12a
1018
(K12a
1018
)
A knot diagram
1
Linearized knot diagam
4 6 1 10 9 11 12 3 5 2 8 7
Solving Sequence
4,10 2,5
11 1 3 9 6 7 8 12
c
4
c
10
c
1
c
3
c
9
c
5
c
6
c
8
c
12
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.80811 × 10
120
u
82
3.74088 × 10
121
u
81
+ ··· + 1.73742 × 10
122
b + 3.18684 × 10
122
,
6.10199 × 10
123
u
82
+ 1.07219 × 10
124
u
81
+ ··· + 2.95362 × 10
123
a 9.13225 × 10
123
,
u
83
2u
82
+ ··· + 2u 1i
I
u
2
= hb + 1, u
3
+ 11u
2
+ 17a 9u + 5, u
4
u
3
+ u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 87 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−8.81 × 10
120
u
82
3.74 × 10
121
u
81
+ · · · + 1.74 × 10
122
b + 3.19 ×
10
122
, 6.10 × 10
123
u
82
+ 1.07 × 10
124
u
81
+ · · · + 2.95 × 10
123
a 9.13 ×
10
123
, u
83
2u
82
+ · · · + 2u 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
2.06594u
82
3.63008u
81
+ ··· + 1.45256u + 3.09189
0.0506964u
82
+ 0.215312u
81
+ ··· 0.518239u 1.83424
a
5
=
1
u
2
a
11
=
2.65834u
82
+ 5.40550u
81
+ ··· + 3.14748u 8.59296
0.367078u
82
1.09517u
81
+ ··· + 0.336880u + 1.82664
a
1
=
2.11663u
82
3.41477u
81
+ ··· + 0.934318u + 1.25765
0.0506964u
82
+ 0.215312u
81
+ ··· 0.518239u 1.83424
a
3
=
1.68022u
82
2.87266u
81
+ ··· + 2.28099u + 2.27888
0.146416u
82
+ 0.413543u
81
+ ··· + 0.0785799u 1.71128
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
2u
2
a
7
=
0.532917u
82
0.701603u
81
+ ··· + 1.65138u + 3.72914
0.144848u
82
0.280506u
81
+ ··· + 0.0803900u + 0.0568371
a
8
=
0.858192u
82
+ 1.37862u
81
+ ··· 7.54635u 4.74270
0.321807u
82
0.770401u
81
+ ··· 0.119629u + 0.879748
a
12
=
2.24967u
82
+ 4.84113u
81
+ ··· + 6.28939u 7.92112
0.114212u
82
0.200029u
81
+ ··· + 1.38569u 0.0353137
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4.42394u
82
7.99659u
81
+ ··· 18.0819u + 5.80601
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
83
5u
82
+ ··· + 1900u + 289
c
2
u
83
7u
82
+ ··· 9656u 4624
c
4
, c
5
, c
9
u
83
2u
82
+ ··· + 2u 1
c
6
u
83
2u
82
+ ··· 220u + 740
c
7
, c
11
, c
12
u
83
+ 2u
82
+ ··· + 4u + 1
c
8
17(17u
83
+ 146u
82
+ ··· 1099060u 237379)
c
10
17(17u
83
44u
82
+ ··· 5.84920 × 10
7
u 1.51215 × 10
7
)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
83
69y
82
+ ··· + 2397356y 83521
c
2
y
83
+ 27y
82
+ ··· 556859072y 21381376
c
4
, c
5
, c
9
y
83
+ 84y
82
+ ··· 10y 1
c
6
y
83
24y
82
+ ··· 10786680y 547600
c
7
, c
11
, c
12
y
83
+ 72y
82
+ ··· 10y 1
c
8
289(289y
83
5404y
82
+ ··· 2.06281 × 10
11
y 5.63488 × 10
10
)
c
10
289
· (289y
83
33114y
82
+ ··· + 5536442937181744y 228659701764004)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.782805 + 0.622350I
a = 0.52929 + 1.38447I
b = 1.37711 0.46112I
1.01915 + 12.79430I 0
u = 0.782805 0.622350I
a = 0.52929 1.38447I
b = 1.37711 + 0.46112I
1.01915 12.79430I 0
u = 0.885475 + 0.494695I
a = 0.967396 + 0.215086I
b = 1.283710 + 0.275470I
0.56758 7.31597I 0
u = 0.885475 0.494695I
a = 0.967396 0.215086I
b = 1.283710 0.275470I
0.56758 + 7.31597I 0
u = 0.798818 + 0.627121I
a = 0.582618 1.256350I
b = 1.37805 + 0.37911I
6.14698 8.49089I 0
u = 0.798818 0.627121I
a = 0.582618 + 1.256350I
