12a
0121
(K12a
0121
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 11 9 4 1 7 6 10
Solving Sequence
4,8 1,9
10 3 2 5 7 11 6 12
c
8
c
9
c
3
c
1
c
4
c
7
c
10
c
6
c
12
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.70426 × 10
59
u
73
+ 1.40507 × 10
59
u
72
+ ··· + 3.05010 × 10
59
b + 6.17432 × 10
60
,
− 5.99855 × 10
59
u
73
+ 1.15828 × 10
59
u
72
+ ··· + 6.10019 × 10
59
a − 1.21152 × 10
61
, u
74
+ u
73
+ ··· + 8u + 16i
I
v
1
= ha, −v
3
+ b − v + 1, v
4
+ v
2
− v + 1i
* 2 irreducible components of dim
C
= 0, with total 78 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h3.70×10
59
u
73
+1.41×10
59
u
72
+· · ·+3.05×10
59
b+6.17×10
60
, −6.00×
10
59
u
73
+1.16×10
59
u
72
+· · ·+6.10×10
59
a−1.21×10
61
, u
74
+u
73
+· · ·+8u+16i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
1
=
0.983338u
73
− 0.189877u
72
+ ··· + 5.71968u + 19.8603
−1.21447u
73
− 0.460663u
72
+ ··· + 16.1377u − 20.2430
a
9
=
1
−u
2
a
10
=
0.138891u
73
+ 0.179714u
72
+ ··· − 5.47228u − 11.2643
−0.298191u
73
− 0.945298u
72
+ ··· + 28.6342u + 19.9267
a
3
=
−u
u
a
2
=
0.602949u
73
− 0.0755376u
72
+ ··· − 1.33370u + 13.1498
−0.834082u
73
− 0.575003u
72
+ ··· + 23.1911u − 13.5325
a
5
=
0.231133u
73
+ 0.650540u
72
+ ··· − 21.8574u + 0.382698
−0.834082u
73
− 0.575003u
72
+ ··· + 23.1911u − 13.5325
a
7
=
−u
2
+ 1
u
4
a
11
=
−0.683959u
73
− 0.130336u
72
+ ··· − 1.49771u − 10.9000
0.331838u
73
− 1.01634u
72
+ ··· + 31.2725u + 30.4644
a
6
=
−0.576445u
73
− 0.941694u
72
+ ··· + 3.90277u − 0.454644
0.294240u
73
+ 0.616016u
72
+ ··· − 15.4748u − 3.92866
a
12
=
0.0885217u
73
− 0.151798u
72
+ ··· + 9.13405u + 14.7379
−1.20808u
73
− 1.72858u
72
+ ··· + 42.1635u + 0.443963
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.992562u
73
− 1.56064u
72
+ ··· + 18.3687u + 67.7778
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 39u
73
+ ··· + 5u + 1
c
2
, c
4
u
74
− 5u
73
+ ··· − 5u + 1
c
3
, c
8
u
74
+ u
73
+ ··· + 8u + 16
c
5
, c
6
, c
10
c
11
u
74
+ 2u
73
+ ··· + u + 1
c
7
u
74
− 27u
73
+ ··· − 3648u + 256
c
9
, c
12
u
74
− 14u
73
+ ··· − 401u + 131
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
− 3y
73
+ ··· + 31y + 1
c
2
, c
4
y
74
− 39y
73
+ ··· − 5y + 1
c
3
, c
8
y
74
− 27y
73
+ ··· − 3648y + 256
c
5
, c
6
, c
10
c
11
y
74
+ 82y
73
+ ··· + 13y + 1
c
7
y
74
+ 33y
73
+ ··· + 733184y + 65536
c
9
, c
12
y
74
+ 38y
73
+ ··· + 804669y + 17161
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.423407 + 0.908405I
a = 0.333736 + 0.370914I
b = 0.795329 − 0.678802I
−6.68590 − 0.24691I −2.05218 + 1.39856I
