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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.
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