12a
0563
(K12a
0563
)
A knot diagram
1
Linearized knot diagam
3 7 9 8 11 12 2 4 1 5 6 10
Solving Sequence
3,9 2,4
1 10 8 5 11 7 12 6
c
3
c
1
c
9
c
8
c
4
c
10
c
7
c
12
c
6
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.21428 × 10
21
u
47
+ 3.07657 × 10
21
u
46
+ ··· + 1.91294 × 10
22
b + 2.10944 × 10
22
,
8.01226 × 10
20
u
47
− 8.31592 × 10
20
u
46
+ ··· + 9.56472 × 10
20
a + 3.53130 × 10
21
, u
48
− u
47
+ ··· + u + 2i
I
u
2
= h−u
2
+ b, a − 1, u
18
+ 6u
16
+ ··· + u − 1i
I
u
3
= hb + 1, a
4
+ a
3
u − 4a
3
− 3a
2
u + 5a
2
+ 3au − 2a − u + 1, u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 74 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−3.21×10
21
u
47
+3.08×10
21
u
46
+· · ·+1.91×10
22
b+2.11×10
22
, 8.01×
10
20
u
47
−8.32×10
20
u
46
+· · ·+9.56×10
20
a+3.53×10
21
, u
48
−u
47
+· · ·+u+2i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
2
=
−0.837689u
47
+ 0.869438u
46
+ ··· + 13.2059u − 3.69201
0.168028u
47
− 0.160829u
46
+ ··· − 1.56252u − 1.10272
a
4
=
1
u
2
a
1
=
−0.669662u
47
+ 0.708609u
46
+ ··· + 11.6434u − 4.79473
0.168028u
47
− 0.160829u
46
+ ··· − 1.56252u − 1.10272
a
10
=
−0.573968u
47
+ 0.0603230u
46
+ ··· + 9.04562u + 5.11395
0.0433537u
47
+ 0.0687272u
46
+ ··· − 4.47263u + 1.08386
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
−0.775286u
47
+ 0.102961u
46
+ ··· + 16.4932u + 5.06341
0.115161u
47
− 0.190045u
46
+ ··· − 4.11240u + 0.828323
a
7
=
−0.519611u
47
+ 0.601722u
46
+ ··· + 25.7485u + 2.68654
−0.0513589u
47
− 0.116669u
46
+ ··· − 1.89721u + 1.51116
a
12
=
−1.34327u
47
+ 1.07781u
46
+ ··· + 27.0507u + 5.07361
−0.273830u
47
+ 0.198143u
46
+ ··· + 3.26013u − 0.158606
a
6
=
1.33343u
47
− 1.45372u
46
+ ··· − 17.4102u − 8.92856
0.00796109u
47
+ 0.0832675u
46
+ ··· − 0.966904u + 0.230758
(ii) Obstruction class = −1
(iii) Cusp Shapes =
27465448057329986227
27804404382329290780
u
47
−
1722649487279789829
2780440438232929078
u
46
+ ··· −
776992786016705604511
27804404382329290780
u −
198347232390961135567
13902202191164645390
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
48
+ 17u
47
+ ··· + 35u + 4
c
2
, c
7
u
48
+ u
47
+ ··· − 3u + 2
c
3
, c
4
, c
8
u
48
+ u
47
+ ··· − u + 2
c
5
, c
6
, c
10
c
11
u
48
− 2u
47
+ ··· + u + 2
c
9
, c
12
u
48
− 8u
47
+ ··· − 7639u + 1016
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
48
+ 37y
47
+ ··· + 12799y + 16
c
2
, c
7
y
48
+ 17y
47
+ ··· + 35y + 4
c
3
, c
4
, c
8
y
48
+ 53y
47
+ ··· − 237y + 4
c
5
, c
6
, c
10
c
11
y
48
− 52y
47
+ ··· + 19y + 4
c
9
, c
12
y
48
+ 32y
47
+ ··· − 318369y + 1032256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.279405 + 0.971105I
a = 0.633756 + 0.239746I
b = 0.165180 + 0.161172I
−4.68544 + 3.19221I −6.37639 − 4.16497I
u = −0.279405 − 0.971105I
