1 1
3 2 0 0 0 3
1 or 2
105
First homology
of the double branched cover of 12n_0832
Z/105
4 4
12n_0833
1

detected by
an unknotting move
3-11t+22t^2-27t^3+22t^4-11t^5+3t^6
Seifert matrix of 12n_0833
-2 -3 -2 0 0 -2
-1 -3 -1 0 0 -1
-1 -1 0 0 0 0
1 2 1 1 1 0
0 0 0 0 1 0
-2 -2 0 0 -1 1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
-3t^-2+9t^-1-13+9t-3t^2
99
First homology
of the double branched cover of 12n_0833
Z/99
2 2
12n_0834
2

detected by
the signature
-2+12t-26t^2+33t^3-26t^4+12t^5-2t^6
Seifert matrix of 12n_0834
1 0 0 0 0 0
0 -1 0 -1 0 -1
1 0 -1 -1 0 -1
0 0 -1 -2 0 -1
1 0 0 -1 -1 -1
0 0 0 -1 0 -2
1
Generator of the Alexander module
(0,-t,0,1,0,1)
the Blanchfield form on it
-2t^-2+11t^-1-17+11t-2t^2
113
First homology
of the double branched cover of 12n_0834
Z/113
-4 4
12n_0835
1

detected by
an unknotting move
1-4t^2+7t^3-4t^4+t^6
Seifert matrix of 12n_0835
-1 0 -1 0 -1 0
0 -1 0 -1 0 -1
0 0 0 0 -1 -1
0 0 0 0 0 -1
0 0 -1 -1 0 -1
0 0 0 -1 0 0
1
Generator of the Alexander module
(t,-t,0,1,t,0)
the Blanchfield form on it
t^-2+t^-1-3+t+t^2
13
First homology
of the double branched cover of 12n_0835
Z/13
0 2
12n_0836
2

detected by
the signature
-2+12t-27t^2+35t^3-27t^4+12t^5-2t^6
Seifert matrix of 12n_0836
-1 0 -1 0 -1 0
0 -1 0 -1 0 -1
0 0 -2 -1 -1 -1
0 0 -1 -2 0 -1
0 0 -1 -1 0 -1
0 0 0 -1 0 -2
1
Generator of the Alexander module
(0,1,0,0,0,0)
the Blanchfield form on it
-2t^-2+8t^-1-11+8t-2t^2
117
First homology
of the double branched cover of 12n_0836
Z/117
-4 4
12n_0837
2

detected by
the Nakanishi index
1-7t+21t^2-35t^3+41t^4-35t^5+21t^6-7t^7+t^8
Seifert matrix of 12n_0837
-1 -1 0 0 -1 0 0 0
0 -1 0 0 0 -1 -1 0
-1 0 1 0 0 0 0 0
0 0 0 1 0 1 0 0
0 -1 0 0 -1 0 -1 0
0 0 0 0 0 1 0 0
0 0 0 -1 0 -1 -1 0
-1 0 1 0 -1 0 0 1
2
169
First homology
of the double branched cover of 12n_0837
Z/13+Z/13
0 2
12n_0838
2

detected by
the Nakanishi index
1-6t+11t^2-6t^3+t^4
Seifert matrix of 12n_0838
1 0 1 -1
1 0 1 0
0 1 -2 0
-2 0 -1 0
2
25
First homology
of the double branched cover of 12n_0838
Z/5+Z/5
0 0
12n_0839
2

detected by
the Nakanishi index
1-7t+18t^2-23t^3+23t^4-23t^5+18t^6-7t^7+t^8
Seifert matrix of 12n_0839
-1 -1 0 0 -1 0 0 0
0 1 0 0 0 -1 0 0
-1 0 1 0 0 0 0 0
0 0 0 1 0 1 0 0
0 -1 0 0 -1 0 -1 0
0 0 0 0 0 1 0 0
0 1 0 -1 0 -1 1 0
-1 0 1 0 -1 0 0 1
2
121
First homology
of the double branched cover of 12n_0839
Z/11+Z/11
4 4
12n_0840
2

detected by
A(F_2)
-1+6t-16t^2+24t^3-25t^4+24t^5-16t^6+6t^7-t^8
Seifert matrix of 12n_0840
-1 -1 0 0 0 -1 0 0
0 1 0 0 0 0 -1 0
-1 0 1 -1 0 0 0 0
-1 0 0 -1 0 -1 0 0
0 0 0 0 1 0 1 0
0 -1 0 0 0 -1 0 -1
0 0 0 0 0 0 1 0
0 1 0 0 -1 0 -1 1
2
119
First homology
of the double branched cover of 12n_0840
Z/119
2 2
12n_0841
1

