12a
0304
(K12a
0304
)
A knot diagram
1
Linearized knot diagam
3 6 8 10 7 2 1 11 12 4 9 5
Solving Sequence
2,6
3 7 1 8
5,10
4 11 12 9
c
2
c
6
c
1
c
7
c
5
c
4
c
10
c
12
c
9
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
76
+ u
75
+ ··· + 7u
2
+ b, 2u
76
+ 2u
75
+ ··· + a − 1, u
77
+ 2u
76
+ ··· − u − 1i
I
u
2
= h−u
8
+ u
7
− u
6
+ u
5
− u
4
+ u
3
+ b + u, u
6
+ u
4
+ u
2
+ a + u, u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
* 2 irreducible components of dim
C
= 0, with total 86 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
= h2u
76
+u
75
+· · ·+7u
2
+b, 2u
76
+2u
75
+· · ·+a−1, u
77
+2u
76
+· · ·−u−1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
1
=
u
2
+ 1
−u
4
a
8
=
u
7
+ 2u
5
+ 2u
3
+ 2u
−u
9
− u
7
− u
5
+ u
a
5
=
u
3
u
3
+ u
a
10
=
−2u
76
− 2u
75
+ ··· + 5u + 1
−2u
76
− u
75
+ ··· − 15u
3
− 7u
2
a
4
=
−u
14
− 3u
12
− 6u
10
− 9u
8
− 8u
6
− 6u
4
− 2u
2
+ 1
u
16
+ 2u
14
+ 4u
12
+ 4u
10
+ 2u
8
− 2u
4
− 2u
2
a
11
=
u
73
+ u
72
+ ··· + 8u
2
+ 5u
−u
75
− u
74
+ ··· − 6u
2
− u
a
12
=
u
10
+ u
8
+ 2u
6
+ u
4
+ u
2
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
9
=
−u
76
− u
75
+ ··· + 6u + 1
−u
76
− u
75
+ ··· − 14u
3
− 6u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
76
− 6u
75
+ ··· + 4u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
77
+ 24u
76
+ ··· + 11u − 1
c
2
, c
6
u
77
− 2u
76
+ ··· − u + 1
c
3
, c
12
u
77
− 2u
76
+ ··· − 645u + 241
c
4
, c
10
u
77
− u
76
+ ··· + 512u + 512
c
7
u
77
+ 10u
76
+ ··· + 45303u + 6643
c
8
, c
9
, c
11
u
77
+ 10u
76
+ ··· + 7u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
77
+ 60y
76
+ ··· + 131y −1
c
2
, c
6
y
77
+ 24y
76
+ ··· + 11y −1
c
3
, c
12
y
77
− 72y
76
+ ··· − 658353y −58081
c
4
, c
10
y
77
+ 57y
76
+ ··· + 786432y −262144
c
7
y
77
− 24y
76
+ ··· + 567824027y −44129449
c
8
, c
9
, c
11
y
77
− 80y
76
+ ··· + 15y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.699304 + 0.727429I
a = −0.81750 + 1.62981I
b = 1.09069 + 1.48911I
1.98631 − 1.49498I 0
u = 0.699304 − 0.727429I
a = −0.81750 − 1.62981I
b = 1.09069 − 1.48911I
1.98631 + 1.49498I 0
u = 0.744909 + 0.652303I
a = 1.26089 − 1.11132I
b = −0.58742 − 1.53965I
7.63346 − 4.09071I 11.11372 + 0.I
u = 0.744909 − 0.652303I
a = 1.26089 + 1.11132I
b = −0.58742 + 1.53965I
7.63346 + 4.09071I 11.11372 + 0.I
u = 0.255824 + 0.983693I
a = −2.12297 + 1.21195I
b = −0.696626 + 0.485271I
2.47634 + 0.27430I 0
u = 0.255824 − 0.983693I
a = −2.12297 − 1.21195I
b = −0.696626 − 0.485271I
2.47634 − 0.27430I 0
u = −0.170505 + 0.968417I
a = −0.123996 + 0.383932I
b = 0.236307 + 0.425064I
−1.37887 − 2.37996I 0. + 4.42703I
u = −0.170505 − 0.968417I
a = −0.123996 − 0.383932I
