12n
0650
(K12n
0650
)
A knot diagram
1
Linearized knot diagam
3 8 6 1 10 9 2 11 3 4 8 4
Solving Sequence
3,8
2 1
7,10
9 6 4 11 5 12
c
2
c
1
c
7
c
9
c
6
c
3
c
10
c
5
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1989385u
25
− 36760790u
24
+ ··· + 9723136b − 272866048,
− 3511211u
25
− 66741367u
24
+ ··· + 9723136a − 730323648, u
26
+ 20u
25
+ ··· + 1536u + 256i
I
u
2
= h1174u
17
+ 443u
16
+ ··· + 2225b − 946, 13156u
17
+ 10017u
16
+ ··· + 6675a − 37699,
u
18
− 8u
16
+ ··· + 5u + 3i
* 2 irreducible components of dim
C
= 0, with total 44 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−1.99×10
6
u
25
−3.68×10
7
u
24
+· · ·+9.72×10
6
b−2.73×10
8
, −3.51×10
6
u
25
−
6.67 × 10
7
u
24
+ · · · + 9.72 × 10
6
a − 7.30 × 10
8
, u
26
+ 20u
25
+ · · · + 1536u + 256i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
−u
3
+ u
a
10
=
0.361119u
25
+ 6.86418u
24
+ ··· + 406.596u + 75.1119
0.204603u
25
+ 3.78075u
24
+ ··· + 161.401u + 28.0636
a
9
=
0.156516u
25
+ 3.08343u
24
+ ··· + 245.195u + 47.0484
0.204603u
25
+ 3.78075u
24
+ ··· + 161.401u + 28.0636
a
6
=
0.110888u
25
+ 2.05128u
24
+ ··· + 135.662u + 27.3983
−0.168663u
25
− 3.00422u
24
+ ··· − 83.4070u − 14.2327
a
4
=
0.132026u
25
+ 2.48277u
24
+ ··· + 132.959u + 25.2820
0.306676u
25
+ 5.66909u
24
+ ··· + 248.834u + 44.7104
a
11
=
−0.0156496u
25
− 0.512299u
24
+ ··· − 170.823u − 36.1491
−0.731644u
25
− 13.8490u
24
+ ··· − 665.992u − 115.163
a
5
=
0.168353u
25
+ 3.05304u
24
+ ··· + 177.060u + 35.1491
0.500752u
25
+ 9.22376u
24
+ ··· + 470.444u + 88.3760
a
12
=
0.0156496u
25
+ 0.512299u
24
+ ··· + 170.823u + 36.1491
0.266199u
25
+ 5.25708u
24
+ ··· + 355.852u + 64.1406
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
1519127
151924
u
25
−
228486283
1215392
u
24
+ ··· −
399437504
37981
u −
3997508
1999
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
26
+ 16u
25
+ ··· + 65536u + 65536
c
2
, c
7
u
26
− 20u
25
+ ··· − 1536u + 256
c
3
u
26
+ 3u
25
+ ··· + 5u + 1
c
4
, c
12
u
26
+ u
25
+ ··· − 2u + 1
c
5
u
26
+ u
25
+ ··· + 217u + 193
c
6
, c
9
u
26
+ 2u
25
+ ··· + 2u + 1
c
8
, c
11
u
26
− 4u
25
+ ··· − 6u + 1
c
10
u
26
+ 24u
24
+ ··· + 107u + 43
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
26
+ 120y
25
+ ··· + 122406567936y + 4294967296
c
2
, c
7
y
26
− 16y
25
+ ··· − 65536y + 65536
c
3
y
26
+ 3y
25
+ ··· + 13y + 1
c
4
, c
12
y
26
− 47y
25
+ ··· − 2y + 1
c
5
y
26
+ 53y
25
+ ··· + 99205y + 37249
c
6
, c
9
y
26
− 54y
25
+ ··· − 2y + 1
c
8
, c
11
y
26
+ 30y
24
+ ··· + 2y + 1
c
10
y
26
+ 48y
25
+ ··· + 3085y + 1849
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.016860 + 0.515617I
a = −0.547952 − 0.593599I
b = −0.005131 − 0.349931I
1.14259 + 4.55293I 0.67584 − 2.96671I
u = −1.016860 − 0.515617I