detected by
an unknotting move
-2+9t-18t^2+23t^3-18t^4+9t^5-2t^6
Seifert matrix of 12n_0841
-1 0 0 1 0 0
-1 0 -1 1 1 0
-1 -1 0 0 0 -1
0 1 0 2 2 1
0 1 0 1 2 1
-1 1 -1 1 1 0
1
Generator of the Alexander module
(0,0,0,2,1,1+t-t^2)
the Blanchfield form on it
2t^-2-6t^-1+7-6t+2t^2
81
First homology
of the double branched cover of 12n_0841
Z/81
0 0
12n_0842
1

detected by
an unknotting move
1-7t+21t^2-38t^3+47t^4-38t^5+21t^6-7t^7+t^8
Seifert matrix of 12n_0842
1 0 1 -1 0 0 0 1
-1 -1 -1 0 0 -1 0 -1
0 0 1 -1 -1 0 -1 1
0 0 0 -1 0 0 0 0
0 0 0 -1 -1 0 0 0
-1 0 -1 0 0 -1 0 0
0 0 0 0 0 0 1 0
0 0 0 -1 -1 0 -1 1
1
Generator of the Alexander module
(0,-2-37t+105t^2-113t^3+104t^4-46t^5+12t^6-2t^7,0,1-t+19t^2-15t^3+10t^5-6t^6+t^7,-1+3t-t^2,-1-5t+3t^2-7t^3+16t^4-14t^5+6t^6-t^7,0,6t^2-22t^3+22t^4-16t^5+4t^6)
the Blanchfield form on it
x
181
First homology
of the double branched cover of 12n_0842
Z/181
0 0
12n_0843
2

detected by
the Nakanishi index
3-15t+34t^2-43t^3+34t^4-15t^5+3t^6
Seifert matrix of 12n_0843
-1 -1 0 0 0 0
0 1 0 0 1 0
-1 -1 -1 0 -1 0
1 0 0 -2 0 -1
0 0 0 0 1 0
1 0 1 -1 0 -2
2
147
First homology
of the double branched cover of 12n_0843
Z/21+Z/7
-2 2
12n_0844
2

detected by
the Nakanishi index
3-12t+16t^2-13t^3+16t^4-12t^5+3t^6
Seifert matrix of 12n_0844
1 -1 1 0 0 0
0 1 0 0 1 0
0 -1 1 0 -1 0
1 0 0 -2 0 -1
0 0 0 0 1 0
1 0 1 -1 0 -2
2
75
First homology
of the double branched cover of 12n_0844
Z/15+Z/5
2 2
12n_0845
2

detected by
the Lickorish test
3-12t+22t^2-25t^3+22t^4-12t^5+3t^6
Seifert matrix of 12n_0845
-9 -3 -3 -6 -6 -6
0 -1 0 0 0 0
-6 -2 -3 -4 -4 -3
-7 -2 -2 -4 -4 -4
-8 -2 -3 -5 -5 -4
-4 -1 -1 -3 -2 -2
1 or 2
99
First homology
of the double branched cover of 12n_0845
Z/99
-2 2
12n_0846
2

detected by
the Nakanishi index
5-20t+31t^2-20t^3+5t^4
Seifert matrix of 12n_0846
-25 -25 -15 -10
-21 -20 -12 -8
-14 -14 -8 -5
-11 -11 -6 -4
2
81
First homology
of the double branched cover of 12n_0846
Z/9+Z/9
0 0
12n_0847
2

detected by
the Nakanishi index
1-7t+18t^2-23t^3+18t^4-7t^5+t^6
Seifert matrix of 12n_0847
-1 0 0 0 0 0
-1 -1 0 0 0 0
-1 -1 1 -1 0 1
-1 -1 0 -1 0 0
0 -1 0 0 1 0
0 0 0 -1 -1 -1
2
75
First homology
of the double branched cover of 12n_0847
Z/15+Z/5
-2 2
12n_0848
2