b = 0.236307 − 0.425064I
−1.37887 + 2.37996I 0. − 4.42703I
u = −0.049028 + 0.970113I
a = 0.677255 + 0.372469I
b = 0.574789 − 0.544320I
−3.09814 − 1.84421I −3.35735 + 5.07051I
u = −0.049028 − 0.970113I
a = 0.677255 − 0.372469I
b = 0.574789 + 0.544320I
−3.09814 + 1.84421I −3.35735 − 5.07051I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.241315 + 1.005140I
a = 0.101331 − 0.745818I
b = −0.473125 − 0.927993I
4.49560 − 2.98378I 0
u = −0.241315 − 1.005140I
a = 0.101331 + 0.745818I
b = −0.473125 + 0.927993I
4.49560 + 2.98378I 0
u = −0.624221 + 0.829893I
a = 0.010477 + 0.678321I
b = −0.085050 + 0.648925I
0.50764 − 1.96211I 0
u = −0.624221 − 0.829893I
a = 0.010477 − 0.678321I
b = −0.085050 − 0.648925I
0.50764 + 1.96211I 0
u = 0.223875 + 1.016610I
a = 1.84493 − 1.38311I
b = 0.493359 − 0.072238I
2.19034 + 5.64361I 0
u = 0.223875 − 1.016610I
a = 1.84493 + 1.38311I
b = 0.493359 + 0.072238I
2.19034 − 5.64361I 0
u = −0.078493 + 1.040650I
a = −0.401232 − 0.523528I
b = −0.931882 + 0.327502I
1.89327 − 3.83436I 0
u = −0.078493 − 1.040650I
a = −0.401232 + 0.523528I
b = −0.931882 − 0.327502I
1.89327 + 3.83436I 0
u = 0.310575 + 0.996870I
a = 2.14157 − 1.01275I
b = 1.167780 − 0.616429I
9.61828 − 3.45293I 0
u = 0.310575 − 0.996870I
a = 2.14157 + 1.01275I
b = 1.167780 + 0.616429I
9.61828 + 3.45293I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.717183 + 0.773636I
a = −0.688793 − 1.001440I
b = −0.47922 − 1.34039I
4.52846 − 0.10642I 0
u = −0.717183 − 0.773636I
a = −0.688793 + 1.001440I
b = −0.47922 + 1.34039I
4.52846 + 0.10642I 0
u = 0.219337 + 1.048440I
a = −1.58099 + 1.23292I
b = −0.576448 − 0.293765I
8.99981 + 9.75853I 0
u = 0.219337 − 1.048440I
a = −1.58099 − 1.23292I
b = −0.576448 + 0.293765I
8.99981 − 9.75853I 0
u = 0.704904 + 0.820857I
a = −0.16649 − 2.37291I
b = −2.35033 − 1.28135I
3.58538 + 2.22665I 0
u = 0.704904 − 0.820857I
a = −0.16649 + 2.37291I
b = −2.35033 + 1.28135I
3.58538 − 2.22665I 0
u = 0.807197 + 0.737360I
a = −0.566438 − 0.328800I
b = −0.580161 + 0.466851I
4.99997 − 1.53810I 0
u = 0.807197 − 0.737360I
a = −0.566438 + 0.328800I
b = −0.580161 − 0.466851I
4.99997 + 1.53810I 0
u = 0.043394 + 0.902576I
a = −1.53012 − 0.31935I
b = −0.469965 + 0.858865I
−0.372258 + 0.930123I 1.97825 + 1.00417I
u = 0.043394 − 0.902576I
a = −1.53012 + 0.31935I
b = −0.469965 − 0.858865I
−0.372258 − 0.930123I 1.97825 − 1.00417I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.563256 + 0.951321I
a = 0.866937 − 0.738751I
b = 1.091910 − 0.695769I
4.66955 − 1.97768I 0
u = −0.563256 − 0.951321I
a = 0.866937 + 0.738751I
b = 1.091910 + 0.695769I
4.66955 + 1.97768I 0
u = −0.837454 + 0.735539I
a = 0.97292 − 2.63486I