u = 0.423407 − 0.908405I
a = 0.333736 − 0.370914I
b = 0.795329 + 0.678802I
−6.68590 + 0.24691I −2.05218 − 1.39856I
u = −0.801884 + 0.590421I
a = −0.687028 + 0.893257I
b = 0.35735 − 2.20178I
−9.54906 + 1.30956I −4.03408 + 2.47435I
u = −0.801884 − 0.590421I
a = −0.687028 − 0.893257I
b = 0.35735 + 2.20178I
−9.54906 − 1.30956I −4.03408 − 2.47435I
u = −0.829553 + 0.543699I
a = 0.978509 − 0.503295I
b = −0.755197 + 0.923555I
−1.52786 − 2.20202I −1.33752 + 3.99333I
u = −0.829553 − 0.543699I
a = 0.978509 + 0.503295I
b = −0.755197 − 0.923555I
−1.52786 + 2.20202I −1.33752 − 3.99333I
u = 0.850830 + 0.554970I
a = 2.05682 + 0.92874I
b = −0.486535 − 1.179000I
−2.05198 + 3.51352I 0. − 6.69469I
u = 0.850830 − 0.554970I
a = 2.05682 − 0.92874I
b = −0.486535 + 1.179000I
−2.05198 − 3.51352I 0. + 6.69469I
u = 0.684502 + 0.755683I
a = 1.19354 + 0.87816I
b = 0.197384 − 1.181150I
−5.16241 − 1.26769I −6.83065 + 0.I
u = 0.684502 − 0.755683I
a = 1.19354 − 0.87816I
b = 0.197384 + 1.181150I
−5.16241 + 1.26769I −6.83065 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.857556 + 0.558345I
a = 0.684895 + 0.677632I
b = −0.37941 − 1.93637I
−2.02581 + 0.94411I 0
u = 0.857556 − 0.558345I
a = 0.684895 − 0.677632I
b = −0.37941 + 1.93637I
−2.02581 − 0.94411I 0
u = −0.547569 + 0.920117I
a = −0.474236 + 0.749588I
b = −0.753401 − 1.013480I
−0.84622 + 2.33865I 0
u = −0.547569 − 0.920117I
a = −0.474236 − 0.749588I
b = −0.753401 + 1.013480I
−0.84622 − 2.33865I 0
u = 0.428504 + 0.823370I
a = −0.336458 − 0.903865I
b = −0.092714 + 1.043080I
−6.30073 − 4.37712I −0.70444 + 1.63184I
u = 0.428504 − 0.823370I
a = −0.336458 + 0.903865I
b = −0.092714 − 1.043080I
−6.30073 + 4.37712I −0.70444 − 1.63184I
u = −0.897117 + 0.590669I
a = −2.07001 + 1.11773I
b = 0.51805 − 1.33705I
−9.24424 − 5.99219I 0
u = −0.897117 − 0.590669I
a = −2.07001 − 1.11773I
b = 0.51805 + 1.33705I
−9.24424 + 5.99219I 0
u = 0.832703 + 0.681766I
a = −1.039600 − 0.747085I
b = 0.724020 + 1.159500I
−9.45633 + 2.62273I 0
u = 0.832703 − 0.681766I
a = −1.039600 + 0.747085I
b = 0.724020 − 1.159500I
−9.45633 − 2.62273I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.769283 + 0.488778I
a = −2.05548 + 0.60852I
b = 0.438285 − 0.921897I
−1.384040 + 0.132047I 2.16067 + 0.30955I
u = −0.769283 − 0.488778I
a = −2.05548 − 0.60852I
b = 0.438285 + 0.921897I
−1.384040 − 0.132047I 2.16067 − 0.30955I
u = −0.944570 + 0.558179I
a = −0.818444 + 0.415309I
b = 0.57504 − 1.64298I
−0.71686 − 4.42426I 0
u = −0.944570 − 0.558179I
a = −0.818444 − 0.415309I
b = 0.57504 + 1.64298I