detected by
the signature
-1+5t-12t^2+16t^3-17t^4+16t^5-12t^6+5t^7-t^8
Seifert matrix of 12n_0848
1 0 0 1 0 0 0 0
-1 -1 -1 -1 -1 0 -1 0
-1 0 -1 -1 -1 0 0 0
0 0 0 1 0 0 0 0
1 0 0 1 -1 0 0 -1
0 -1 -1 -1 0 -1 -1 0
-1 0 -1 -1 -1 0 -1 0
1 0 0 1 0 0 0 -1
2
85
First homology
of the double branched cover of 12n_0848
Z/85
-4 4
12n_0849
2

detected by
the signature
-3+17t-37t^2+47t^3-37t^4+17t^5-3t^6
Seifert matrix of 12n_0849
-2 0 0 1 0 0
-1 -2 -1 0 -1 -2
0 0 -1 0 0 0
1 -1 -1 -2 -1 -1
-1 -1 0 0 0 -1
-1 -1 -1 0 -1 -2
1
Generator of the Alexander module
(0,0,-5+24t-46t^2+54t^3-30t^4+6t^5,6-13t+24t^2-21t^3+6t^4,-7+32t-76t^2+103t^3-84t^4+36t^5-6t^6,7t-32t^2+76t^3-103t^4+84t^5-36t^6+6t^7)
the Blanchfield form on it
-214564t^-4+1471065t^-3-4310496t^-2+7734980t^-1-9304514+7734980t-4310496t^2+1471065t^3-214564t^4
161
First homology
of the double branched cover of 12n_0849
Z/161
-4 4
12n_0850
3

detected by
the signature
1-2t^2+4t^3-5t^4+4t^5-2t^6+t^8
Seifert matrix of 12n_0850
-1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0
-1 0 -1 0 0 -1 0 0
0 0 0 -1 -1 0 -1 -1
0 0 0 0 -1 0 0 -1
0 -1 0 0 0 -1 0 0
0 0 0 0 -1 0 -1 -1
1 -1 0 0 0 0 0 -1
1 or 2
15
First homology
of the double branched cover of 12n_0850
Z/15
-6 6
12n_0851
2

detected by
the signature
2-t-3t^2+5t^3-3t^4-t^5+2t^6
Seifert matrix of 12n_0851
-1 0 0 0 0 0
0 -1 0 0 0 0
-1 0 -1 -1 0 0
0 -1 0 -1 0 0
0 0 0 0 -2 0
1 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,-1,1,t,0,1)
the Blanchfield form on it
2t^-2+t^-1-5+t+2t^2
5
First homology
of the double branched cover of 12n_0851
Z/5
-4 4
12n_0852
1

detected by
an unknotting move
1-5t+14t^2-26t^3+33t^4-26t^5+14t^6-5t^7+t^8
Seifert matrix of 12n_0852
-1 0 0 0 0 0 0 0
0 1 1 0 -1 0 1 0
0 0 -1 0 0 0 0 0
0 0 1 -1 -1 0 0 0
-1 0 0 0 -1 0 0 0
-1 1 0 0 -1 1 1 1
0 0 1 0 -1 0 1 0
0 1 1 0 -1 0 1 1
1
Generator of the Alexander module
(0,-1+t-2t^2+t^3,0,2t-t^2,0,1+t-t^2,0,0)
the Blanchfield form on it
-t^-3+6t^-2-15t^-1+20-15t+6t^2-t^3
125
First homology
of the double branched cover of 12n_0852
Z/125
0 0
12n_0853
1

detected by
an unknotting move
-3+13t-28t^2+37t^3-28t^4+13t^5-3t^6
Seifert matrix of 12n_0853
0 1 0 -1 -2 0
1 1 0 1 0 0
0 -1 -1 0 1 -1
0 1 0 0 -2 0
-1 1 0 -1 -1 0
0 -1 0 0 1 -1
1
Generator of the Alexander module
(1-10t-37t^2-5t^3+58t^4-t^5+10t^6-6t^7,0,-22-50t+52t^2-2t^3-4t^4+4t^5,-9-21t+20t^2-t^3-2t^4+2t^5,52+101t-171t^2+22t^3+3t^4-6t^5+2t^6,-26-55t+74t^2-t^3-2t^4+2t^5)
the Blanchfield form on it
x
125
First homology
of the double branched cover of 12n_0853
Z/125
0 0
12n_0854
1

