12n
0455
(K12n
0455
)
A knot diagram
1
Linearized knot diagam
3 6 8 7 2 11 4 3 12 1 7 10
Solving Sequence
4,7 8,11
12 3 9 10 6 2 1 5
c
7
c
11
c
3
c
8
c
9
c
6
c
2
c
1
c
5
c
4
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3.50811 × 10
48
u
55
+ 5.98520 × 10
48
u
54
+ ··· + 2.69358 × 10
47
b + 4.89292 × 10
49
,
2.55712 × 10
50
u
55
+ 4.32535 × 10
50
u
54
+ ··· + 5.65653 × 10
48
a + 3.41422 × 10
51
, u
56
+ 2u
55
+ ··· + 44u + 4i
I
u
2
= hb, 3a + u + 1, u
2
− u + 1i
I
u
3
= h−au + 9b − 4a + u − 5, 2a
2
− au + 5u − 9, u
2
+ 2i
I
v
1
= ha, b + v + 2, v
2
+ 3v + 1i
* 4 irreducible components of dim
C
= 0, with total 64 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
=
h3.51×10
48
u
55
+5.99×10
48
u
54
+· · ·+2.69×10
47
b+4.89×10
49
, 2.56×10
50
u
55
+
4.33 × 10
50
u
54
+ · · · + 5.66 × 10
48
a + 3.41 × 10
51
, u
56
+ 2u
55
+ · · · + 44u + 4i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
11
=
−45.2065u
55
− 76.4665u
54
+ ··· − 4615.91u − 603.589
−13.0239u
55
− 22.2202u
54
+ ··· − 1365.32u − 181.651
a
12
=
−32.1825u
55
− 54.2463u
54
+ ··· − 3250.59u − 421.938
−13.0239u
55
− 22.2202u
54
+ ··· − 1365.32u − 181.651
a
3
=
−u
u
3
+ u
a
9
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
33.0942u
55
+ 56.4532u
54
+ ··· + 3417.51u + 449.013
−28.0321u
55
− 47.5425u
54
+ ··· − 2839.05u − 370.800
a
6
=
27.7411u
55
+ 46.8651u
54
+ ··· + 2813.09u + 362.109
24.2434u
55
+ 41.0750u
54
+ ··· + 2515.79u + 329.906
a
2
=
−27.7411u
55
− 46.8651u
54
+ ··· − 2813.09u − 362.109
27.3678u
55
+ 46.3317u
54
+ ··· + 2783.98u + 364.375
a
1
=
−28.1461u
55
− 47.2742u
54
+ ··· − 2852.14u − 366.930
28.0321u
55
+ 47.5425u
54
+ ··· + 2839.05u + 370.800
a
5
=
u
u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −46.3572u
55
− 80.1696u
54
+ ··· − 5049.53u − 698.513
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
56
+ 24u
55
+ ··· + 25165u + 361
c
2
, c
5
u
56
+ 4u
55
+ ··· − 41u + 19
c
3
, c
4
, c
7
c
8
u
56
+ 2u
55
+ ··· + 44u + 4
c
6
, c
11
u
56
− 2u
55
+ ··· − 108u + 36
c
9
, c
10
, c
12
u
56
− 6u
55
+ ··· + 31u + 9
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
56
+ 16y
55
+ ··· − 427912989y + 130321
c
2
, c
5
y
56
− 24y
55
+ ··· − 25165y + 361
c
3
, c
4
, c
7
c
8
y
56
+ 50y
55
+ ··· − 464y + 16
c
6
, c
11
y
56
− 24y
55
+ ··· − 17784y + 1296
c
9
, c
10
, c
12
y
56
− 50y
55
+ ··· + 605y + 81
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.357425 + 0.939932I
a = −0.508559 + 0.668079I
b = −0.709734 + 0.751032I
0.10978 + 1.51144I 0
u = −0.357425 − 0.939932I
a = −0.508559 − 0.668079I
b = −0.709734 − 0.751032I
0.10978 − 1.51144I 0
u = 0.916252 + 0.279624I
a = −0.263707 − 0.445797I
b = −0.801946 + 0.644092I
0.01268 + 4.06286I −6.20066 − 5.47620I
u = 0.916252 − 0.279624I
a = −0.263707 + 0.445797I
b = −0.801946 − 0.644092I
0.01268 − 4.06286I −6.20066 + 5.47620I
u = −0.870458 + 0.356425I
a = −0.654647 + 0.719979I
b = −1.104950 − 0.815677I
−2.43509 − 10.45620I −7.88871 + 7.69025I
u = −0.870458 − 0.356425I
a = −0.654647 − 0.719979I