b = 1.37805 0.37911I
6.14698 + 8.49089I 0
u = 0.826346 + 0.637145I
a = 0.601005 + 1.051130I
b = 1.341300 0.264474I
3.82816 + 3.80053I 0
u = 0.826346 0.637145I
a = 0.601005 1.051130I
b = 1.341300 + 0.264474I
3.82816 3.80053I 0
u = 0.901864 + 0.528328I
a = 0.899335 0.371904I
b = 1.304330 0.167248I
5.75352 + 2.88332I 0
u = 0.901864 0.528328I
a = 0.899335 + 0.371904I
b = 1.304330 + 0.167248I
5.75352 2.88332I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.525308 + 0.797208I
a = 0.503368 0.745095I
b = 0.675910 + 0.313019I
5.31452 3.79971I 0
u = 0.525308 0.797208I
a = 0.503368 + 0.745095I
b = 0.675910 0.313019I
5.31452 + 3.79971I 0
u = 0.213461 + 0.908633I
a = 0.630364 + 0.227953I
b = 0.459200 0.065535I
0.80476 + 1.66407I 0
u = 0.213461 0.908633I
a = 0.630364 0.227953I
b = 0.459200 + 0.065535I
0.80476 1.66407I 0
u = 0.913020 + 0.584196I
a = 0.750655 + 0.558331I
b = 1.290260 + 0.025129I
3.54948 + 2.00682I 0
u = 0.913020 0.584196I
a = 0.750655 0.558331I
b = 1.290260 0.025129I
3.54948 2.00682I 0
u = 0.953333 + 0.808111I
a = 0.237270 0.569947I
b = 1.063910 + 0.103135I
5.08289 3.43351I 0
u = 0.953333 0.808111I
a = 0.237270 + 0.569947I
b = 1.063910 0.103135I
5.08289 + 3.43351I 0
u = 0.620259 + 0.336913I
a = 0.283924 + 0.862450I
b = 0.387199 0.684158I
6.55292 0.16961I 5.64340 + 1.50558I
u = 0.620259 0.336913I
a = 0.283924 0.862450I
b = 0.387199 + 0.684158I
6.55292 + 0.16961I 5.64340 1.50558I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.520975 + 0.447008I
a = 0.07501 1.56719I
b = 0.072867 + 1.069050I
3.58604 + 7.43559I 0.66258 8.91411I
u = 0.520975 0.447008I
a = 0.07501 + 1.56719I
b = 0.072867 1.069050I
3.58604 7.43559I 0.66258 + 8.91411I
u = 0.488053 + 0.429242I
a = 0.11248 + 1.52114I
b = 0.184482 0.935678I
1.22427 3.86628I 4.46809 + 8.48691I
u = 0.488053 0.429242I
a = 0.11248 1.52114I
b = 0.184482 + 0.935678I
1.22427 + 3.86628I 4.46809 8.48691I
u = 0.408975 + 0.441083I
a = 1.81487 + 0.58604I
b = 0.028839 0.549577I
3.48331 4.12239I 1.39758 + 0.54471I
u = 0.408975 0.441083I
a = 1.81487 0.58604I
b = 0.028839 + 0.549577I
3.48331 + 4.12239I 1.39758 0.54471I
u = 0.223262 + 0.556235I
a = 0.78004 + 1.47977I
b = 1.31601 0.58172I
0.65938 5.19774I 6.58071 + 7.61362I
u = 0.223262 0.556235I
a = 0.78004 1.47977I
b = 1.31601 + 0.58172I
0.65938 + 5.19774I 6.58071 7.61362I
u = 0.392922 + 0.435677I
a = 0.49360 1.64916I
b = 0.555247 + 0.749866I
1.53412 + 0.79906I 2.20367 5.32165I
u = 0.392922 0.435677I
a = 0.49360 + 1.64916I
b = 0.555247 0.749866I
1.53412 0.79906I 2.20367 + 5.32165I
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.116182 + 0.566131I
a = 0.701849 + 0.864198I
b = 1.45040 0.29162I
1.20129 + 1.76650I 7.97021 0.46497I
u = 0.116182 0.566131I
a = 0.701849 0.864198I
b = 1.45040 + 0.29162I
1.20129 1.76650I 7.97021 + 0.46497I
u = 0.06981 + 1.42084I
a = 1.052230 0.762563I
b = 0.290686 + 0.045735I
2.33913 2.71471I 0
u = 0.06981 1.42084I
a = 1.052230 + 0.762563I
b = 0.290686 0.045735I
2.33913 + 2.71471I 0
u = 0.175745 + 0.549432I
a = 0.68890 1.25274I
b = 1.35592 + 0.43714I
4.85678 + 1.65891I 12.61039 4.40196I