−0.71686 + 4.42426I 0
u = −0.766571 + 0.807568I
a = −1.19792 + 1.21825I
b = −0.20218 − 1.45363I
−13.17610 + 1.37303I 0
u = −0.766571 − 0.807568I
a = −1.19792 − 1.21825I
b = −0.20218 + 1.45363I
−13.17610 − 1.37303I 0
u = −0.078416 + 0.870824I
a = 0.015544 − 0.645299I
b = 0.570597 + 0.489818I
−5.43606 − 3.66476I −0.14387 + 4.42422I
u = −0.078416 − 0.870824I
a = 0.015544 + 0.645299I
b = 0.570597 − 0.489818I
−5.43606 + 3.66476I −0.14387 − 4.42422I
u = 0.596490 + 0.957647I
a = 0.432293 + 0.957849I
b = 0.81695 − 1.18139I
−1.53922 − 6.15680I 0
u = 0.596490 − 0.957647I
a = 0.432293 − 0.957849I
b = 0.81695 + 1.18139I
−1.53922 + 6.15680I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.791891 + 0.295773I
a = 2.48374 + 0.34198I
b = −0.709497 − 0.587590I
−7.51454 − 2.01833I −0.618134 − 0.685391I
u = 0.791891 − 0.295773I
a = 2.48374 − 0.34198I
b = −0.709497 + 0.587590I
−7.51454 + 2.01833I −0.618134 + 0.685391I
u = 0.812781 + 0.230945I
a = −0.756305 − 0.135352I
b = 0.786320 + 0.593647I
1.252930 + 0.387938I 8.38658 − 1.11749I
u = 0.812781 − 0.230945I
a = −0.756305 + 0.135352I
b = 0.786320 − 0.593647I
1.252930 − 0.387938I 8.38658 + 1.11749I
u = −0.630186 + 0.982770I
a = −0.404159 + 1.105010I
b = −0.85849 − 1.30364I
−8.74555 + 8.73953I 0
u = −0.630186 − 0.982770I
a = −0.404159 − 1.105010I
b = −0.85849 + 1.30364I
−8.74555 − 8.73953I 0
u = −0.333081 + 0.761545I
a = 0.259564 − 0.774462I
b = 0.132468 + 0.828249I
0.73066 + 2.03280I 3.01596 − 3.03284I
u = −0.333081 − 0.761545I
a = 0.259564 + 0.774462I
b = 0.132468 − 0.828249I
0.73066 − 2.03280I 3.01596 + 3.03284I
u = −1.092490 + 0.457930I
a = 1.349320 − 0.120256I
b = −1.137890 + 0.725457I
−2.31150 − 0.67313I 0
u = −1.092490 − 0.457930I
a = 1.349320 + 0.120256I
b = −1.137890 − 0.725457I
−2.31150 + 0.67313I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.988326 + 0.663791I
a = 1.224120 + 0.440000I
b = −1.03796 − 1.72015I
−4.21784 + 6.66573I 0
u = 0.988326 − 0.663791I
a = 1.224120 − 0.440000I
b = −1.03796 + 1.72015I
−4.21784 − 6.66573I 0
u = −0.962589 + 0.726029I
a = −1.38552 + 0.63239I
b = 1.20458 − 1.95240I
−12.5517 − 7.1340I 0
u = −0.962589 − 0.726029I
a = −1.38552 − 0.63239I
b = 1.20458 + 1.95240I
−12.5517 + 7.1340I 0
u = 0.167715 + 0.775430I
a = −0.121087 − 0.691281I
b = −0.316447 + 0.584410I
1.04424 + 1.49891I 4.26534 − 5.16915I
u = 0.167715 − 0.775430I
a = −0.121087 + 0.691281I
b = −0.316447 − 0.584410I
1.04424 − 1.49891I 4.26534 + 5.16915I
u = 1.205340 + 0.081481I
a = −0.387742 − 0.668125I
b = 0.409851 − 0.226615I
6.07576 + 0.60640I 0