detected by
an unknotting move
3-14t+33t^2-43t^3+33t^4-14t^5+3t^6
Seifert matrix of 12n_0854
-2 0 0 -1 0 0
1 -1 -1 0 0 0
1 0 -1 1 0 0
-1 0 0 -2 0 0
1 0 -1 1 1 1
1 0 -1 0 0 1
1
Generator of the Alexander module
(0,-t,0,1,-t,1)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
143
First homology
of the double branched cover of 12n_0854
Z/143
-2 2
12n_0855
1

detected by
an unknotting move
-3+10t-18t^2+23t^3-18t^4+10t^5-3t^6
Seifert matrix of 12n_0855
1 -1 0 0 -1 0
-1 0 0 -1 -1 0
0 -1 -1 0 -1 -1
1 -1 0 1 -1 0
0 -2 0 0 -1 0
0 -1 0 0 -1 -1
1
Generator of the Alexander module
(0,-1+3t+4t^2+5t^3+5t^4,-t^2-t^3-2t^4,1-t^3-t^4,1+t+t^2,0)
the Blanchfield form on it
-14t^-5+33t^-4-44t^-3+59t^-2-74t^-1+88-74t+59t^2-44t^3+33t^4-14t^5
85
First homology
of the double branched cover of 12n_0855
Z/85
0 0
12n_0856
2

detected by
the Lickorish test
-5+14t-17t^2+14t^3-5t^4
Seifert matrix of 12n_0856
1 -1 0 -1
-1 -1 -1 -2
1 -1 1 -1
0 -3 0 -2
1 or 2
55
First homology
of the double branched cover of 12n_0856
Z/55
2 2
12n_0857
1

detected by
an unknotting move
-1+6t-17t^2+29t^3-33t^4+29t^5-17t^6+6t^7-t^8
Seifert matrix of 12n_0857
1 0 0 0 1 1 0 1
-1 -1 0 0 -1 -1 0 0
0 0 -1 0 0 0 -1 0
0 0 0 1 0 0 0 0
0 0 0 -1 1 1 -1 1
0 0 -1 -1 0 1 -1 1
0 0 0 0 0 0 -1 0
0 0 -1 -1 0 0 -1 1
1
Generator of the Alexander module
(0,2-t,0,0,1-t,1-t,0,0)
the Blanchfield form on it
t^-3-5t^-2+12t^-1-16+12t-5t^2+t^3
139
First homology
of the double branched cover of 12n_0857
Z/139
2 2
12n_0858
1

detected by
an unknotting move
2-11t+26t^2-33t^3+26t^4-11t^5+2t^6
Seifert matrix of 12n_0858
0 0 1 1 -1 1
0 -1 -1 -1 0 -1
1 0 2 1 -1 1
1 0 1 2 0 1
0 0 0 0 1 0
1 0 2 1 -1 2
1
Generator of the Alexander module
(t,-2t,0,1,0,1+t)
the Blanchfield form on it
t^-1-2+t
111
First homology
of the double branched cover of 12n_0858
Z/111
2 2
12n_0859
1

detected by
an unknotting move
1-6t+16t^2-31t^3+41t^4-31t^5+16t^6-6t^7+t^8
Seifert matrix of 12n_0859
1 0 0 0 1 0 0 1
-1 -1 0 0 -1 0 0 0
0 0 -1 0 0 0 -1 0
0 0 0 1 0 0 0 0
0 0 -1 -1 1 0 -1 1
0 0 -1 0 0 -1 -1 0
0 0 0 0 0 0 -1 0
0 0 -1 -1 0 -1 -1 1
1 or 2
149
First homology
of the double branched cover of 12n_0859
Z/149
0 0
12n_0860
2

detected by
the Lickorish test
3-15t+33t^2-41t^3+33t^4-15t^5+3t^6
Seifert matrix of 12n_0860
3 4 4 2 2 2
2 5 4 2 2 2
2 5 5 2 2 2
3 4 4 3 2 2
2 3 3 2 1 1
3 4 4 3 2 1
1 or 2
143
First homology
of the double branched cover of 12n_0860
Z/143
2 2
12n_0861
1

detected by
an unknotting move
2-9t+22t^2-29t^3+22t^4-9t^5+2t^6
Seifert matrix of 12n_0861
-1 0 0 0 0 0
0 0 0 1 0 -1
0 0 -2 -1 -1 0
1 1 0 -2 -1 1
1 0 -1 -1 -2 0
-1 0 0 1 1 0
1
Generator of the Alexander module
(0,1,0,0,1,0)
the Blanchfield form on it
t^-2-4t^-1+6-4t+t^2
95
First homology
of the double branched cover of 12n_0861
Z/95
-2 2
12n_0862
1

