12a
0144
(K12a
0144
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 11 12 4 1 6 8 7
Solving Sequence
5,10
6 11
3,7
2 1 4 9 8 12
c
5
c
10
c
6
c
2
c
1
c
4
c
9
c
8
c
12
c
3
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.00279 × 10
169
u
80
+ 6.54285 × 10
169
u
79
+ ··· + 5.58362 × 10
170
b − 5.37338 × 10
170
,
2.70498 × 10
170
u
80
+ 4.42960 × 10
170
u
79
+ ··· + 1.67509 × 10
171
a + 1.36068 × 10
171
, u
81
+ 2u
80
+ ··· − 27u − 9i
I
u
2
= hb + 1, a + 1, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 87 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
= h−1.00 × 10
169
u
80
+ 6.54 × 10
169
u
79
+ · · · + 5.58 × 10
170
b − 5.37 ×
10
170
, 2.70 × 10
170
u
80
+ 4.43 × 10
170
u
79
+ · · · + 1.68 × 10
171
a + 1.36 ×
10
171
, u
81
+ 2u
80
+ · · · − 27u − 9i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
11
=
−u
−u
3
+ u
a
3
=
−0.161483u
80
− 0.264440u
79
+ ··· − 4.05452u − 0.812307
0.0179595u
80
− 0.117179u
79
+ ··· − 1.66032u + 0.962347
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−0.143524u
80
− 0.381620u
79
+ ··· − 5.71484u + 0.150039
0.0179595u
80
− 0.117179u
79
+ ··· − 1.66032u + 0.962347
a
1
=
−0.428496u
80
− 0.583915u
79
+ ··· + 12.7602u + 6.52385
−0.131228u
80
− 0.0542263u
79
+ ··· + 3.05402u + 0.800318
a
4
=
0.259446u
80
+ 0.204971u
79
+ ··· − 18.6233u − 5.57768
0.157772u
80
+ 0.183340u
79
+ ··· − 4.83114u − 3.19296
a
9
=
0.111704u
80
+ 0.397558u
79
+ ··· − 6.23678u − 4.64153
0.0545258u
80
+ 0.0419649u
79
+ ··· − 0.269902u − 0.998356
a
8
=
0.184153u
80
+ 0.220811u
79
+ ··· − 11.7267u − 4.50953
0.273077u
80
+ 0.267431u
79
+ ··· − 5.04554u − 3.85646
a
12
=
−0.493301u
80
− 0.569619u
79
+ ··· + 16.6789u + 6.41142
0.0147144u
80
+ 0.0729091u
79
+ ··· + 0.464872u − 0.795811
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.191745u
80
− 0.688940u
79
+ ··· + 3.61897u − 7.41512
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
81
+ 39u
80
+ ··· + 52u + 1
c
2
, c
4
u
81
− 7u
80
+ ··· + 2u + 1
c
3
, c
8
u
81
− u
80
+ ··· + 64u + 64
c
5
, c
6
, c
10
u
81
− 2u
80
+ ··· − 27u + 9
c
7
, c
11
, c
12
u
81
+ 2u
80
+ ··· + 3u + 1
c
9
u
81
+ 8u
80
+ ··· − 3141u + 2537
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
81
+ 13y
80
+ ··· + 3164y −1
c
2
, c
4
y
81
− 39y
80
+ ··· + 52y −1
c
3
, c
8
y
81
+ 39y
80
+ ··· − 40960y −4096
c
5
, c
6
, c
10
y
81
− 80y
80
+ ··· − 693y −81
c
7
, c
11
, c
12
y
81
+ 64y
80
+ ··· + 11y −1
c
9
y
81
+ 4y
80
+ ··· + 43125951y −6436369
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.549854 + 0.817265I
a = −0.668883 + 0.232142I
b = −1.240880 + 0.079920I
2.18909 − 2.68944I 0
u = 0.549854 − 0.817265I
a = −0.668883 − 0.232142I
b = −1.240880 − 0.079920I
2.18909 + 2.68944I 0