a = 0.633756 − 0.239746I
b = 0.165180 − 0.161172I
−4.68544 − 3.19221I −6.37639 + 4.16497I
u = 0.881286 + 0.378029I
a = −0.468437 + 0.143230I
b = −0.67254 − 1.34172I
−5.10511 − 9.85415I −11.23414 + 7.48976I
u = 0.881286 − 0.378029I
a = −0.468437 − 0.143230I
b = −0.67254 + 1.34172I
−5.10511 + 9.85415I −11.23414 − 7.48976I
u = −0.845379 + 0.414724I
a = −0.399315 − 0.163435I
b = −0.586845 + 1.279740I
1.89498 + 7.08453I −7.53014 − 8.63075I
u = −0.845379 − 0.414724I
a = −0.399315 + 0.163435I
b = −0.586845 − 1.279740I
1.89498 − 7.08453I −7.53014 + 8.63075I
u = −0.757362 + 0.544501I
a = −0.177555 − 0.142317I
b = −0.315094 + 1.121340I
−3.80725 + 0.44416I −9.21656 − 2.62442I
u = −0.757362 − 0.544501I
a = −0.177555 + 0.142317I
b = −0.315094 − 1.121340I
−3.80725 − 0.44416I −9.21656 + 2.62442I
u = 0.801878 + 0.461107I
a = −0.308887 + 0.177382I
b = −0.484403 − 1.202350I
2.31942 − 3.03168I −5.96588 + 2.35658I
u = 0.801878 − 0.461107I
a = −0.308887 − 0.177382I
b = −0.484403 + 1.202350I
2.31942 + 3.03168I −5.96588 − 2.35658I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.094584 + 0.916633I
a = 0.842564 − 0.081921I
b = −0.0039149 − 0.0498200I
1.88453 − 1.52925I −1.27440 + 5.26025I
u = 0.094584 − 0.916633I
a = 0.842564 + 0.081921I
b = −0.0039149 + 0.0498200I
1.88453 + 1.52925I −1.27440 − 5.26025I
u = 0.019449 + 1.296200I
a = 0.96626 + 1.66275I
b = −0.218022 − 0.686915I
−4.87695 + 2.29360I 0
u = 0.019449 − 1.296200I
a = 0.96626 − 1.66275I
b = −0.218022 + 0.686915I
−4.87695 − 2.29360I 0
u = 0.662333 + 0.127045I
a = −0.823194 + 0.695101I
b = −1.028930 − 0.838109I
−10.70200 − 3.57800I −16.9686 + 4.2625I
u = 0.662333 − 0.127045I
a = −0.823194 − 0.695101I
b = −1.028930 + 0.838109I
−10.70200 + 3.57800I −16.9686 − 4.2625I
u = −0.027632 + 1.374070I
a = 0.60190 − 1.62387I
b = −0.134767 + 0.924503I
3.01436 − 0.56771I 0
u = −0.027632 − 1.374070I
a = 0.60190 + 1.62387I
b = −0.134767 − 0.924503I
3.01436 + 0.56771I 0
u = 0.218315 + 1.358270I
a = 0.09353 + 2.15802I
b = −0.696041 − 1.142180I
−5.99306 − 6.70057I 0
u = 0.218315 − 1.358270I
a = 0.09353 − 2.15802I
b = −0.696041 + 1.142180I
−5.99306 + 6.70057I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.574563 + 0.232091I
a = −0.449839 − 0.845197I
b = −0.830134 + 0.745730I
−2.99542 + 2.92052I −16.1336 − 6.6064I
u = −0.574563 − 0.232091I
a = −0.449839 + 0.845197I
b = −0.830134 − 0.745730I
−2.99542 − 2.92052I −16.1336 + 6.6064I
u = −0.17592 + 1.40998I
a = 0.17221 − 1.93269I
b = −0.509228 + 1.232380I
2.29935 + 5.57635I 0
u = −0.17592 − 1.40998I
a = 0.17221 + 1.93269I
b = −0.509228 − 1.232380I
2.29935 − 5.57635I 0
u = 0.09301 + 1.43048I
a = 0.33273 + 1.72234I
b = −0.243029 − 1.177930I
5.11959 − 2.66046I 0
u = 0.09301 − 1.43048I
a = 0.33273 − 1.72234I
b = −0.243029 + 1.177930I