b = 3.85435 − 1.42730I
9.14362 + 4.92278I 0
u = −0.837454 − 0.735539I
a = 0.97292 + 2.63486I
b = 3.85435 + 1.42730I
9.14362 − 4.92278I 0
u = −0.848212 + 0.723641I
a = −0.65408 + 2.75056I
b = −3.60857 + 1.61834I
16.0825 + 9.2947I 0
u = −0.848212 − 0.723641I
a = −0.65408 − 2.75056I
b = −3.60857 − 1.61834I
16.0825 − 9.2947I 0
u = 0.837918 + 0.744240I
a = 1.131590 + 0.579415I
b = 1.08747 − 1.03259I
11.50510 − 2.10024I 0
u = 0.837918 − 0.744240I
a = 1.131590 − 0.579415I
b = 1.08747 + 1.03259I
11.50510 + 2.10024I 0
u = −0.646096 + 0.917216I
a = −0.846044 − 0.138690I
b = −0.772032 − 0.322959I
0.20183 − 3.00562I 0
u = −0.646096 − 0.917216I
a = −0.846044 + 0.138690I
b = −0.772032 + 0.322959I
0.20183 + 3.00562I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.833767 + 0.752545I
a = −1.13895 + 2.12752I
b = −3.71757 + 0.92447I
9.45729 − 0.80584I 0
u = −0.833767 − 0.752545I
a = −1.13895 − 2.12752I
b = −3.71757 − 0.92447I
9.45729 + 0.80584I 0
u = −0.842397 + 0.771277I
a = 0.72246 − 1.71278I
b = 3.13729 − 0.92017I
16.9497 − 4.8229I 0
u = −0.842397 − 0.771277I
a = 0.72246 + 1.71278I
b = 3.13729 + 0.92017I
16.9497 + 4.8229I 0
u = 0.695171 + 0.910303I
a = −1.68350 − 1.82196I
b = −3.07562 + 0.18717I
3.30878 + 3.15042I 0
u = 0.695171 − 0.910303I
a = −1.68350 + 1.82196I
b = −3.07562 − 0.18717I
3.30878 − 3.15042I 0
u = 0.778091 + 0.876907I
a = 0.78071 + 1.84733I
b = 2.58901 + 0.36941I
11.68920 + 2.92576I 0
u = 0.778091 − 0.876907I
a = 0.78071 − 1.84733I
b = 2.58901 − 0.36941I
11.68920 − 2.92576I 0
u = −0.701213 + 0.941339I
a = 1.24030 + 1.13056I
b = 0.57088 + 1.33782I
4.01964 − 5.33236I 0
u = −0.701213 − 0.941339I
a = 1.24030 − 1.13056I
b = 0.57088 − 1.33782I
4.01964 + 5.33236I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.686147 + 0.961876I
a = 1.75231 + 0.57908I
b = 2.14537 − 1.15325I
1.28678 + 6.84249I 0
u = 0.686147 − 0.961876I
a = 1.75231 − 0.57908I
b = 2.14537 + 1.15325I
1.28678 − 6.84249I 0
u = 0.685651 + 1.000130I
a = −1.67169 + 0.22266I
b = −1.46366 + 1.84464I
6.61216 + 9.54266I 0
u = 0.685651 − 1.000130I
a = −1.67169 − 0.22266I
b = −1.46366 − 1.84464I
6.61216 − 9.54266I 0
u = 0.736625 + 0.987761I
a = 0.098715 − 0.670264I
b = −0.640229 − 0.744065I
4.23362 + 7.34344I 0
u = 0.736625 − 0.987761I
a = 0.098715 + 0.670264I
b = −0.640229 + 0.744065I
4.23362 − 7.34344I 0
u = −0.757169 + 0.989788I
a = −2.14867 + 2.91335I
b = −3.80389 + 0.43415I
8.72641 − 5.14321I 0
u = −0.757169 − 0.989788I
a = −2.14867 − 2.91335I
b = −3.80389 − 0.43415I
8.72641 + 5.14321I 0
u = −0.771017 + 0.982703I
a = 1.78254 − 2.31369I
b = 3.04363 − 0.00238I
16.2966 − 1.1968I 0
u = −0.771017 − 0.982703I
a = 1.78254 + 2.31369I