u = 0.175745 0.549432I
a = 0.68890 + 1.25274I
b = 1.35592 0.43714I
4.85678 1.65891I 12.61039 + 4.40196I
u = 0.03751 + 1.43024I
a = 0.11758 3.57447I
b = 0.911378 + 0.077861I
3.37555 + 2.94604I 0
u = 0.03751 1.43024I
a = 0.11758 + 3.57447I
b = 0.911378 0.077861I
3.37555 2.94604I 0
u = 0.07652 + 1.42904I
a = 0.641968 + 1.151170I
b = 0.470044 0.240065I
6.90616 0.48127I 0
u = 0.07652 1.42904I
a = 0.641968 1.151170I
b = 0.470044 + 0.240065I
6.90616 + 0.48127I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.472143 + 0.295646I
a = 0.361448 0.938111I
b = 0.025837 + 0.465349I
0.819548 + 0.994646I 3.41663 3.70418I
u = 0.472143 0.295646I
a = 0.361448 + 0.938111I
b = 0.025837 0.465349I
0.819548 0.994646I 3.41663 + 3.70418I
u = 0.17229 + 1.44421I
a = 0.074823 + 0.428015I
b = 0.169329 0.919425I
0.80655 2.93738I 0
u = 0.17229 1.44421I
a = 0.074823 0.428015I
b = 0.169329 + 0.919425I
0.80655 + 2.93738I 0
u = 0.11983 + 1.45548I
a = 0.007865 0.755387I
b = 0.328958 + 0.823755I
4.92161 + 3.00725I 0
u = 0.11983 1.45548I
a = 0.007865 + 0.755387I
b = 0.328958 0.823755I
4.92161 3.00725I 0
u = 0.02245 + 1.47774I
a = 1.23231 + 0.76609I
b = 1.250300 0.204227I
7.82085 1.05745I 0
u = 0.02245 1.47774I
a = 1.23231 0.76609I
b = 1.250300 + 0.204227I
7.82085 + 1.05745I 0
u = 0.345026 + 0.375822I
a = 1.82514 0.01402I
b = 0.174745 + 0.326519I
1.31064 + 0.88896I 4.75289 + 0.24255I
u = 0.345026 0.375822I
a = 1.82514 + 0.01402I
b = 0.174745 0.326519I
1.31064 0.88896I 4.75289 0.24255I
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.11513 + 1.49082I
a = 0.191306 0.823782I
b = 0.612194 + 1.160240I
4.80565 + 2.60717I 0
u = 0.11513 1.49082I
a = 0.191306 + 0.823782I
b = 0.612194 1.160240I
4.80565 2.60717I 0
u = 0.13971 + 1.49410I
a = 0.247651 + 0.725073I
b = 0.324935 1.355310I
7.56485 6.08862I 0
u = 0.13971 1.49410I
a = 0.247651 0.725073I
b = 0.324935 + 1.355310I
7.56485 + 6.08862I 0
u = 0.15069 + 1.49801I
a = 0.297418 0.685274I
b = 0.19342 + 1.45635I
2.81837 + 9.82043I 0
u = 0.15069 1.49801I
a = 0.297418 + 0.685274I
b = 0.19342 1.45635I
2.81837 9.82043I 0
u = 0.04275 + 1.52628I
a = 0.299429 0.574584I
b = 1.75212 + 0.68776I
11.77850 + 2.40546I 0
u = 0.04275 1.52628I
a = 0.299429 + 0.574584I
b = 1.75212 0.68776I
11.77850 2.40546I 0
u = 0.02949 + 1.52815I
a = 0.317392 + 0.417495I
b = 1.85898 0.48742I
8.17636 + 1.26217I 0
u = 0.02949 1.52815I
a = 0.317392 0.417495I
b = 1.85898 + 0.48742I
8.17636 1.26217I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.05381 + 1.52754I
a = 0.255814 + 0.673122I
b = 1.68693 0.86794I
7.60320 6.14298I 0
u = 0.05381 1.52754I
a = 0.255814 0.673122I
b = 1.68693 + 0.86794I
7.60320 + 6.14298I 0
u = 0.370668 + 0.270581I
a = 2.90500 0.92129I
b = 0.644155 0.280257I
1.93886 + 1.76536I 0.91281 6.54865I
u = 0.370668 0.270581I
a = 2.90500 + 0.92129I
b = 0.644155 + 0.280257I
1.93886 1.76536I 0.91281 + 6.54865I
u = 0.26189 + 1.57321I
a = 0.443692 + 1.155900I
b = 1.51111 0.56191I
8.2311 + 16.6555I 0
u = 0.26189 1.57321I
a = 0.443692 1.155900I
b = 1.51111 + 0.56191I
8.2311 16.6555I 0
u = 0.26540 + 1.57646I
