12a
0424
(K12a
0424
)
A knot diagram
1
Linearized knot diagam
3 6 10 7 2 5 12 1 11 4 9 8
Solving Sequence
3,10
4
6,11
2 1 5 7 9 8 12
c
3
c
10
c
2
c
1
c
5
c
6
c
9
c
8
c
12
c
4
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−6.05060 × 10
58
u
67
− 1.04724 × 10
59
u
66
+ ··· + 1.01515 × 10
59
b + 8.01162 × 10
59
,
7.86149 × 10
58
u
67
+ 1.36435 × 10
59
u
66
+ ··· + 3.38385 × 10
58
a − 9.50671 × 10
59
, u
68
+ u
67
+ ··· − 4u + 8i
I
v
1
= ha, b − v + 1, v
3
− 2v
2
+ v −1i
* 2 irreducible components of dim
C
= 0, with total 71 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−6.05×10
58
u
67
−1.05×10
59
u
66
+· · ·+1.02×10
59
b+8.01×10
59
, 7.86×
10
58
u
67
+1.36×10
59
u
66
+· · ·+3.38×10
58
a−9.51×10
59
, u
68
+u
67
+· · ·−4u+8i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
−u
2
a
6
=
−2.32324u
67
− 4.03195u
66
+ ··· + 33.5515u + 28.0944
0.596027u
67
+ 1.03160u
66
+ ··· − 6.46797u − 7.89203
a
11
=
u
−u
3
+ u
a
2
=
−1.77029u
67
− 2.91509u
66
+ ··· + 24.3748u + 22.7432
0.564882u
67
+ 0.682242u
66
+ ··· − 5.65045u − 4.24863
a
1
=
−1.20541u
67
− 2.23285u
66
+ ··· + 18.7243u + 18.4946
0.564882u
67
+ 0.682242u
66
+ ··· − 5.65045u − 4.24863
a
5
=
−0.694072u
67
− 1.44115u
66
+ ··· + 11.5944u + 11.4434
0.204815u
67
+ 0.394112u
66
+ ··· − 0.0438270u − 5.62061
a
7
=
−1.77029u
67
− 2.91509u
66
+ ··· + 24.3748u + 22.7432
0.269738u
67
+ 0.621521u
66
+ ··· − 3.93271u − 4.90972
a
9
=
−u
3
u
5
− u
3
+ u
a
8
=
1.22840u
67
+ 2.01698u
66
+ ··· − 18.5328u − 16.9508
−0.265656u
67
− 0.556698u
66
+ ··· + 4.05685u + 6.12494
a
12
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.40934u
67
− 1.84025u
66
+ ··· + 36.8272u + 15.8368
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
u
68
+ 18u
67
+ ··· + 11u + 1
c
2
, c
5
u
68
+ 2u
67
+ ··· + 3u − 1
c
3
, c
10
u
68
+ u
67
+ ··· − 4u + 8
c
7
, c
8
, c
12
u
68
+ 4u
67
+ ··· − 8u
2
− 1
c
9
, c
11
u
68
− 21u
67
+ ··· − 720u + 64
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
y
68
+ 66y
67
+ ··· − 19y + 1
c
2
, c
5
y
68
− 18y
67
+ ··· − 11y + 1
c
3
, c
10
y
68
− 21y
67
+ ··· − 720y + 64
c
7
, c
8
, c
12
y
68
− 56y
67
+ ··· + 16y + 1
c
9
, c
11
y
68
+ 47y
67
+ ··· − 19712y + 4096
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.993071 + 0.113125I
a = −1.89033 − 2.06207I
b = 0.881273 + 0.827269I
6.85914 − 0.90233I 8.48968 − 1.09090I
u = 0.993071 − 0.113125I
a = −1.89033 + 2.06207I
b = 0.881273 − 0.827269I
6.85914 + 0.90233I 8.48968 + 1.09090I
u = 0.659498 + 0.764722I
a = 0.550961 + 0.309922I
b = 0.040503 − 0.569798I
0.588563 − 1.246350I 5.81021 + 0.45012I
u = 0.659498 − 0.764722I
a = 0.550961 − 0.309922I
b = 0.040503 + 0.569798I
0.588563 + 1.246350I 5.81021 − 0.45012I
u = −1.000140 + 0.155243I
a = −0.98075 − 2.90583I
b = 0.913795 + 0.817365I
6.75864 − 5.23492I 7.99359 + 6.56298I
u = −1.000140 − 0.155243I