5.11959 + 2.66046I 0
u = 0.328252 + 0.355874I
a = 0.529736 + 1.011980I
b = −0.606974 − 0.412729I
−0.575619 − 1.189230I −7.30572 + 5.21199I
u = 0.328252 − 0.355874I
a = 0.529736 − 1.011980I
b = −0.606974 + 0.412729I
−0.575619 + 1.189230I −7.30572 − 5.21199I
u = 0.33907 + 1.49289I
a = −0.27071 + 1.81325I
b = −0.88608 − 1.67141I
0.9224 − 14.2869I 0
u = 0.33907 − 1.49289I
a = −0.27071 − 1.81325I
b = −0.88608 + 1.67141I
0.9224 + 14.2869I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31588 + 1.50354I
a = −0.22485 − 1.79337I
b = −0.80439 + 1.67797I
8.10317 + 11.31590I 0
u = −0.31588 − 1.50354I
a = −0.22485 + 1.79337I
b = −0.80439 − 1.67797I
8.10317 − 11.31590I 0
u = 0.28776 + 1.51291I
a = −0.17153 + 1.77103I
b = −0.70857 − 1.67398I
8.73649 − 7.00574I 0
u = 0.28776 − 1.51291I
a = −0.17153 − 1.77103I
b = −0.70857 + 1.67398I
8.73649 + 7.00574I 0
u = −0.23601 + 1.52628I
a = 0.268656 + 1.050800I
b = 0.809501 − 0.930896I
3.13587 + 8.05851I 0
u = −0.23601 − 1.52628I
a = 0.268656 − 1.050800I
b = 0.809501 + 0.930896I
3.13587 − 8.05851I 0
u = −0.24303 + 1.52669I
a = −0.09228 − 1.72690I
b = −0.55642 + 1.66139I
2.98841 + 4.04672I 0
u = −0.24303 − 1.52669I
a = −0.09228 + 1.72690I
b = −0.55642 − 1.66139I
2.98841 − 4.04672I 0
u = 0.20089 + 1.53586I
a = 0.267467 − 1.098980I
b = 0.735565 + 1.017990I
10.08960 − 5.05548I 0
u = 0.20089 − 1.53586I
a = 0.267467 + 1.098980I
b = 0.735565 − 1.017990I
10.08960 + 5.05548I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.16329 + 1.54443I
a = 0.262928 + 1.151930I
b = 0.650504 − 1.106080I
10.46800 + 0.72296I 0
u = −0.16329 − 1.54443I
a = 0.262928 − 1.151930I
b = 0.650504 + 1.106080I
10.46800 − 0.72296I 0
u = 0.11419 + 1.55675I
a = 0.245810 − 1.222640I
b = 0.537126 + 1.223150I
4.35322 + 2.28070I 0
u = 0.11419 − 1.55675I
a = 0.245810 + 1.222640I
b = 0.537126 − 1.223150I
4.35322 − 2.28070I 0
u = 0.276434 + 0.095381I
a = −2.68244 − 2.75338I
b = −1.136770 + 0.255170I
−8.62006 − 3.30984I −17.2557 + 2.3212I
u = 0.276434 − 0.095381I
a = −2.68244 + 2.75338I
b = −1.136770 − 0.255170I
−8.62006 + 3.30984I −17.2557 − 2.3212I
u = −0.198964 + 0.041420I
a = −0.39851 − 4.51714I
b = −0.975718 + 0.209762I
−1.51896 − 1.35228I −14.3368 + 4.1508I
u = −0.198964 − 0.041420I
a = −0.39851 + 4.51714I
b = −0.975718 − 0.209762I
−1.51896 + 1.35228I −14.3368 − 4.1508I
9
II. I
u
2
= h−u
2
+ b, a − 1, u
18
+ 6u
16
+ · · · + u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
2
=
1
u
2
a
4
=
1
u
2
a
1
=
u
2
+ 1
u
2
a
10
=
−u
5
− 2u
3
− u
−u
5
− u
3
+ u
a
8
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
11
=
−u
11
− 4u
9
− 6u
7
− 6u
5
− 5u
3
− 2u
−u
13
− 5u
11
− 9u
9
− 8u
7
− 6u
5
− 3u
3
+ u
a
7
=
0
u
a
12
=
u
8
+ 3u
6
+ 3u
4
+ 2u
2
+ 1
u
8
+ 2u
6
a
6
=
u
17
+ 6u
15
+ 15u