detected by
an unknotting move
3-13t+29t^2-37t^3+29t^4-13t^5+3t^6
Seifert matrix of 12n_0862
1 0 0 0 0 0
0 -1 1 0 1 1
0 0 -2 0 -1 -1
1 -1 1 0 1 0
0 0 -1 0 -2 -1
-1 1 -1 -1 -2 -1
1
Generator of the Alexander module
(2t+2t^2,-2-t,1,1+t,1,-t)
the Blanchfield form on it
17t^-3-87t^-2+209t^-1-270+209t-87t^2+17t^3
127
First homology
of the double branched cover of 12n_0862
Z/127
-2 2
12n_0863
2

detected by
the signature
-3+16t-33t^2+41t^3-33t^4+16t^5-3t^6
Seifert matrix of 12n_0863
-6 -9 0 0 -9 3
-5 -5 0 -1 -6 2
2 3 -1 0 3 -1
-1 -3 0 0 -3 1
-9 -11 0 -1 -14 3
0 1 0 0 0 -1
1 or 2
145
First homology
of the double branched cover of 12n_0863
Z/145
-4 4
12n_0864 1 or 2
1-5t+15t^2-28t^3+33t^4-28t^5+15t^6-5t^7+t^8
Seifert matrix of 12n_0864
-1 0 0 0 0 0 0 0
1 1 0 1 1 1 1 1
-1 0 -1 0 -1 -1 0 -1
0 0 0 1 0 1 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 -1 -1 0 -1
1 0 0 1 1 1 1 1
0 0 0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,-t-t^2+t^3,1+2t+t^2-t^3,1+t-t^2,-1,t,1-t^2,t)
the Blanchfield form on it
t^-3-4t^-2+10t^-1-15+10t-4t^2+t^3
131
First homology
of the double branched cover of 12n_0864
Z/131
-2 2
12n_0865
1

detected by
an unknotting move
1-4t+11t^2-21t^3+25t^4-21t^5+11t^6-4t^7+t^8
Seifert matrix of 12n_0865
-1 0 0 0 0 0 0 0
1 1 0 1 1 1 1 1
-1 0 -1 0 0 -1 0 0
0 0 0 1 0 0 0 0
0 0 0 1 1 1 0 1
0 0 0 0 0 -1 0 0
1 0 0 1 1 1 1 1
0 0 0 1 0 0 0 1
1
Generator of the Alexander module
(0,-2t-4t^2+t^3+5t^4-3t^5,1-2t^2+8t^3-3t^4,2+3t-4t^2-5t^3+3t^4,1+3t+3t^2+3t^3+2t^4-3t^5,1+3t,-2t-3t^2+3t^3+2t^4-3t^5,1+t-3t^2+4t^3+5t^4-3t^5)
the Blanchfield form on it
x
99
First homology
of the double branched cover of 12n_0865
Z/99
2 2
12n_0866
1

detected by
an unknotting move
-1+5t-15t^2+30t^3-39t^4+30t^5-15t^6+5t^7-t^8
Seifert matrix of 12n_0866
-1 0 0 0 0 0 0 0
1 1 0 1 1 1 1 1
-1 0 -1 0 -1 -1 0 0
0 0 0 1 0 0 0 0
0 0 0 0 -1 0 0 0
0 0 0 0 -1 -1 0 0
1 0 0 1 1 1 1 1
0 0 0 1 0 1 0 1
1 or 2
141
First homology
of the double branched cover of 12n_0866
Z/141
0 0
12n_0867
2

detected by
the signature
-2+14t-31t^2+39t^3-31t^4+14t^5-2t^6
Seifert matrix of 12n_0867
0 0 0 0 -1 0
0 1 0 0 0 0
0 0 2 0 1 0
-1 0 0 0 -1 0
-1 1 0 -1 0 0
-1 0 -1 -1 -1 1
1
Generator of the Alexander module
(0,0,1,1,t,2t)
the Blanchfield form on it
-2t^-2+4t^-1-5+4t-2t^2
133
First homology
of the double branched cover of 12n_0867
Z/133
4 4
12n_0868
1