b = −1.104950 + 0.815677I
−2.43509 + 10.45620I −7.88871 − 7.69025I
u = −0.672518 + 0.823461I
a = 0.189263 − 0.600931I
b = 0.930657 − 0.635738I
−3.85927 + 5.20665I 0
u = −0.672518 − 0.823461I
a = 0.189263 + 0.600931I
b = 0.930657 + 0.635738I
−3.85927 − 5.20665I 0
u = 0.138429 + 1.163150I
a = 2.11508 + 0.18189I
b = 0.981368 − 0.595861I
−3.70144 − 0.59074I 0
u = 0.138429 − 1.163150I
a = 2.11508 − 0.18189I
b = 0.981368 + 0.595861I
−3.70144 + 0.59074I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.796673 + 0.217361I
a = 0.732692 − 0.735103I
b = 1.047550 + 0.754047I
2.36888 − 5.77663I −3.49704 + 6.12922I
u = −0.796673 − 0.217361I
a = 0.732692 + 0.735103I
b = 1.047550 − 0.754047I
2.36888 + 5.77663I −3.49704 − 6.12922I
u = −0.813175
a = 0.696477
b = −0.998455
−7.46368 −11.8850
u = 0.786622 + 0.053183I
a = 0.235360 + 0.517834I
b = 0.691285 − 0.845614I
3.46294 + 0.21119I −6 − 0.626193 + 0.10I
u = 0.786622 − 0.053183I
a = 0.235360 − 0.517834I
b = 0.691285 + 0.845614I
3.46294 − 0.21119I −6 − 0.626193 + 0.10I
u = 0.686659 + 1.019540I
a = 0.152248 + 0.372794I
b = 0.649441 + 0.261695I
−2.10341 + 1.46035I 0
u = 0.686659 − 1.019540I
a = 0.152248 − 0.372794I
b = 0.649441 − 0.261695I
−2.10341 − 1.46035I 0
u = 0.363201 + 1.199600I
a = 0.050246 − 0.686716I
b = −0.360705 − 0.909449I
−0.05819 + 3.93594I 0
u = 0.363201 − 1.199600I
a = 0.050246 + 0.686716I
b = −0.360705 + 0.909449I
−0.05819 − 3.93594I 0
u = 0.694825 + 0.177977I
a = −0.175933 + 0.543419I
b = −0.679667 − 1.057170I
−1.07651 + 3.71517I −5.64023 − 4.49934I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.694825 − 0.177977I
a = −0.175933 − 0.543419I
b = −0.679667 + 1.057170I
−1.07651 − 3.71517I −5.64023 + 4.49934I
u = −0.222724 + 1.263850I
a = 0.746580 − 0.478205I
b = 0.691653 − 0.998010I
−4.19144 − 2.28903I 0
u = −0.222724 − 1.263850I
a = 0.746580 + 0.478205I
b = 0.691653 + 0.998010I
−4.19144 + 2.28903I 0
u = 0.212493 + 0.663538I
a = −0.798139 + 0.138816I
b = −0.332186 + 0.507658I
−0.238433 + 1.252040I −2.82125 − 5.02862I
u = 0.212493 − 0.663538I
a = −0.798139 − 0.138816I
b = −0.332186 − 0.507658I
−0.238433 − 1.252040I −2.82125 + 5.02862I
u = −0.125478 + 1.304740I
a = −0.84758 + 1.18038I
b = −0.758335 − 0.376703I
−6.56363 − 1.59389I 0
u = −0.125478 − 1.304740I
a = −0.84758 − 1.18038I
b = −0.758335 + 0.376703I
−6.56363 + 1.59389I 0
u = −0.098940 + 1.329620I
a = −2.59434 + 0.37087I
b = −1.79675 + 0.14155I
−14.6366 − 1.4158I 0
u = −0.098940 − 1.329620I
a = −2.59434 − 0.37087I
b = −1.79675 − 0.14155I
−14.6366 + 1.4158I 0
u = 0.326495 + 1.296350I
a = −1.68324 − 0.31227I
b = −0.993147 + 0.745876I
−0.74471 + 4.21273I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.326495 − 1.296350I
a = −1.68324 + 0.31227I
b = −0.993147 − 0.745876I
−0.74471 − 4.21273I 0
u = −0.261932 + 1.315040I
a = 2.39778 − 0.42809I
b = 1.291360 + 0.390540I
−4.85102 − 4.10127I 0
u = −0.261932 − 1.315040I
a = 2.39778 + 0.42809I
b = 1.291360 − 0.390540I
−4.85102 + 4.10127I 0
u = −0.646445 + 0.063362I