u = −0.423119 + 0.878378I
a = 0.92747 + 1.27632I
b = −0.735616 − 0.474491I
3.90058 + 0.83925I 0
u = −0.423119 − 0.878378I
a = 0.92747 − 1.27632I
b = −0.735616 + 0.474491I
3.90058 − 0.83925I 0
u = −0.629386 + 0.882957I
a = 0.11503 − 1.99991I
b = −0.920437 + 0.512641I
3.30143 + 4.94717I 0
u = −0.629386 − 0.882957I
a = 0.11503 + 1.99991I
b = −0.920437 − 0.512641I
3.30143 − 4.94717I 0
u = 0.871043 + 0.244839I
a = 0.226267 − 0.008099I
b = 0.923001 − 0.532162I
−1.18559 + 2.18588I 0
u = 0.871043 − 0.244839I
a = 0.226267 + 0.008099I
b = 0.923001 + 0.532162I
−1.18559 − 2.18588I 0
u = 0.285149 + 1.085700I
a = −0.262963 + 1.112650I
b = 1.035310 − 0.663440I
7.49110 + 4.12587I 0
u = 0.285149 − 1.085700I
a = −0.262963 − 1.112650I
b = 1.035310 + 0.663440I
7.49110 − 4.12587I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.404547 + 1.051810I
a = −0.220162 − 1.151750I
b = 0.573320 + 0.814273I
8.88154 − 1.39549I 0
u = 0.404547 − 1.051810I
a = −0.220162 + 1.151750I
b = 0.573320 − 0.814273I
8.88154 + 1.39549I 0
u = 0.669709 + 0.987448I
a = −0.659904 + 0.714844I
b = 0.453835 − 0.861154I
8.12466 − 5.17001I 0
u = 0.669709 − 0.987448I
a = −0.659904 − 0.714844I
b = 0.453835 + 0.861154I
8.12466 + 5.17001I 0
u = −0.743128 + 0.238456I
a = 0.936570 − 0.552245I
b = 0.670993 + 0.510713I
2.69972 + 1.11767I −8.46846 − 0.34647I
u = −0.743128 − 0.238456I
a = 0.936570 + 0.552245I
b = 0.670993 − 0.510713I
2.69972 − 1.11767I −8.46846 + 0.34647I
u = −0.528811 + 0.566420I
a = 0.30265 + 2.22515I
b = 1.101470 − 0.618329I
0.93164 + 8.30570I −13.1243 − 9.3739I
u = −0.528811 − 0.566420I
a = 0.30265 − 2.22515I
b = 1.101470 + 0.618329I
0.93164 − 8.30570I −13.1243 + 9.3739I
u = 0.761650 + 0.974344I
a = 0.37235 − 1.64135I
b = 1.113920 + 0.647715I
6.14001 − 10.75700I 0
u = 0.761650 − 0.974344I
a = 0.37235 + 1.64135I
b = 1.113920 − 0.647715I
6.14001 + 10.75700I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.245470 + 0.133358I
a = 0.291110 − 0.847829I
b = 0.746809 + 0.711067I
−0.83961 − 2.58594I 0
u = 1.245470 − 0.133358I
a = 0.291110 + 0.847829I
b = 0.746809 − 0.711067I
−0.83961 + 2.58594I 0
u = −1.202630 + 0.422167I
a = 0.159393 − 0.613266I
b = 0.866243 + 0.666328I
2.92901 + 1.26794I 0
u = −1.202630 − 0.422167I
a = 0.159393 + 0.613266I
b = 0.866243 − 0.666328I
2.92901 − 1.26794I 0
u = −0.434384 + 0.537078I
a = −1.142120 − 0.805181I
b = 0.438054 + 0.799462I
2.90437 + 2.98477I −9.55591 − 5.23848I
u = −0.434384 − 0.537078I
a = −1.142120 + 0.805181I
b = 0.438054 − 0.799462I
2.90437 − 2.98477I −9.55591 + 5.23848I
u = −1.312810 + 0.029010I
a = −0.553493 − 0.125261I
b = 0.324181 + 0.863693I
0.185868 + 1.219880I 0
u = −1.312810 − 0.029010I
a = −0.553493 + 0.125261I