a = −0.98075 + 2.90583I
b = 0.913795 − 0.817365I
6.75864 + 5.23492I 7.99359 − 6.56298I
u = 0.021687 + 1.023690I
a = −0.218747 + 0.841325I
b = −0.898997 − 0.825730I
8.72956 − 3.07936I 8.43070 + 2.69230I
u = 0.021687 − 1.023690I
a = −0.218747 − 0.841325I
b = −0.898997 + 0.825730I
8.72956 + 3.07936I 8.43070 − 2.69230I
u = 0.991893 + 0.263165I
a = −0.412778 − 1.347760I
b = −0.884341 + 0.498364I
5.18458 + 4.97460I 7.77509 − 7.49917I
u = 0.991893 − 0.263165I
a = −0.412778 + 1.347760I
b = −0.884341 − 0.498364I
5.18458 − 4.97460I 7.77509 + 7.49917I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.829279 + 0.618745I
a = −0.332097 − 0.896610I
b = −0.970966 + 0.736214I
3.84635 + 0.92115I 5.28354 + 1.08542I
u = −0.829279 − 0.618745I
a = −0.332097 + 0.896610I
b = −0.970966 − 0.736214I
3.84635 − 0.92115I 5.28354 − 1.08542I
u = −0.697002 + 0.783946I
a = −0.105875 + 0.873399I
b = −0.785825 − 0.814885I
0.83003 − 1.22443I 2.00000 + 2.28588I
u = −0.697002 − 0.783946I
a = −0.105875 − 0.873399I
b = −0.785825 + 0.814885I
0.83003 + 1.22443I 2.00000 − 2.28588I
u = 0.884256 + 0.567359I
a = −0.044342 − 0.919731I
b = −0.732492 + 0.772305I
4.53565 + 4.78229I 7.19204 − 6.23856I
u = 0.884256 − 0.567359I
a = −0.044342 + 0.919731I
b = −0.732492 − 0.772305I
4.53565 − 4.78229I 7.19204 + 6.23856I
u = −1.061960 + 0.111325I
a = 0.459698 − 0.837106I
b = −0.392765 + 0.607634I
6.64379 − 0.94912I 11.95029 + 0.I
u = −1.061960 − 0.111325I
a = 0.459698 + 0.837106I
b = −0.392765 − 0.607634I
6.64379 + 0.94912I 11.95029 + 0.I
u = 0.890731 + 0.590142I
a = −1.76219 − 0.11747I
b = 0.809278 + 0.829802I
4.59428 − 0.22084I 6.48510 + 0.I
u = 0.890731 − 0.590142I
a = −1.76219 + 0.11747I
b = 0.809278 − 0.829802I
4.59428 + 0.22084I 6.48510 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.716202 + 0.821100I
a = −0.311479 + 0.865388I
b = −0.969652 − 0.768571I
0.27108 − 4.71837I 0
u = 0.716202 − 0.821100I
a = −0.311479 − 0.865388I
b = −0.969652 + 0.768571I
0.27108 + 4.71837I 0
u = −0.800894 + 0.745034I
a = −1.40099 + 1.63231I
b = −0.971234 − 0.263287I
−2.36206 − 1.49059I 0
u = −0.800894 − 0.745034I
a = −1.40099 − 1.63231I
b = −0.971234 + 0.263287I
−2.36206 + 1.49059I 0
u = −0.909702 + 0.630284I
a = 0.94341 − 2.77762I
b = 0.964261 + 0.783946I
4.11637 − 5.81729I 0
u = −0.909702 − 0.630284I
a = 0.94341 + 2.77762I
b = 0.964261 − 0.783946I
4.11637 + 5.81729I 0
u = 0.876321
a = 0.998697
b = 0.963850
2.31122 4.45630
u = −0.867744 + 0.719052I
a = 0.502678 − 0.415224I
b = −0.051505 + 0.630284I
−2.78825 − 2.74528I 0
u = −0.867744 − 0.719052I
a = 0.502678 + 0.415224I
b = −0.051505 − 0.630284I
−2.78825 + 2.74528I 0
u = −0.723892 + 0.871174I
a = 1.099390 − 0.016027I
b = 0.977262 − 0.289069I
−2.20577 + 4.23347I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.723892 − 0.871174I
a = 1.099390 + 0.016027I
b = 0.977262 + 0.289069I
