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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.
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