detected by
an unknotting move
2-8t+13t^2-8t^3+2t^4
Seifert matrix of 12n_0868
-2 0 2 0
-1 0 0 0
0 -1 -2 0
-2 0 1 1
1
Generator of the Alexander module
(0,0,2,1)
the Blanchfield form on it
-1
33
First homology
of the double branched cover of 12n_0868
Z/33
0 0
12n_0869
2

detected by
the Nakanishi index
2-12t+32t^2-43t^3+32t^4-12t^5+2t^6
Seifert matrix of 12n_0869
-1 0 -1 0 0 0
0 0 -1 0 0 -1
0 -1 -2 0 0 -1
1 1 1 1 -1 0
0 1 1 0 -1 1
0 -1 -1 0 0 -2
2
135
First homology
of the double branched cover of 12n_0869
Z/45+Z/3
-2 2
12n_0870
2

detected by
the Lickorish test
-1+3t-5t^2+7t^3-5t^4+3t^5-t^6
Seifert matrix of 12n_0870
1 0 0 0 0 0
-1 -1 -1 0 -1 0
0 1 -1 0 0 0
-2 2 -2 2 -1 1
-1 0 -1 0 0 0
-1 1 -1 1 0 0
1
Generator of the Alexander module
(0,-t,-t^2+t^3-2t^4+t^5,1+3t-2t^2-5t^4+2t^5,-t,t-2t^4+t^5)
the Blanchfield form on it
-t^-1+1-t
25
First homology
of the double branched cover of 12n_0870
Z/25
0 0
12n_0871
1

detected by
an unknotting move
1-9t+29t^2-41t^3+29t^4-9t^5+t^6
Seifert matrix of 12n_0871
-1 0 0 0 0 0
-1 -1 -1 0 -1 0
0 1 -1 0 0 0
-2 2 -2 2 -1 1
-1 0 -1 0 0 0
-1 1 -1 1 0 0
1
Generator of the Alexander module
(-4t^2+8t^3+68t^4-324t^5+524t^6+188t^7-1900t^8+2976t^9-2392t^10+1088t^11-256t^12+24t^13,2+10t-26t^2-24t^3+346t^4-756t^5+772t^6-428t^7+116t^8-12t^9,1-2t-6t^2+88t^3-348t^4+686t^5-464t^6-1134t^7+3388t^8-4172t^9+2936t^10-1216t^11+268t^12-24t^13,2-30t^2+116t^3-142t^4-284t^5+1516t^6-3322t^7+4240t^8-3288t^
the Blanchfield form on it
x
119
First homology
of the double branched cover of 12n_0871
Z/119
-2 2
12n_0872
1

detected by
an unknotting move
-1+6t-16t^2+27t^3-31t^4+27t^5-16t^6+6t^7-t^8
Seifert matrix of 12n_0872
1 0 -1 0 1 0 -1 0
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 0 0 0
1 -1 -1 1 1 1 -1 0
0 0 0 0 1 0 0 0
1 0 -1 0 1 1 -1 0
0 0 0 0 0 0 1 0
-1 0 0 0 -1 -1 0 -1
1
Generator of the Alexander module
(0,2t-2t^2+4t^3-4t^4+2t^5-2t^6,-1-2t^2-t^4,0,-t-2t^3-t^5,-2t-2t^2-2t^3-4t^4+2t^5-2t^6+2t^7,0,-2-4t+t^2-6t^3+7t^4-3t^5+3t^6-t^8)
the Blanchfield form on it
x
131
First homology
of the double branched cover of 12n_0872
Z/131
2 2
12n_0873
2

detected by
A(F_2)
1-5t+10t^2-16t^3+21t^4-16t^5+10t^6-5t^7+t^8
Seifert matrix of 12n_0873
1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
-1 -1 -1 -1 -1 -1 -1 0
0 -1 0 -1 0 0 0 0
0 0 0 0 -1 0 0 0
1 0 0 0 0 1 0 0
-1 -1 0 -1 -1 -1 -1 0
1 0 0 0 1 1 0 1
2
85
First homology
of the double branched cover of 12n_0873
Z/85
0 0
12n_0874
2

detected by
the Lickorish test
-1+5t-14t^2+26t^3-31t^4+26t^5-14t^6+5t^7-t^8
Seifert matrix of 12n_0874
1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
-1 -1 -1 -1 -1 -1 -1 0
0 -1 0 -1 0 0 0 0
0 0 0 0 -1 0 0 0
1 0 0 0 0 1 0 0
-1 -1 0 -1 -1 -1 -1 0
1 0 0 0 1 1 0 -1
2
123
First homology
of the double branched cover of 12n_0874
Z/123
-2 2
12n_0875
1