−2.20577 − 4.23347I 0
u = 0.829532 + 0.792287I
a = 1.069520 + 0.001488I
b = 0.995888 + 0.247406I
−6.00877 − 0.07335I 0
u = 0.829532 − 0.792287I
a = 1.069520 − 0.001488I
b = 0.995888 − 0.247406I
−6.00877 + 0.07335I 0
u = 0.637253 + 0.973593I
a = −0.123805 − 0.840626I
b = −0.805330 + 0.845791I
5.07615 − 2.51950I 0
u = 0.637253 − 0.973593I
a = −0.123805 + 0.840626I
b = −0.805330 − 0.845791I
5.07615 + 2.51950I 0
u = −0.781819 + 0.294985I
a = −0.05603 + 1.97815I
b = −0.755261 − 0.362856I
0.13820 − 2.92436I 2.59443 + 9.53509I
u = −0.781819 − 0.294985I
a = −0.05603 − 1.97815I
b = −0.755261 + 0.362856I
0.13820 + 2.92436I 2.59443 − 9.53509I
u = −0.933508 + 0.715246I
a = 1.048350 + 0.008631I
b = 1.016160 − 0.211403I
−1.94942 − 4.06921I 0
u = −0.933508 − 0.715246I
a = 1.048350 − 0.008631I
b = 1.016160 + 0.211403I
−1.94942 + 4.06921I 0
u = −0.667756 + 0.982329I
a = −0.302229 − 0.843220I
b = −0.972548 + 0.790652I
4.55831 + 8.62464I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.667756 − 0.982329I
a = −0.302229 + 0.843220I
b = −0.972548 − 0.790652I
4.55831 − 8.62464I 0
u = 0.923270 + 0.765436I
a = −1.25292 − 1.44461I
b = −0.999457 + 0.296326I
−5.71945 + 5.92897I 0
u = 0.923270 − 0.765436I
a = −1.25292 + 1.44461I
b = −0.999457 − 0.296326I
−5.71945 − 5.92897I 0
u = −0.996451 + 0.711234I
a = −1.309380 + 0.201391I
b = 0.794344 − 0.853811I
1.73332 − 4.42504I 0
u = −0.996451 − 0.711234I
a = −1.309380 − 0.201391I
b = 0.794344 + 0.853811I
1.73332 + 4.42504I 0
u = 0.170683 + 0.754290I
a = 0.848846 + 0.211083I
b = 0.635194 + 0.359962I
2.32891 − 1.45239I 4.90559 + 4.31092I
u = 0.170683 − 0.754290I
a = 0.848846 − 0.211083I
b = 0.635194 − 0.359962I
2.32891 + 1.45239I 4.90559 − 4.31092I
u = 1.008450 + 0.698435I
a = 0.456475 + 0.467018I
b = −0.098986 − 0.677355I
1.62108 + 6.80691I 0
u = 1.008450 − 0.698435I
a = 0.456475 − 0.467018I
b = −0.098986 + 0.677355I
1.62108 − 6.80691I 0
u = 1.003540 + 0.733346I
a = 0.89900 + 2.36045I
b = 0.981570 − 0.789856I
1.15325 + 10.54940I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.003540 − 0.733346I
a = 0.89900 − 2.36045I
b = 0.981570 + 0.789856I
1.15325 − 10.54940I 0
u = −1.234530 + 0.258857I
a = −1.25723 + 1.36690I
b = 0.873045 − 0.864648I
13.36960 − 1.32073I 0
u = −1.234530 − 0.258857I
a = −1.25723 − 1.36690I
b = 0.873045 + 0.864648I
13.36960 + 1.32073I 0
u = 1.231130 + 0.291396I
a = −0.32877 + 2.27833I
b = 0.940263 − 0.838288I
13.1585 + 7.6380I 0
u = 1.231130 − 0.291396I
a = −0.32877 − 2.27833I
b = 0.940263 + 0.838288I
13.1585 − 7.6380I 0
u = −1.017380 + 0.758083I
a = −1.15099 + 1.34572I
b = −1.016370 − 0.322893I
−1.29085 − 10.28430I 0
u = −1.017380 − 0.758083I
a = −1.15099 − 1.34572I
b = −1.016370 + 0.322893I
−1.29085 + 10.28430I 0
u = 0.676957 + 0.032911I
a = 1.18518 + 1.04468I
b = −0.420279 − 0.292993I