b = 3.04363 + 0.00238I
16.2966 + 1.1968I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.755925 + 0.996210I
a = −0.272181 + 1.258230I
b = 1.18503 + 1.51805I
10.72910 + 8.05684I 0
u = 0.755925 − 0.996210I
a = −0.272181 − 1.258230I
b = 1.18503 − 1.51805I
10.72910 − 8.05684I 0
u = −0.751986 + 1.000640I
a = 2.80724 − 2.79451I
b = 4.40681 − 0.00361I
8.32809 − 10.86460I 0
u = −0.751986 − 1.000640I
a = 2.80724 + 2.79451I
b = 4.40681 + 0.00361I
8.32809 + 10.86460I 0
u = −0.752276 + 1.011150I
a = −2.96847 + 2.38538I
b = −4.43046 − 0.42786I
15.1972 − 15.2671I 0
u = −0.752276 − 1.011150I
a = −2.96847 − 2.38538I
b = −4.43046 + 0.42786I
15.1972 + 15.2671I 0
u = 0.689816 + 0.059020I
a = −0.29428 + 1.98529I
b = 0.338685 + 1.336490I
12.6051 + 6.8095I 13.22063 − 3.73865I
u = 0.689816 − 0.059020I
a = −0.29428 − 1.98529I
b = 0.338685 − 1.336490I
12.6051 − 6.8095I 13.22063 + 3.73865I
u = −0.663161
a = 1.42211
b = 0.101068
7.71855 12.4530
u = −0.572725 + 0.325539I
a = 1.04804 − 1.33507I
b = 0.476521 − 0.202237I
6.14632 − 2.18923I 11.48807 + 3.23279I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.572725 − 0.325539I
a = 1.04804 + 1.33507I
b = 0.476521 + 0.202237I
6.14632 + 2.18923I 11.48807 − 3.23279I
u = 0.658043 + 0.024681I
a = 0.12020 − 1.83501I
b = −0.17074 − 1.56090I
5.53553 + 2.75768I 11.68630 − 3.17781I
u = 0.658043 − 0.024681I
a = 0.12020 + 1.83501I
b = −0.17074 + 1.56090I
5.53553 − 2.75768I 11.68630 + 3.17781I
u = −0.561476
a = −0.758314
b = −0.0994541
1.63385 5.54490
u = −0.295497 + 0.256148I
a = −0.84022 + 1.42123I
b = −0.128866 + 0.378321I
0.365640 − 0.941295I 6.48634 + 7.23621I
u = −0.295497 − 0.256148I
a = −0.84022 − 1.42123I
b = −0.128866 − 0.378321I
0.365640 + 0.941295I 6.48634 − 7.23621I
u = 0.266849
a = 1.64859
b = −0.897687
2.07814 2.50950
12
II. I
u
2
= h−u
8
+ u
7
− u
6
+ u
5
− u
4
+ u
3
+ b + u, u
6
+ u
4
+ u
2
+ a + u, u
9
−
u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
−u
2
a
7
=
u
u
a
1
=
u
2
+ 1
−u
4
a
8
=
u
7
+ 2u
5
+ 2u
3
+ 2u
−u
8
+ u
7
− u
6
+ 2u
5
− u
4
+ 2u
3
+ 2u + 1
a
5
=
u
3
u
3
+ u
a
10
=
−u
6
− u
4
− u
2
− u
u
8
− u
7
+ u
6
− u
5
+ u
4
− u
3
− u
a
4
=
u
3
u
3
+ u
a
11
=
−u
6
− u
4
− u
2
− u
u
8
− u
7
+ u
6
− u
5
+ u
4
− u
3
− u
a
12
=
−u
7
− 2u
5
− 2u
3
− 2u
u
8
− u
7
+ u
6
− 2u
5
+ u
4
− 2u
3
− 2u − 1
a
9
=
u
7
− u
6
+ 2u
5
− u
4
+ 2u
3
− u
2
+ u
u
5
+ u
3
+ u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
7
+ 4u
6
− 5u
5
+ 5u
4
− 10u
3
+ 5u
2
− u + 11
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1
c
2
u
9
− u
8
+ 2u
7
− u
6
+ 3u
5
− u
4
+ 2u
3
+ u + 1
c
3
, c
12
u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1
c
4
, c
10
u
9
c
6
u
9
+ u
8
+ 2u