detected by
an unknotting move
-1+4t-11t^2+21t^3-25t^4+21t^5-11t^6+4t^7-t^8
Seifert matrix of 12n_0875
1 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0
0 -1 -1 0 0 -1 0 0
0 0 0 -1 0 0 0 -1
1 0 0 0 1 0 0 0
0 0 0 0 0 -1 0 0
0 0 0 -1 0 0 -1 -1
1 0 0 0 1 -1 0 -1
1 or 2
99
First homology
of the double branched cover of 12n_0875
Z/99
-2 2
12n_0876
2

detected by
the Nakanishi index
-2+8t-18t^2+25t^3-18t^4+8t^5-2t^6
Seifert matrix of 12n_0876
1 0 0 0 0 0
1 1 0 0 1 0
0 -1 -1 0 0 -1
-1 0 0 -2 -1 1
1 0 0 0 1 0
0 0 0 0 0 -1
2
81
First homology
of the double branched cover of 12n_0876
Z/9+Z/9
0 0
12n_0877
2

detected by
the Lickorish test
-1+7t-20t^2+32t^3-35t^4+32t^5-20t^6+7t^7-t^8
Seifert matrix of 12n_0877
-1 -1 0 0 0 0 -1 -1
0 1 0 0 0 -1 0 1
-1 0 1 -1 0 0 0 0
-1 0 0 -1 0 0 -1 -1
0 1 0 0 1 -1 0 1
0 0 0 0 0 1 0 0
0 -1 0 0 -1 0 -1 -1
0 0 0 0 0 0 0 1
2
155
First homology
of the double branched cover of 12n_0877
Z/155
2 2
12n_0878
2

detected by
A(F_2)
1-11t+34t^2-47t^3+34t^4-11t^5+t^6
Seifert matrix of 12n_0878
1 0 0 0 0 0
-1 -1 -1 -1 0 -2
0 0 -2 1 0 0
0 -1 0 -2 0 -1
-1 -1 0 -1 -1 -1
-1 -1 -1 -1 0 -1
2
139
First homology
of the double branched cover of 12n_0878
Z/139
-2 2
12n_0879
2

detected by
the Lickorish test
-1+6t-17t^2+30t^3-35t^4+30t^5-17t^6+6t^7-t^8
Seifert matrix of 12n_0879
1 0 -1 0 0 0 0 -1
0 -1 0 0 0 0 0 0
0 -1 -1 0 0 -1 0 0
1 0 -1 1 0 -1 0 -1
0 -1 -1 0 1 -1 0 -1
0 -1 0 0 0 -1 0 0
1 -1 -1 1 0 -1 1 -1
0 0 0 0 0 0 0 1
2
143
First homology
of the double branched cover of 12n_0879
Z/143
2 2
12n_0880
1

detected by
an unknotting move
-3+14t-30t^2+39t^3-30t^4+14t^5-3t^6
Seifert matrix of 12n_0880
1 2 0 1 2 2
3 3 0 2 4 3
2 2 1 1 2 1
3 3 0 1 2 3
4 4 0 1 3 4
1 2 0 1 2 1
1
Generator of the Alexander module
(0,0,0,0,1,0)
the Blanchfield form on it
3t^-2-11t^-1+15-11t+3t^2
133
First homology
of the double branched cover of 12n_0880
Z/133
0 0
12n_0881
2

detected by
the Nakanishi index
9-30t+43t^2-30t^3+9t^4
Seifert matrix of 12n_0881
-2 0 -1 0
-1 -2 0 -1
-1 0 -2 0
-1 -1 -1 -2
2
121
First homology
of the double branched cover of 12n_0881
Z/11+Z/11
-4 4
12n_0882
3

detected by
the signature
1-6t+13t^2-19t^3+21t^4-19t^5+13t^6-6t^7+t^8
Seifert matrix of 12n_0882
0 0 0 0 1 0 0 0
-1 1 1 0 0 0 1 -1
0 0 1 0 0 0 1 0
0 0 0 1 1 0 0 0
1 0 -1 0 0 0 -1 1
-1 1 1 0 0 1 1 -1
0 0 0 0 0 0 1 0
-1 0 0 0 1 0 0 0
1 or 2
99
First homology
of the double branched cover of 12n_0882
Z/99
6 6
12n_0883
2