u = 1.205340 − 0.081481I
a = −0.387742 + 0.668125I
b = 0.409851 + 0.226615I
6.07576 − 0.60640I 0
u = 1.078680 + 0.547501I
a = −1.43333 − 0.30857I
b = 1.17233 + 0.88754I
3.46309 + 3.10149I 0
u = 1.078680 − 0.547501I
a = −1.43333 + 0.30857I
b = 1.17233 − 0.88754I
3.46309 − 3.10149I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.213100 + 0.013999I
a = 0.570854 − 0.662659I
b = −0.563202 − 0.195923I
−0.36122 + 2.07176I 0
u = −1.213100 − 0.013999I
a = 0.570854 + 0.662659I
b = −0.563202 + 0.195923I
−0.36122 − 2.07176I 0
u = −1.210260 + 0.140063I
a = 0.224459 − 0.692691I
b = −0.262372 − 0.239344I
5.95478 − 4.66035I 0
u = −1.210260 − 0.140063I
a = 0.224459 + 0.692691I
b = −0.262372 + 0.239344I
5.95478 + 4.66035I 0
u = 1.222830 + 0.196731I
a = −0.057216 − 0.731230I
b = 0.102347 − 0.239238I
−0.73392 + 7.38939I 0
u = 1.222830 − 0.196731I
a = −0.057216 + 0.731230I
b = 0.102347 + 0.239238I
−0.73392 − 7.38939I 0
u = −1.086840 + 0.598051I
a = 1.50608 − 0.40586I
b = −1.21482 + 0.98108I
2.80968 − 7.08642I 0
u = −1.086840 − 0.598051I
a = 1.50608 + 0.40586I
b = −1.21482 − 0.98108I
2.80968 + 7.08642I 0
u = −0.737181 + 0.016255I
a = 0.608089 + 0.151860I
b = −1.007570 − 0.658891I
−0.28063 − 2.21410I 2.85810 + 7.13012I
u = −0.737181 − 0.016255I
a = 0.608089 − 0.151860I
b = −1.007570 + 0.658891I
−0.28063 + 2.21410I 2.85810 − 7.13012I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.093160 + 0.636688I
a = −1.56028 − 0.48571I
b = 1.24648 + 1.05875I
−4.37061 + 9.78663I 0
u = 1.093160 − 0.636688I
a = −1.56028 + 0.48571I
b = 1.24648 − 1.05875I
−4.37061 − 9.78663I 0
u = 1.104620 + 0.631964I
a = 1.294020 − 0.006338I
b = −1.16434 − 1.23107I
−4.58482 + 5.78561I 0
u = 1.104620 − 0.631964I
a = 1.294020 + 0.006338I
b = −1.16434 + 1.23107I
−4.58482 − 5.78561I 0
u = −1.105360 + 0.697204I
a = −1.52864 + 0.08925I
b = 1.41065 − 1.36000I
0.88109 − 8.27754I 0
u = −1.105360 − 0.697204I
a = −1.52864 − 0.08925I
b = 1.41065 + 1.36000I
0.88109 + 8.27754I 0
u = 1.109560 + 0.728597I
a = 1.64987 + 0.12497I
b = −1.53970 − 1.40988I
0.08090 + 12.33240I 0
u = 1.109560 − 0.728597I
a = 1.64987 − 0.12497I
b = −1.53970 + 1.40988I
0.08090 − 12.33240I 0
u = 0.656185 + 0.099687I
a = −0.698777 + 0.324084I
b = 1.40628 − 0.89471I
−7.75228 + 3.74107I 1.87141 − 6.31684I
u = 0.656185 − 0.099687I
a = −0.698777 − 0.324084I
b = 1.40628 + 0.89471I
−7.75228 − 3.74107I 1.87141 + 6.31684I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.110460 + 0.753116I
a = −1.74170 + 0.16320I
b = 1.63659 − 1.45911I
−7.2134 − 15.0818I 0
u = −1.110460 − 0.753116I