7
+ u
6
+ 3u
5
+ u
4
+ 2u
3
+ u − 1
c
7
u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1
c
8
, c
9
(u + 1)
9
c
11
(u − 1)
9
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1
c
2
, c
6
y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1
c
3
, c
12
y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1
c
4
, c
10
y
9
c
7
y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1
c
8
, c
9
, c
11
(y −1)
9
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140343 + 0.966856I
a = 0.855828 − 0.530357I
b = 0.154190 + 0.257272I
−0.13850 − 2.09337I 4.27981 + 4.44592I
u = −0.140343 − 0.966856I
a = 0.855828 + 0.530357I
b = 0.154190 − 0.257272I
−0.13850 + 2.09337I 4.27981 − 4.44592I
u = −0.628449 + 0.875112I
a = 0.77654 − 1.46791I
b = 1.76111 − 0.42995I
2.26187 − 2.45442I 4.16203 + 2.47153I
u = −0.628449 − 0.875112I
a = 0.77654 + 1.46791I
b = 1.76111 + 0.42995I
2.26187 + 2.45442I 4.16203 − 2.47153I
u = 0.796005 + 0.733148I
a = 0.852888 − 0.566992I
b = 0.430151 − 1.332530I
6.01628 − 1.33617I 13.03110 + 0.17445I
u = 0.796005 − 0.733148I
a = 0.852888 + 0.566992I
b = 0.430151 + 1.332530I
6.01628 + 1.33617I 13.03110 − 0.17445I
u = 0.728966 + 0.986295I
a = −1.06667 + 0.97795I
b = −0.23704 + 1.46509I
5.24306 + 7.08493I 11.12684 − 5.18429I
u = 0.728966 − 0.986295I
a = −1.06667 − 0.97795I
b = −0.23704 − 1.46509I
5.24306 − 7.08493I 11.12684 + 5.18429I
u = −0.512358
a = 0.162845
b = 0.783184
2.84338 14.8000
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
9
− 3u
8
+ 8u
7
− 13u
6
+ 17u
5
− 17u
4
+ 12u
3
− 6u
2
+ u + 1)
· (u
77
+ 24u
76
+ ··· + 11u − 1)
c
2
(u
9
− u
8
+ ··· + u + 1)(u
77
− 2u
76
+ ··· − u + 1)
c
3
, c
12
(u
9
− u
8
− 2u
7
+ 3u
6
+ u
5
− 3u
4
+ 2u
3
− u + 1)
· (u
77
− 2u
76
+ ··· − 645u + 241)
c
4
, c
10
u
9
(u
77
− u
76
+ ··· + 512u + 512)
c
6
(u
9
+ u
8
+ ··· + u − 1)(u
77
− 2u
76
+ ··· − u + 1)
c
7
(u
9
− 5u
8
+ 12u
7
− 15u
6
+ 9u
5
+ u
4
− 4u
3
+ 2u
2
+ u − 1)
· (u
77
+ 10u
76
+ ··· + 45303u + 6643)
c
8
, c
9
((u + 1)
9
)(u
77
+ 10u
76
+ ··· + 7u + 1)
c
11
((u − 1)
9
)(u
77
+ 10u
76
+ ··· + 7u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
9
+ 7y
8
+ 20y
7
+ 25y
6
+ 5y
5
− 15y
4
+ 22y
2
+ 13y −1)
· (y
77
+ 60y
76
+ ··· + 131y −1)
c
2
, c
6
(y
9
+ 3y
8
+ 8y
7
+ 13y
6
+ 17y
5
+ 17y
4
+ 12y
3
+ 6y
2
+ y −1)
· (y
77
+ 24y
76
+ ··· + 11y −1)
c
3
, c
12
(y
9
− 5y
8
+ 12y
7
− 15y
6
+ 9y
5
+ y
4
− 4y
3
+ 2y
2
+ y −1)
· (y
77
− 72y
76
+ ··· − 658353y −58081)
c
4
, c
10
y
9
(y
77
+ 57y
76
+ ··· + 786432y −262144)
c
7
(y
9
− y
8
+ 12y
7
− 7y
6
+ 37y
5
+ y
4
− 10y
2
+ 5y −1)
· (y
77
− 24y
76
+ ··· + 567824027y −44129449)
c
8
, c
9
, c
11
((y −1)
9
)(y
77
− 80y
76
+ ··· + 15y −1)
18