13
+ 22u
11
+ 23u
9
+ 18u
7
+ 10u
5
+ 4u
3
+ u
u
17
+ 5u
15
+ 9u
13
+ 8u
11
+ 5u
9
+ 2u
7
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
12
− 16u
10
− 4u
9
− 24u
8
− 12u
7
− 24u
6
− 12u
5
− 20u
4
− 8u
3
− 8u
2
− 4u − 10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 12u
17
+ ··· − 5u + 1
c
2
, c
3
, c
4
c
7
, c
8
u
18
+ 6u
16
+ ··· − u − 1
c
5
, c
6
, c
10
c
11
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
3
c
9
, c
12
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
3
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 12y
17
+ ··· − 57y + 1
c
2
, c
3
, c
4
c
7
, c
8
y
18
+ 12y
17
+ ··· − 5y + 1
c
5
, c
6
, c
10
c
11
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
3
c
9
, c
12
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
3
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.637469 + 0.735789I
a = 1.00000
b = −0.135019 − 0.938086I
2.96024 − 1.97241I −4.57572 + 3.68478I
u = −0.637469 − 0.735789I
a = 1.00000
b = −0.135019 + 0.938086I
2.96024 + 1.97241I −4.57572 − 3.68478I
u = 0.639652 + 0.826288I
a = 1.00000
b = −0.273597 + 1.057070I
−3.69558 + 4.59213I −8.58114 − 3.20482I
u = 0.639652 − 0.826288I
a = 1.00000
b = −0.273597 − 1.057070I
−3.69558 − 4.59213I −8.58114 + 3.20482I
u = −0.182330 + 1.048680I
a = 1.00000
b = −1.066490 − 0.382411I
−0.738851 −13.41678 + 0.I
u = −0.182330 − 1.048680I
a = 1.00000
b = −1.066490 + 0.382411I
−0.738851 −13.41678 + 0.I
u = 0.667042 + 0.642083I
a = 1.00000
b = 0.032675 + 0.856592I
2.96024 − 1.97241I −4.57572 + 3.68478I
u = 0.667042 − 0.642083I
a = 1.00000
b = 0.032675 − 0.856592I
2.96024 + 1.97241I −4.57572 − 3.68478I
u = −0.724676 + 0.565991I
a = 1.00000
b = 0.204809 − 0.820320I
−3.69558 + 4.59213I −8.58114 − 3.20482I
u = −0.724676 − 0.565991I
a = 1.00000
b = 0.204809 + 0.820320I
−3.69558 − 4.59213I −8.58114 + 3.20482I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.313436 + 1.137860I
a = 1.00000
b = −1.196490 + 0.713294I
−7.66009 −12.26950 + 0.I
u = 0.313436 − 1.137860I
a = 1.00000
b = −1.196490 − 0.713294I
−7.66009 −12.26950 + 0.I
u = −0.626873
a = 1.00000
b = 0.392969
−7.66009 −12.2690
u = −0.029572 + 1.377870I
a = 1.00000
b = −1.89766 − 0.08149I
2.96024 + 1.97241I −4.57572 − 3.68478I
u = −0.029572 − 1.377870I
a = 1.00000
b = −1.89766 + 0.08149I
2.96024 − 1.97241I −4.57572 + 3.68478I
u = 0.085024 + 1.392280I
a = 1.00000
b = −1.93121 + 0.23675I
−3.69558 − 4.59213I −8.58114 + 3.20482I
u = 0.085024 − 1.392280I
a = 1.00000
b = −1.93121 − 0.23675I
−3.69558 + 4.59213I −8.58114 − 3.20482I
u = 0.364659
a = 1.00000
b = 0.132976
−0.738851 −13.4170
14
III. I
u
3
= hb + 1, a
3
u − 3a
2
u + · · · − 2a + 1, u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
2
=
a
−1
a
4
=
1
−1
a
1
=
a − 1
−1
a
10
=
−a
2