a = −1.74170 − 0.16320I
b = 1.63659 + 1.45911I
−7.2134 + 15.0818I 0
u = −0.288561 + 0.445663I
a = −1.36152 − 0.89813I
b = −0.019180 − 0.276110I
−1.69767 + 0.56736I −4.68375 + 1.20836I
u = −0.288561 − 0.445663I
a = −1.36152 + 0.89813I
b = −0.019180 + 0.276110I
−1.69767 − 0.56736I −4.68375 − 1.20836I
12
II. I
v
1
= ha, −v
3
+ b − v + 1, v
4
+ v
2
− v + 1i
(i) Arc colorings
a
4
=
v
0
a
8
=
1
0
a
1
=
0
v
3
+ v − 1
a
9
=
1
0
a
10
=
1
−v
3
− v
2
− v
a
3
=
v
0
a
2
=
v
v
3
+ v − 1
a
5
=
0
−v
3
− v + 1
a
7
=
1
0
a
11
=
−v
3
− v
2
− v + 1
−v
3
− v
2
− v
a
6
=
−v
2
− v − 1
v
3
− 2
a
12
=
v
3
+ v − 1
v
3
+ v
2
+ 2v
(ii) Obstruction class = 1
(iii) Cusp Shapes = v
3
− 4v
2
+ v − 6
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
4
c
3
, c
7
, c
8
u
4
c
4
(u + 1)
4
c
5
, c
6
u
4
+ u
3
+ 3u
2
+ 2u + 1
c
9
u
4
+ u
3
+ u
2
+ 1
c
10
, c
11
u
4
− u
3
+ 3u
2
− 2u + 1
c
12
u
4
− u
3
+ u
2
+ 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
4
c
3
, c
7
, c
8
y
4
c
5
, c
6
, c
10
c
11
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
9
, c
12
y
4
+ y
3
+ 3y
2
+ 2y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.547424 + 0.585652I
a = 0
b = −0.851808 + 0.911292I
−8.43568 + 3.16396I −5.67855 − 1.65351I
v = 0.547424 − 0.585652I
a = 0
b = −0.851808 − 0.911292I
−8.43568 − 3.16396I −5.67855 + 1.65351I
v = −0.547424 + 1.120870I
a = 0
b = 0.351808 + 0.720342I
−1.43393 − 1.41510I −0.82145 + 5.62908I
v = −0.547424 − 1.120870I
a = 0
b = 0.351808 − 0.720342I
−1.43393 + 1.41510I −0.82145 − 5.62908I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
74
+ 39u
73
+ ··· + 5u + 1)
c
2
((u − 1)
4
)(u
74
− 5u
73
+ ··· − 5u + 1)
c
3
, c
8
u
4
(u
74
+ u
73
+ ··· + 8u + 16)
c
4
((u + 1)
4
)(u
74
− 5u
73
+ ··· − 5u + 1)
c
5
, c
6
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
74
+ 2u
73
+ ··· + u + 1)
c
7
u
4
(u
74
− 27u
73
+ ··· − 3648u + 256)
c
9
(u
4
+ u
3
+ u
2
+ 1)(u
74
− 14u
73
+ ··· − 401u + 131)
c
10
, c
11
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
74
+ 2u
73
+ ··· + u + 1)
c
12
(u
4
− u
3
+ u
2
+ 1)(u
74
− 14u
73
+ ··· − 401u + 131)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
4
)(y
74
− 3y
73
+ ··· + 31y + 1)
c
2
, c
4
((y − 1)
4
)(y
74
− 39y
73
+ ··· − 5y + 1)
c
3
, c
8
y
4
(y
74
− 27y
73
+ ··· − 3648y + 256)
c
5
, c
6
, c
10
c
11
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
74
+ 82y
73
+ ··· + 13y + 1)
c
7
y
4
(y
74
+ 33y
73
+ ··· + 733184y + 65536)
c
9
, c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
74
+ 38y
73
+ ··· + 804669y + 17161)
18