a = −0.928542 + 0.691777I
b = −0.988563 − 0.589361I
−0.514192 − 0.792549I −4.90653 + 2.84844I
u = −0.646445 − 0.063362I
a = −0.928542 − 0.691777I
b = −0.988563 + 0.589361I
−0.514192 + 0.792549I −4.90653 − 2.84844I
u = −0.341280 + 1.316540I
a = 0.817304 − 0.783388I
b = 1.073100 + 0.391226I
−11.62750 − 4.16517I 0
u = −0.341280 − 1.316540I
a = 0.817304 + 0.783388I
b = 1.073100 − 0.391226I
−11.62750 + 4.16517I 0
u = 0.288431 + 1.366350I
a = 0.141585 + 0.969892I
b = 0.55694 + 1.31146I
−5.96654 + 7.30226I 0
u = 0.288431 − 1.366350I
a = 0.141585 − 0.969892I
b = 0.55694 − 1.31146I
−5.96654 − 7.30226I 0
u = 0.085846 + 1.404690I
a = −0.72751 − 1.48763I
b = 0.118836 + 0.664953I
−8.80079 + 0.29511I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.085846 − 1.404690I
a = −0.72751 + 1.48763I
b = 0.118836 − 0.664953I
−8.80079 − 0.29511I 0
u = −0.33202 + 1.39409I
a = −2.13548 + 0.45520I
b = −1.242450 − 0.672303I
−2.74251 − 9.86043I 0
u = −0.33202 − 1.39409I
a = −2.13548 − 0.45520I
b = −1.242450 + 0.672303I
−2.74251 + 9.86043I 0
u = −0.04599 + 1.47574I
a = 1.78492 − 0.56193I
b = 0.697621 − 0.210255I
−7.13747 + 0.98410I 0
u = −0.04599 − 1.47574I
a = 1.78492 + 0.56193I
b = 0.697621 + 0.210255I
−7.13747 − 0.98410I 0
u = 0.37725 + 1.42997I
a = 1.48324 + 0.27092I
b = 1.064050 − 0.776573I
−5.40146 + 8.69654I 0
u = 0.37725 − 1.42997I
a = 1.48324 − 0.27092I
b = 1.064050 + 0.776573I
−5.40146 − 8.69654I 0
u = −0.34531 + 1.47025I
a = 1.95103 − 0.36645I
b = 1.27086 + 0.84602I
−8.2789 − 14.8605I 0
u = −0.34531 − 1.47025I
a = 1.95103 + 0.36645I
b = 1.27086 − 0.84602I
−8.2789 + 14.8605I 0
u = 0.146752 + 0.464276I
a = 3.63219 + 0.90440I
b = 0.425085 − 0.514946I
−3.04021 − 0.77078I −13.4195 − 5.3259I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.146752 − 0.464276I
a = 3.63219 − 0.90440I
b = 0.425085 + 0.514946I
−3.04021 + 0.77078I −13.4195 + 5.3259I
u = −0.07154 + 1.61009I
a = −1.293690 + 0.377349I
b = −1.078470 + 0.249906I
−12.46720 + 2.72041I 0
u = −0.07154 − 1.61009I
a = −1.293690 − 0.377349I
b = −1.078470 − 0.249906I
−12.46720 − 2.72041I 0
u = −0.308833
a = −4.42147
b = 0.567778
−2.38389 8.02900
u = −0.296374
a = 0.686807
b = 1.68419
−10.2992 9.48110
u = −0.250665
a = −2.26479
b = −0.539323
−1.17956 −7.76820
10
II. I
u
2
= hb, 3a + u + 1, u
2
− u + 1i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
−u + 1
a
11
=
−
1
3
u −
1
3
0
a
12
=
−
1
3
u −
1
3
0
a
3
=
−u
u − 1
a
9
=
u
−u + 2
a
10
=
2
3
u −
1
3
−u + 2
a
6
=
1
0
a
2
=
−1
u − 1
a
1
=
−u
u − 2
a
5
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
20
3
u − 3
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
4
c
5
u
2
+ u + 1
c
2
, c
7
, c
8
u
2
− u + 1
c
6
, c
11
u
2
c
9
, c
10
(u − 1)
2
c
12
(u + 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
7
c
8
y
2
+ y + 1
c
6
, c
11
y
2
c
9
, c
10
, c
12
(y −1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.500000 − 0.288675I
b = 0
−1.64493 + 2.02988I −6.33333 − 5.77350I
u = 0.500000 − 0.866025I
a = −0.500000 + 0.288675I
b = 0