a = −0.547952 + 0.593599I
b = −0.005131 + 0.349931I
1.14259 − 4.55293I 0.67584 + 2.96671I
u = −0.367875 + 0.728872I
a = −0.726824 + 0.229748I
b = −0.305544 + 0.145494I
1.79332 − 1.76675I 0.88475 + 2.70026I
u = −0.367875 − 0.728872I
a = −0.726824 − 0.229748I
b = −0.305544 − 0.145494I
1.79332 + 1.76675I 0.88475 − 2.70026I
u = −0.527735 + 0.607198I
a = −0.345868 − 0.800773I
b = −0.121889 − 0.310496I
2.58885 − 0.08583I 6.93906 − 0.29216I
u = −0.527735 − 0.607198I
a = −0.345868 + 0.800773I
b = −0.121889 + 0.310496I
2.58885 + 0.08583I 6.93906 + 0.29216I
u = 1.203720 + 0.288453I
a = 0.465886 + 0.245129I
b = 0.749365 + 0.223786I
−2.65605 − 1.02761I −3.38805 + 0.66160I
u = 1.203720 − 0.288453I
a = 0.465886 − 0.245129I
b = 0.749365 − 0.223786I
−2.65605 + 1.02761I −3.38805 − 0.66160I
u = −1.102930 + 0.577266I
a = 0.450976 − 0.348600I
b = 0.295113 + 0.026156I
−0.34242 + 6.74821I 1.68908 − 12.55727I
u = −1.102930 − 0.577266I
a = 0.450976 + 0.348600I
b = 0.295113 − 0.026156I
−0.34242 − 6.74821I 1.68908 + 12.55727I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.296079 + 0.669488I
a = −1.52910 + 0.28993I
b = −0.675653 + 0.872173I
−0.13239 − 2.18215I −1.31091 + 4.66032I
u = 0.296079 − 0.669488I
a = −1.52910 − 0.28993I
b = −0.675653 − 0.872173I
−0.13239 + 2.18215I −1.31091 − 4.66032I
u = −1.398550 + 0.175389I
a = 0.859045 − 0.438947I
b = 0.029505 + 1.040670I
−6.70940 + 3.17946I −11.81324 + 0.I
u = −1.398550 − 0.175389I
a = 0.859045 + 0.438947I
b = 0.029505 − 1.040670I
−6.70940 − 3.17946I −11.81324 + 0.I
u = −1.42731 + 0.24870I
a = 1.005720 − 0.776152I
b = 0.774240 + 1.177450I
−5.69335 + 5.51976I 0. − 13.25882I
u = −1.42731 − 0.24870I
a = 1.005720 + 0.776152I
b = 0.774240 − 1.177450I
−5.69335 − 5.51976I 0. + 13.25882I
u = 0.407621 + 0.360624I
a = −0.738146 + 0.444980I
b = 0.212985 + 0.764335I
−1.12681 − 1.09104I −5.44567 + 3.98120I
u = 0.407621 − 0.360624I
a = −0.738146 − 0.444980I
b = 0.212985 − 0.764335I
−1.12681 + 1.09104I −5.44567 − 3.98120I
u = −1.44306 + 1.35548I
a = 3.43426 − 0.14475I
b = 2.80277 + 0.65564I
14.1380 + 5.5276I 0
u = −1.44306 − 1.35548I
a = 3.43426 + 0.14475I
b = 2.80277 − 0.65564I
14.1380 − 5.5276I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.56135 + 1.29391I
a = −3.52741 − 0.39308I
b = −2.83872 − 1.22660I
13.8077 + 5.1544I 0
u = −1.56135 − 1.29391I
a = −3.52741 + 0.39308I
b = −2.83872 + 1.22660I
13.8077 − 5.1544I 0
u = −1.52058 + 1.37669I
a = 3.67620 + 0.32681I
b = 2.97403 + 1.10938I
13.8209 + 12.8202I 0
u = −1.52058 − 1.37669I
a = 3.67620 − 0.32681I
b = 2.97403 − 1.10938I
13.8209 − 12.8202I 0
u = −1.54118 + 1.38126I
a = −3.47680 − 0.05371I
b = −2.89107 − 0.84018I
13.78230 − 1.84091I 0
u = −1.54118 − 1.38126I
a = −3.47680 + 0.05371I
b = −2.89107 + 0.84018I