b = 0.324181 − 0.863693I
0.185868 − 1.219880I 0
u = 1.359630 + 0.023425I
a = −0.90230 − 1.79054I
b = −1.053060 + 0.510916I
−4.34022 + 0.45005I 0
u = 1.359630 − 0.023425I
a = −0.90230 + 1.79054I
b = −1.053060 − 0.510916I
−4.34022 − 0.45005I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.364690 + 0.077002I
a = 1.17174 + 1.47880I
b = 1.160950 − 0.604080I
−2.30932 + 6.62917I 0
u = −1.364690 − 0.077002I
a = 1.17174 − 1.47880I
b = 1.160950 + 0.604080I
−2.30932 − 6.62917I 0
u = 0.457361 + 0.415520I
a = 0.10898 + 2.86219I
b = −0.946808 − 0.440327I
−1.58018 − 2.82736I −15.3914 + 7.4030I
u = 0.457361 − 0.415520I
a = 0.10898 − 2.86219I
b = −0.946808 + 0.440327I
−1.58018 + 2.82736I −15.3914 − 7.4030I
u = −1.383020 + 0.067923I
a = −1.162760 + 0.218155I
b = −1.266990 + 0.222352I
−5.03426 + 2.16541I 0
u = −1.383020 − 0.067923I
a = −1.162760 − 0.218155I
b = −1.266990 − 0.222352I
−5.03426 − 2.16541I 0
u = 1.378230 + 0.145858I
a = 0.679555 + 0.442834I
b = −0.377108 − 0.555718I
−2.43296 − 3.85164I 0
u = 1.378230 − 0.145858I
a = 0.679555 − 0.442834I
b = −0.377108 + 0.555718I
−2.43296 + 3.85164I 0
u = −0.327143 + 0.472697I
a = 0.912647 + 0.072753I
b = 0.063180 + 0.313296I
2.85428 + 1.54452I −7.25846 − 4.25517I
u = −0.327143 − 0.472697I
a = 0.912647 − 0.072753I
b = 0.063180 − 0.313296I
2.85428 − 1.54452I −7.25846 + 4.25517I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.44455 + 0.07637I
a = 0.681802 + 0.524693I
b = −0.430423 − 0.562966I
−6.23300 + 0.57167I 0
u = −1.44455 − 0.07637I
a = 0.681802 − 0.524693I
b = −0.430423 + 0.562966I
−6.23300 − 0.57167I 0
u = −1.38481 + 0.42788I
a = 0.190392 + 0.906474I
b = 0.729122 − 0.763915I
3.37635 + 6.67232I 0
u = −1.38481 − 0.42788I
a = 0.190392 − 0.906474I
b = 0.729122 + 0.763915I
3.37635 − 6.67232I 0
u = −0.166020 + 0.514578I
a = −0.44693 + 1.85551I
b = 0.518731 − 0.743814I
3.42589 + 0.03376I −7.43382 − 3.19727I
u = −0.166020 − 0.514578I
a = −0.44693 − 1.85551I
b = 0.518731 + 0.743814I
3.42589 − 0.03376I −7.43382 + 3.19727I
u = −0.442772 + 0.285049I
a = −0.529533 − 0.735122I
b = −1.155150 − 0.126670I
−2.38286 + 0.75626I −14.3003 − 8.7966I
u = −0.442772 − 0.285049I
a = −0.529533 + 0.735122I
b = −1.155150 + 0.126670I
−2.38286 − 0.75626I −14.3003 + 8.7966I
u = −0.050728 + 0.520709I
a = −1.27689 − 1.67775I
b = 1.053540 + 0.606874I
1.82638 − 5.10869I −10.33632 + 2.79274I
u = −0.050728 − 0.520709I
a = −1.27689 + 1.67775I
b = 1.053540 − 0.606874I
1.82638 + 5.10869I −10.33632 − 2.79274I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.48422 + 0.11960I
a = −1.091750 + 0.198604I
b = −1.280200 + 0.207550I
−8.74917 − 2.34681I 0
u = 1.48422 − 0.11960I
a = −1.091750 − 0.198604I
b = −1.280200 − 0.207550I