u + 2au − u
au
a
8
=
u
0
a
5
=
0
−1
a
11
=
−a
2
u + 2au − u
−a
2
u + 3au − u
a
7
=
−au + u
u
a
12
=
−a
3
+ 3a
2
− 2a
a
2
− a − 1
a
6
=
a
3
u − 3a
2
u − a
2
+ 3au + 2a − u
a
3
u + a
3
− 3a
2
u − 3a
2
+ 3au + 3a − u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
− 4au + 8a + 4u − 12
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
8
c
2
, c
3
, c
4
c
7
, c
8
(u
2
+ 1)
4
c
5
, c
6
, c
10
c
11
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
c
9
(u
4
+ u
3
+ u
2
+ 1)
2
c
12
(u
4
− u
3
+ u
2
+ 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y − 1)
8
c
2
, c
3
, c
4
c
7
, c
8
(y + 1)
8
c
5
, c
6
, c
10
c
11
(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
c
9
, c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.000000I
a = 0.088708 − 0.851808I
b = −1.00000
−6.79074 + 3.16396I −11.82674 − 2.56480I
u = 1.000000I
a = 0.279658 + 0.351808I
b = −1.00000
0.21101 − 1.41510I −8.17326 + 4.90874I
u = 1.000000I
a = 1.72034 + 0.35181I
b = −1.00000
0.21101 + 1.41510I −8.17326 − 4.90874I
u = 1.000000I
a = 1.91129 − 0.85181I
b = −1.00000
−6.79074 − 3.16396I −11.82674 + 2.56480I
u = − 1.000000I
a = 0.088708 + 0.851808I
b = −1.00000
−6.79074 − 3.16396I −11.82674 + 2.56480I
u = − 1.000000I
a = 0.279658 − 0.351808I
b = −1.00000
0.21101 + 1.41510I −8.17326 − 4.90874I
u = − 1.000000I
a = 1.72034 − 0.35181I
b = −1.00000
0.21101 − 1.41510I −8.17326 + 4.90874I
u = − 1.000000I
a = 1.91129 + 0.85181I
b = −1.00000
−6.79074 + 3.16396I −11.82674 − 2.56480I
18
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u
18
+ 12u
17
+ ··· − 5u + 1)(u
48
+ 17u
47
+ ··· + 35u + 4)
c
2
, c
7
((u
2
+ 1)
4
)(u
18
+ 6u
16
+ ··· − u − 1)(u
48
+ u
47
+ ··· − 3u + 2)
c
3
, c
4
, c
8
((u
2
+ 1)
4
)(u
18
+ 6u
16
+ ··· − u − 1)(u
48
+ u
47
+ ··· − u + 2)
c
5
, c
6
, c
10
c
11
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
3
(u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1)
· (u
48
− 2u
47
+ ··· + u + 2)
c
9
(u
4
+ u
3
+ u
2
+ 1)
2
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
3
· (u
48
− 8u
47
+ ··· − 7639u + 1016)
c
12
(u
4
− u
3
+ u
2
+ 1)
2
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)
3
· (u
48
− 8u
47
+ ··· − 7639u + 1016)
19
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
8
)(y
18
− 12y
17
+ ··· − 57y + 1)
· (y
48
+ 37y
47
+ ··· + 12799y + 16)
c
2
, c
7
((y + 1)
8
)(y
18
+ 12y
17
+ ··· − 5y + 1)(y
48
+ 17y
47
+ ··· + 35y + 4)
c
3
, c
4
, c
8
((y + 1)
8
)(y
18
+ 12y
17
+ ··· − 5y + 1)(y
48
+ 53y
47
+ ··· − 237y + 4)
c
5
, c
6
, c
10
c
11
(y
4
− 5y
3
+ 7y
2
− 2y + 1)
2
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
3
· (y
48
− 52y
47
+ ··· + 19y + 4)
c
9
, c
12
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
3
· (y
48
+ 32y
47
+ ··· − 318369y + 1032256)
20