1.049650 + 0.101234I 9.47396 − 0.04712I
u = 0.676957 − 0.032911I
a = 1.18518 − 1.04468I
b = −0.420279 + 0.292993I
1.049650 − 0.101234I 9.47396 + 0.04712I
u = 1.094230 + 0.755851I
a = −1.129750 − 0.325888I
b = 0.793548 + 0.872752I
6.52598 + 8.82716I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.094230 − 0.755851I
a = −1.129750 + 0.325888I
b = 0.793548 − 0.872752I
6.52598 − 8.82716I 0
u = −1.091090 + 0.774273I
a = 0.79093 − 2.16616I
b = 0.990918 + 0.798516I
5.9100 − 15.0350I 0
u = −1.091090 − 0.774273I
a = 0.79093 + 2.16616I
b = 0.990918 − 0.798516I
5.9100 + 15.0350I 0
u = −0.022492 + 0.551897I
a = −0.220910 − 0.899639I
b = −0.884082 + 0.773478I
3.60354 + 2.91698I −1.07047 − 2.93516I
u = −0.022492 − 0.551897I
a = −0.220910 + 0.899639I
b = −0.884082 − 0.773478I
3.60354 − 2.91698I −1.07047 + 2.93516I
u = 0.528183
a = 2.56903
b = −0.477187
1.06452 11.9270
u = −0.298991 + 0.383237I
a = 0.953304 − 0.043713I
b = 0.759455 − 0.112169I
−1.254010 + 0.311770I −6.76966 − 0.58136I
u = −0.298991 − 0.383237I
a = 0.953304 + 0.043713I
b = 0.759455 + 0.112169I
−1.254010 − 0.311770I −6.76966 + 0.58136I
11
II. I
v
1
= ha, b − v + 1, v
3
− 2v
2
+ v − 1i
(i) Arc colorings
a
3
=
1
0
a
10
=
v
0
a
4
=
1
0
a
6
=
0
v − 1
a
11
=
v
0
a
2
=
1
−v
2
+ 2v − 1
a
1
=
−v
2
+ 2v
−v
2
+ 2v − 1
a
5
=
v − 1
v
2
− v − 1
a
7
=
v
2
− 2v
v
2
− 2v + 1
a
9
=
v
0
a
8
=
v
2
− v
v
2
− 2v + 1
a
12
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −2v
2
− 3v + 7
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
3
, c
9
, c
10
c
11
u
3
c
5
u
3
− u
2
+ 1
c
6
u
3
+ u
2
+ 2u + 1
c
7
, c
8
(u + 1)
3
c
12
(u − 1)
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
y
3
+ 3y
2
+ 2y − 1
c
2
, c
5
y
3
− y
2
+ 2y − 1
c
3
, c
9
, c
10
c
11
y
3
c
7
, c
8
, c
12
(y − 1)
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.122561 + 0.744862I
a = 0
b = −0.877439 + 0.744862I
4.66906 + 2.82812I 7.71191 − 2.59975I
v = 0.122561 − 0.744862I
a = 0
b = −0.877439 − 0.744862I
4.66906 − 2.82812I 7.71191 + 2.59975I
v = 1.75488
a = 0
b = 0.754878
0.531480 −4.42380
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
3
− u
2
+ 2u − 1)(u
68
+ 18u
67
+ ··· + 11u + 1)
c
2
(u
3
+ u
2
− 1)(u
68
+ 2u
67
+ ··· + 3u − 1)
c
3
, c
10
u
3
(u
68
+ u
67
+ ··· − 4u + 8)
c
5
(u
3
− u
2
+ 1)(u
68
+ 2u
67
+ ··· + 3u − 1)
c
6
(u
3
+ u
2
+ 2u + 1)(u
68
+ 18u
67
+ ··· + 11u + 1)
c
7
, c
8
((u + 1)
3
)(u
68
+ 4u
67
+ ··· − 8u
2
− 1)
c
9
, c
11
u
3
(u
68
− 21u
67
+ ··· − 720u + 64)
c
12
((u − 1)
3
)(u
68
+ 4u
67
+ ··· − 8u
2
− 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
(y
3
+ 3y
2
+ 2y − 1)(y
68
+ 66y
67
+ ··· − 19y + 1)
c
2
, c
5
(y
3
− y
2
+ 2y − 1)(y
68
− 18y
67
+ ··· − 11y + 1)
c
3
, c
10
y
3
(y
68
− 21y
67
+ ··· − 720y + 64)
c
7
, c
8
, c
12
((y − 1)
3
)(y
68
− 56y
67
+ ··· + 16y + 1)
c
9
, c
11
y
3
(y
68
+ 47y
67
+ ··· − 19712y + 4096)
17