−8.74917 + 2.34681I 0
u = 1.48081 + 0.20261I
a = −0.517683 + 0.219188I
b = 0.336394 − 0.886288I
−3.35067 − 5.75212I 0
u = 1.48081 − 0.20261I
a = −0.517683 − 0.219188I
b = 0.336394 + 0.886288I
−3.35067 + 5.75212I 0
u = −1.48858 + 0.15570I
a = −0.76126 − 1.73875I
b = −1.043700 + 0.528714I
−7.98070 + 4.98123I 0
u = −1.48858 − 0.15570I
a = −0.76126 + 1.73875I
b = −1.043700 − 0.528714I
−7.98070 − 4.98123I 0
u = 1.47731 + 0.29233I
a = 0.676255 − 0.600632I
b = −0.476333 + 0.571535I
−2.13437 − 4.97965I 0
u = 1.47731 − 0.29233I
a = 0.676255 + 0.600632I
b = −0.476333 − 0.571535I
−2.13437 + 4.97965I 0
u = 1.53297 + 0.07025I
a = 0.938110 + 0.143254I
b = 0.984287 + 0.354066I
−5.50382 − 5.89106I 0
u = 1.53297 − 0.07025I
a = 0.938110 − 0.143254I
b = 0.984287 − 0.354066I
−5.50382 + 5.89106I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52594 + 0.21463I
a = 1.05573 − 1.41124I
b = 1.166350 + 0.614109I
−5.84280 − 11.26350I 0
u = 1.52594 − 0.21463I
a = 1.05573 + 1.41124I
b = 1.166350 − 0.614109I
−5.84280 + 11.26350I 0
u = −0.438199 + 0.090942I
a = −0.71864 + 1.28993I
b = 1.023580 + 0.544299I
1.40601 − 5.44440I −11.95126 + 6.52227I
u = −0.438199 − 0.090942I
a = −0.71864 − 1.28993I
b = 1.023580 − 0.544299I
1.40601 + 5.44440I −11.95126 − 6.52227I
u = −1.53643 + 0.30203I
a = −1.038800 − 0.184797I
b = −1.290020 − 0.193740I
−4.57501 + 6.82873I 0
u = −1.53643 − 0.30203I
a = −1.038800 + 0.184797I
b = −1.290020 + 0.193740I
−4.57501 − 6.82873I 0
u = −1.58629 + 0.05555I
a = 0.930451 + 0.108721I
b = 0.969777 + 0.339351I
−9.36860 − 1.19827I 0
u = −1.58629 − 0.05555I
a = 0.930451 − 0.108721I
b = 0.969777 − 0.339351I
−9.36860 + 1.19827I 0
u = 1.56074 + 0.32973I
a = −0.65568 + 1.70420I
b = −1.033980 − 0.542121I
−3.74298 − 9.47180I 0
u = 1.56074 − 0.32973I
a = −0.65568 − 1.70420I
b = −1.033980 + 0.542121I
−3.74298 + 9.47180I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59535 + 0.18384I
a = 0.922475 − 0.080974I
b = 0.953038 − 0.328264I
−5.30238 − 3.47210I 0
u = 1.59535 − 0.18384I
a = 0.922475 + 0.080974I
b = 0.953038 + 0.328264I
−5.30238 + 3.47210I 0
u = −1.57920 + 0.37233I
a = −0.496415 − 0.282202I
b = 0.348581 + 0.901087I
0.96810 + 10.23090I 0
u = −1.57920 − 0.37233I
a = −0.496415 + 0.282202I
b = 0.348581 − 0.901087I
0.96810 − 10.23090I 0
u = 0.164890 + 0.328364I
a = 2.32898 − 1.39189I
b = −0.829025 + 0.304193I
−0.893071 + 0.448349I −12.04732 + 1.92652I
u = 0.164890 − 0.328364I
a = 2.32898 + 1.39189I
b = −0.829025 − 0.304193I
−0.893071 − 0.448349I −12.04732 − 1.92652I
u = 0.361635
a = 1.02021
b = −0.134399
−0.560922 −17.5600
u = −1.62225 + 0.36056I
a = 0.97081 + 1.37626I
b = 1.168610 − 0.622869I
−1.5044 + 15.8184I 0
u = −1.62225 − 0.36056I