13.78230 + 1.84091I 0
7
II. I
u
2
= h1174u
17
+ 443u
16
+ · · · + 2225b − 946, 13156u
17
+ 10017u
16
+ · · · +
6675a − 37699, u
18
− 8u
16
+ · · · + 5u + 3i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
−u
3
+ u
a
10
=
−1.97094u
17
− 1.50067u
16
+ ··· + 18.7823u + 5.64779
−0.527640u
17
− 0.199101u
16
+ ··· + 1.60135u + 0.425169
a
9
=
−1.44330u
17
− 1.30157u
16
+ ··· + 17.1810u + 5.22262
−0.527640u
17
− 0.199101u
16
+ ··· + 1.60135u + 0.425169
a
6
=
−0.390712u
17
+ 0.369888u
16
+ ··· + 2.98816u + 0.0235206
0.185169u
17
− 0.0970787u
16
+ ··· + 3.65438u + 2.28180
a
4
=
−0.419925u
17
+ 0.996854u
16
+ ··· − 10.5714u − 4.42142
1.27910u
17
− 0.282247u
16
+ ··· − 1.02337u + 5.09708
a
11
=
−0.149513u
17
− 0.960449u
16
+ ··· + 6.32599u + 5.44075
−1.02472u
17
+ 0.838202u
16
+ ··· − 3.24270u − 6.53034
a
5
=
0.326592u
17
+ 0.683146u
16
+ ··· − 11.6419u − 4.20524
1.02876u
17
− 0.248090u
16
+ ··· + 0.227865u + 4.05348
a
12
=
−0.149513u
17
− 0.960449u
16
+ ··· + 6.32599u + 5.44075
−1.36584u
17
+ 0.405393u
16
+ ··· + 2.00809u − 3.64899
(ii) Obstruction class = 1
(iii) Cusp Shapes =
8359
2225
u
17
+
13288
2225
u
16
+ ··· −
127808
2225
u −
6186
2225
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
− 16u
17
+ ··· − 109u + 9
c
2
u
18
− 8u
16
+ ··· + 5u + 3
c
3
u
18
+ 8u
17
+ ··· + 5u + 1
c
4
u
18
+ 2u
17
+ ··· + 2u + 1
c
5
u
18
+ 2u
14
+ ··· − u + 3
c
6
, c
9
u
18
− u
17
+ ··· + 2u + 1
c
7
u
18
− 8u
16
+ ··· − 5u + 3
c
8
u
18
− 9u
17
+ ··· − 6u + 1
c
10
u
18
− u
17
+ ··· + u + 1
c
11
u
18
+ 9u
17
+ ··· + 6u + 1
c
12
u
18
− 2u
17
+ ··· − 2u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
− 16y
17
+ ··· − y + 81
c
2
, c
7
y
18
− 16y
17
+ ··· − 109y + 9
c
3
y
18
+ 2y
17
+ ··· + 9y + 1
c
4
, c
12
y
18
+ 2y
15
+ ··· + 2y + 1
c
5
y
18
+ 4y
16
+ ··· − 7y + 9
c
6
, c
9
y
18
+ y
17
+ ··· + 2y + 1
c
8
, c
11
y
18
− y
17
+ ··· − 2y + 1
c
10
y
18
− y
17
+ ··· + y + 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.866748 + 0.339139I
a = 0.585312 − 0.000404I
b = 0.850307 + 0.487196I
1.52696 + 5.64075I 5.02271 − 10.09643I
u = −0.866748 − 0.339139I
a = 0.585312 + 0.000404I
b = 0.850307 − 0.487196I
1.52696 − 5.64075I 5.02271 + 10.09643I
u = 0.835918 + 0.396708I
a = 1.08228 + 1.91732I
b = 0.572770 + 0.331333I
−3.84181 + 1.43571I −2.77803 + 0.44283I
u = 0.835918 − 0.396708I
a = 1.08228 − 1.91732I
b = 0.572770 − 0.331333I
−3.84181 − 1.43571I −2.77803 − 0.44283I
u = −0.556480 + 0.956948I
a = 0.659533 + 0.994382I
b = 0.138758 + 1.050230I
1.155690 + 0.058941I −0.908103 − 0.566791I
u = −0.556480 − 0.956948I
a = 0.659533 − 0.994382I
b = 0.138758 − 1.050230I
1.155690 − 0.058941I −0.908103 + 0.566791I
u = 0.765456 + 0.230677I
a = −0.44776 − 3.06535I
b = −0.332709 − 0.567316I
−2.87507 − 5.25661I 0.15175 + 7.52339I