−1.64493 − 2.02988I −6.33333 + 5.77350I
14
III. I
u
3
= h−au + 9b − 4a + u − 5, 2a
2
− au + 5u − 9, u
2
+ 2i
(i) Arc colorings
a
4
=
0
u
a
7
=
1
0
a
8
=
1
2
a
11
=
a
1
9
au +
4
9
a −
1
9
u +
5
9
a
12
=
−
1
9
au +
5
9
a +
1
9
u −
5
9
1
9
au +
4
9
a −
1
9
u +
5
9
a
3
=
−u
−u
a
9
=
−1
0
a
10
=
1
2
u − 2
−
1
9
au −
4
9
a +
1
9
u −
14
9
a
6
=
−
1
9
au −
4
9
a +
11
18
u −
14
9
−
1
9
au −
4
9
a +
1
9
u −
14
9
a
2
=
−
1
9
au −
4
9
a −
7
18
u −
14
9
−
1
9
au −
4
9
a −
8
9
u −
14
9
a
1
=
−
1
9
au −
4
9
a +
11
18
u −
14
9
−
1
9
au −
4
9
a +
1
9
u −
14
9
a
5
=
u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −16
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
4
c
2
(u + 1)
4
c
3
, c
4
, c
7
c
8
(u
2
+ 2)
2
c
6
, c
12
(u
2
− u − 1)
2
c
9
, c
10
, c
11
(u
2
+ u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
4
c
3
, c
4
, c
7
c
8
(y + 2)
4
c
6
, c
9
, c
10
c
11
, c
12
(y
2
− 3y + 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.414210I
a = 2.23607 − 0.43702I
b = 1.61803
−15.4624 −16.0000
u = 1.414210I
a = −2.23607 + 1.14412I
b = −0.618034
−7.56670 −16.0000
u = − 1.414210I
a = 2.23607 + 0.43702I
b = 1.61803
−15.4624 −16.0000
u = − 1.414210I
a = −2.23607 − 1.14412I
b = −0.618034
−7.56670 −16.0000
18
IV. I
v
1
= ha, b + v + 2, v
2
+ 3v + 1i
(i) Arc colorings
a
4
=
v
0
a
7
=
1
0
a
8
=
1
0
a
11
=
0
−v − 2
a
12
=
v + 2
−v − 2
a
3
=
v
0
a
9
=
1
0
a
10
=
−v − 2
v + 3
a
6
=
1
−v − 3
a
2
=
v − 1
v + 3
a
1
=
−1
v + 3
a
5
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −26
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
4
, c
7
c
8
u
2
c
5
(u + 1)
2
c
6
, c
9
, c
10
u
2
+ u − 1
c
11
, c
12
u
2
− u − 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y − 1)
2
c
3
, c
4
, c
7
c
8
y
2
c
6
, c
9
, c
10
c
11
, c
12
y
2
− 3y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.381966
a = 0
b = −1.61803
−10.5276 −26.0000
v = −2.61803
a = 0
b = 0.618034
−2.63189 −26.0000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
2
+ u + 1)(u
56
+ 24u
55
+ ··· + 25165u + 361)
c
2
((u − 1)
2
)(u + 1)
4
(u
2
− u + 1)(u
56
+ 4u
55
+ ··· − 41u + 19)
c
3
, c
4
u
2
(u
2
+ 2)
2
(u
2
+ u + 1)(u
56
+ 2u
55
+ ··· + 44u + 4)
c
5
((u − 1)
4
)(u + 1)
2
(u
2
+ u + 1)(u
56
+ 4u
55
+ ··· − 41u + 19)
c
6
u
2
(u
2
− u − 1)
2
(u
2
+ u − 1)(u
56
− 2u
55
+ ··· − 108u + 36)
c
7
, c
8
u
2
(u
2
+ 2)
2
(u
2
− u + 1)(u
56
+ 2u
55
+ ··· + 44u + 4)
c
9
, c
10
((u − 1)
2
)(u
2
+ u − 1)
3
(u
56
− 6u
55
+ ··· + 31u + 9)
c
11
u
2
(u
2
− u − 1)(u
2
+ u − 1)
2
(u
56
− 2u
55
+ ··· − 108u + 36)
c
12
((u + 1)
2
)(u
2
− u − 1)
3
(u
56
− 6u
55
+ ··· + 31u + 9)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
6
)(y
2
+ y + 1)(y
56
+ 16y
55
+ ··· − 4.27913 × 10
8
y + 130321)
c
2
, c
5
((y − 1)
6
)(y
2
+ y + 1)(y
56
− 24y
55
+ ··· − 25165y + 361)
c
3
, c
4
, c
7
c
8
y
2
(y + 2)
4
(y
2
+ y + 1)(y
56
+ 50y
55
+ ··· − 464y + 16)
c
6
, c
11
y
2
(y
2
− 3y + 1)
3
(y
56
− 24y
55
+ ··· − 17784y + 1296)
c
9
, c
10
, c
12
((y − 1)
2
)(y
2
− 3y + 1)
3
(y
56
− 50y
55
+ ··· + 605y + 81)
24