a = 0.97081 − 1.37626I
b = 1.168610 + 0.622869I
−1.5044 − 15.8184I 0
u = 0.103264 + 0.221522I
a = −4.46938 − 1.58365I
b = −1.076350 − 0.292667I
−0.176220 − 1.062730I −15.2379 + 0.1443I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.103264 − 0.221522I
a = −4.46938 + 1.58365I
b = −1.076350 + 0.292667I
−0.176220 + 1.062730I −15.2379 − 0.1443I
13
II. I
u
2
= hb + 1, a + 1, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
u
2
a
11
=
−u
−u
3
+ u
a
3
=
−1
−1
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−2
−1
a
1
=
−1
0
a
4
=
−1
−1
a
9
=
u
u
a
8
=
u
u
a
12
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
5
− 4u − 15
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
8
u
6
c
4
(u + 1)
6
c
5
, c
6
, c
9
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
7
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
10
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
c
11
, c
12
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
8
y
6
c
5
, c
6
, c
9
c
10
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
c
7
, c
11
, c
12
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493180 + 0.575288I
a = −1.00000
b = −1.00000
1.31531 + 1.97241I −12.92955 − 2.53106I
u = −0.493180 − 0.575288I
a = −1.00000
b = −1.00000
1.31531 − 1.97241I −12.92955 + 2.53106I
u = 0.483672
a = −1.00000
b = −1.00000
−2.38379 −16.9080
u = 1.52087 + 0.16310I
a = −1.00000
b = −1.00000
−5.34051 − 4.59213I −13.8770 + 3.6103I
u = 1.52087 − 0.16310I
a = −1.00000
b = −1.00000
−5.34051 + 4.59213I −13.8770 − 3.6103I
u = −1.53904
a = −1.00000
b = −1.00000
−9.30502 −17.4790
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
81
+ 39u
80
+ ··· + 52u + 1)
c
2
((u − 1)
6
)(u
81
− 7u
80
+ ··· + 2u + 1)
c
3
, c
8
u
6
(u
81
− u
80
+ ··· + 64u + 64)
c
4
((u + 1)
6
)(u
81
− 7u
80
+ ··· + 2u + 1)
c
5
, c
6
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
81
− 2u
80
+ ··· − 27u + 9)
c
7
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
81
+ 2u
80
+ ··· + 3u + 1)
c
9
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
81
+ 8u
80
+ ··· − 3141u + 2537)
c
10
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
81
− 2u
80
+ ··· − 27u + 9)
c
11
, c
12
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
81
+ 2u
80
+ ··· + 3u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
81
+ 13y
80
+ ··· + 3164y −1)
c
2
, c
4
((y −1)
6
)(y
81
− 39y
80
+ ··· + 52y −1)
c
3
, c
8
y
6
(y
81
+ 39y
80
+ ··· − 40960y −4096)
c
5
, c
6
, c
10
(y
6
− 7y
5
+ ··· − 5y + 1)(y
81
− 80y
80
+ ··· − 693y −81)
c
7
, c
11
, c
12
(y
6
+ 5y
5
+ ··· − 5y + 1)(y
81
+ 64y
80
+ ··· + 11y −1)
c
9
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
81
+ 4y
80
+ ··· + 43125951y −6436369)
19
