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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.
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