u = 0.765456 − 0.230677I
a = −0.44776 + 3.06535I
b = −0.332709 + 0.567316I
−2.87507 + 5.25661I 0.15175 − 7.52339I
u = −1.142420 + 0.682096I
a = −0.060431 + 0.661371I
b = −0.317939 + 0.747295I
−0.62367 + 6.19450I −4.05821 − 1.05531I
u = −1.142420 − 0.682096I
a = −0.060431 − 0.661371I
b = −0.317939 − 0.747295I
−0.62367 − 6.19450I −4.05821 + 1.05531I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.354680 + 0.072381I
a = −1.003230 + 0.341552I
b = −1.47456 + 0.43997I
−0.97412 − 3.24688I −2.87279 + 2.26909I
u = −1.354680 − 0.072381I
a = −1.003230 − 0.341552I
b = −1.47456 − 0.43997I
−0.97412 + 3.24688I −2.87279 − 2.26909I
u = −0.544801 + 0.244143I
a = −0.114341 − 0.566988I
b = 0.906433 − 0.354928I
3.11907 − 2.19821I 8.90400 + 3.10341I
u = −0.544801 − 0.244143I
a = −0.114341 + 0.566988I
b = 0.906433 + 0.354928I
3.11907 + 2.19821I 8.90400 − 3.10341I
u = 1.38521 + 0.32967I
a = −1.44449 − 0.77157I
b = −0.87794 + 1.14508I
−5.93825 − 5.17067I −10.95523 − 1.48147I
u = 1.38521 − 0.32967I
a = −1.44449 + 0.77157I
b = −0.87794 − 1.14508I
−5.93825 + 5.17067I −10.95523 + 1.48147I
u = 1.47855 + 0.08650I
a = −0.423539 − 0.429164I
b = 0.034873 + 1.260500I
−6.35322 − 3.65803I −3.50609 + 6.99719I
u = 1.47855 − 0.08650I
a = −0.423539 + 0.429164I
b = 0.034873 − 1.260500I
−6.35322 + 3.65803I −3.50609 − 6.99719I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
18
− 16u
17
+ ··· − 109u + 9)(u
26
+ 16u
25
+ ··· + 65536u + 65536)
c
2
(u
18
− 8u
16
+ ··· + 5u + 3)(u
26
− 20u
25
+ ··· − 1536u + 256)
c
3
(u
18
+ 8u
17
+ ··· + 5u + 1)(u
26
+ 3u
25
+ ··· + 5u + 1)
c
4
(u
18
+ 2u
17
+ ··· + 2u + 1)(u
26
+ u
25
+ ··· − 2u + 1)
c
5
(u
18
+ 2u
14
+ ··· − u + 3)(u
26
+ u
25
+ ··· + 217u + 193)
c
6
, c
9
(u
18
− u
17
+ ··· + 2u + 1)(u
26
+ 2u
25
+ ··· + 2u + 1)
c
7
(u
18
− 8u
16
+ ··· − 5u + 3)(u
26
− 20u
25
+ ··· − 1536u + 256)
c
8
(u
18
− 9u
17
+ ··· − 6u + 1)(u
26
− 4u
25
+ ··· − 6u + 1)
c
10
(u
18
− u
17
+ ··· + u + 1)(u
26
+ 24u
24
+ ··· + 107u + 43)
c
11
(u
18
+ 9u
17
+ ··· + 6u + 1)(u
26
− 4u
25
+ ··· − 6u + 1)
c
12
(u
18
− 2u
17
+ ··· − 2u + 1)(u
26
+ u
25
+ ··· − 2u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
18
− 16y
17
+ ··· − y + 81)
· (y
26
+ 120y
25
+ ··· + 122406567936y + 4294967296)
c
2
, c
7
(y
18
− 16y
17
+ ··· − 109y + 9)(y
26
− 16y
25
+ ··· − 65536y + 65536)
c
3
(y
18
+ 2y
17
+ ··· + 9y + 1)(y
26
+ 3y
25
+ ··· + 13y + 1)
c
4
, c
12
(y
18
+ 2y
15
+ ··· + 2y + 1)(y
26
− 47y
25
+ ··· − 2y + 1)
c
5
(y
18
+ 4y
16
+ ··· − 7y + 9)(y
26
+ 53y
25
+ ··· + 99205y + 37249)
c
6
, c
9
(y
18
+ y
17
+ ··· + 2y + 1)(y
26
− 54y
25
+ ··· − 2y + 1)
c
8
, c
11
(y
18
− y
17
+ ··· − 2y + 1)(y
26
+ 30y
24
+ ··· + 2y + 1)
c
10
(y
18
− y
17
+ ··· + y + 1)(y
26
+ 48y
25
+ ··· + 3085y + 1849)
14