detected by
the Nakanishi index
3-12t+22t^2-25t^3+22t^4-12t^5+3t^6
Seifert matrix of 12n_0883
-1 -1 -1 -1 0 -1
0 -1 0 -1 0 -1
0 0 1 0 0 0
0 0 0 -1 0 -1
0 0 1 0 1 2
0 0 1 0 2 1
2
99
First homology
of the double branched cover of 12n_0883
Z/33+Z/3
-2 2
12n_0884
1

detected by
an unknotting move
5-20t+31t^2-20t^3+5t^4
Seifert matrix of 12n_0884
-5 -3 0 -2
-4 -1 1 -2
-2 -1 1 -1
-3 -2 0 -2
1
Generator of the Alexander module
(0,1,1,0)
the Blanchfield form on it
-1
81
First homology
of the double branched cover of 12n_0884
Z/81
0 0
12n_0885
1

detected by
an unknotting move
-2+13t-35t^2+49t^3-35t^4+13t^5-2t^6
Seifert matrix of 12n_0885
-1 -1 -1 1 -1 0
0 1 1 0 0 0
0 0 1 0 0 0
0 1 0 1 1 0
0 0 0 0 -2 1
0 -1 0 0 0 -1
1
Generator of the Alexander module
(-t,0,0,-2,1,0)
the Blanchfield form on it
-2t^-2+9t^-1-15+9t-2t^2
149
First homology
of the double branched cover of 12n_0885
Z/149
0 0
12n_0886
2

detected by
the Lickorish test
2-13t+38t^2-53t^3+38t^4-13t^5+2t^6
Seifert matrix of 12n_0886
1 0 -1 0 0 0
0 -1 0 -1 0 0
0 0 -1 1 0 0
0 0 0 -2 0 0
1 1 -1 1 1 0
-1 0 1 -1 -1 -1
1 or 2
159
First homology
of the double branched cover of 12n_0886
Z/159
-2 2
12n_0887
2

detected by
the Nakanishi index
-1+6t-16t^2+25t^3-29t^4+25t^5-16t^6+6t^7-t^8
Seifert matrix of 12n_0887
2 0 1 0 2 1 2 0
-1 -1 -1 0 0 -1 -1 0
2 0 0 0 1 1 2 0
1 -1 0 -1 0 0 1 -1
0 0 0 0 1 0 0 0
1 0 0 0 1 0 1 0
3 0 1 0 2 1 2 0
-1 -1 -1 0 -1 -1 -1 -1
2
125
First homology
of the double branched cover of 12n_0887
Z/25+Z/5
-4 4
12n_0888
4

detected by
the signature
-1+t+t^2-6t^3+11t^4-13t^5+11t^6-6t^7+t^8+t^9-t^10
Seifert matrix of 12n_0888
-1 0 0 0 0 -1 -1 0 0 -1
0 -1 -1 -1 0 0 0 -1 -1 0
0 0 -1 -1 0 0 0 -1 0 0
0 0 0 -1 0 0 0 0 0 0
-1 0 0 0 -1 -1 -1 0 0 -1
0 0 -1 -1 0 -1 -1 -1 0 -1
0 0 -1 -1 0 0 -1 -1 0 0
0 0 0 -1 0 0 0 -1 0 0
0 0 -1 -1 0 0 0 -1 -1 0
0 0 -1 -1 0 0 -1 -1 0 -1
2
45
First homology
of the double branched cover of 12n_0888
Z/15+Z/3
-8 8
12n_0888
4

detected by
the signature
-1+t+t^2-6t^3+11t^4-13t^5+11t^6-6t^7+t^8+t^9-t^10
Seifert matrix of 12n_0888
-1 0 0 0 0 -1 -1 0 0 -1
0 -1 -1 -1 0 0 0 -1 -1 0
0 0 -1 -1 0 0 0 -1 0 0
0 0 0 -1 0 0 0 0 0 0
-1 0 0 0 -1 -1 -1 0 0 -1
0 0 -1 -1 0 -1 -1 -1 0 -1
0 0 -1 -1 0 0 -1 -1 0 0
0 0 0 -1 0 0 0 -1 0 0
0 0 -1 -1 0 0 0 -1 -1 0
0 0 -1 -1 0 0 -1 -1 0 -1
2
45
First homology
of the double branched cover of 12n_0888
Z/15+Z/3
-8 8