a = 0.395466 1.114550I
b = 1.51838 + 0.50049I
13.3848 12.4184I 0
u = 0.26540 1.57646I
a = 0.395466 + 1.114550I
b = 1.51838 0.50049I
13.3848 + 12.4184I 0
u = 0.26971 + 1.58282I
a = 0.351050 + 1.031460I
b = 1.49352 0.41237I
11.12430 + 7.83212I 0
u = 0.26971 1.58282I
a = 0.351050 1.031460I
b = 1.49352 + 0.41237I
11.12430 7.83212I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.373590 + 0.067298I
a = 6.22963 + 0.85922I
b = 1.134360 + 0.116039I
0.84708 + 3.20049I 10.64520 + 4.54047I
u = 0.373590 0.067298I
a = 6.22963 0.85922I
b = 1.134360 0.116039I
0.84708 3.20049I 10.64520 4.54047I
u = 0.28768 + 1.59786I
a = 0.251990 + 0.833989I
b = 1.41939 0.21322I
10.80970 + 6.43057I 0
u = 0.28768 1.59786I
a = 0.251990 0.833989I
b = 1.41939 + 0.21322I
10.80970 6.43057I 0
u = 0.25503 + 1.60505I
a = 0.494464 0.846169I
b = 1.277530 + 0.384526I
2.83571 7.53120I 0
u = 0.25503 1.60505I
a = 0.494464 + 0.846169I
b = 1.277530 0.384526I
2.83571 + 7.53120I 0
u = 0.30802 + 1.59835I
a = 0.160796 0.731799I
b = 1.395700 + 0.082663I
12.77920 1.67211I 0
u = 0.30802 1.59835I
a = 0.160796 + 0.731799I
b = 1.395700 0.082663I
12.77920 + 1.67211I 0
u = 0.33005 + 1.59698I
a = 0.112595 + 0.631850I
b = 1.338780 + 0.012446I
7.38416 2.68840I 0
u = 0.33005 1.59698I
a = 0.112595 0.631850I
b = 1.338780 0.012446I
7.38416 + 2.68840I 0
12
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.150260 + 0.330313I
a = 0.60204 + 2.73035I
b = 1.003660 0.126295I
1.78354 0.56624I 5.83264 3.56726I
u = 0.150260 0.330313I
a = 0.60204 2.73035I
b = 1.003660 + 0.126295I
1.78354 + 0.56624I 5.83264 + 3.56726I
u = 0.342169
a = 7.14812
b = 1.11647
3.19577 13.6620
13
II. I
u
2
= hb + 1, u
3
+ 11u
2
+ 17a 9u + 5, u
4
u
3
+ u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
2
=
0.0588235u
3
0.647059u
2
+ 0.529412u 0.294118
1
a
5
=
1
u
2
a
11
=
0.0103806u
3
0.00346021u
2
+ 0.318339u 0.242215
0.588235u
3
+ 0.470588u
2
+ 0.705882u 0.0588235
a
1
=
0.0588235u
3
0.647059u
2
+ 0.529412u 1.29412
1
a
3
=
0.0588235u
3
0.647059u
2
+ 0.529412u 0.294118
1
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
3
u
2
+ 1
a
7
=
0.0726644u
3
+ 1.02422u
2
0.228374u + 0.695502
0.117647u
3
0.294118u
2
+ 0.0588235u + 0.411765
a
8
=
0.283737u
3
+ 0.238754u
2
0.965398u 0.287197
0.588235u
3
+ 0.529412u
2
+ 0.294118u + 0.0588235
a
12
=
0.737024u
3
0.245675u
2
+ 0.602076u 0.197232
0.235294u
3
0.588235u
2
+ 0.117647u 1.17647
(ii) Obstruction class = 1
(iii) Cusp Shapes =
631
289
u
3
+
403
289
u
2
+
2228
289
u
1268
289
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u 1)
4
c
2
u
4
c
3
(u + 1)
4
c
4
, c
5
u
4
u
3
+ u
2
+ 1
c
6
u
4
+ u
3
+ 5u
2
u + 2
c
7
u
4
u
3
+ 3u
2
2u + 1
c
8
17(17u
4
3u
3
+ 11u
2
+ 1)
c
9
u
4
+ u
3
+ u
2
+ 1
c
10
17(17u
4
+ 3u
3
4u
2
+ u + 2)
c
11
, c
12
u
4
+ u
3
+ 3u
2
+ 2u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
(y 1)
4
c
2
y
4
c
4
, c
5
, c
9
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
6
y
4
+ 9y
3
+ 31y
2
+ 19y + 4
c
7
, c
11
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
8
289(289y
4
+ 365y
3
+ 155y
2
+ 22y + 1)
c
10
289(289y
4
145y
3
+ 78y
2
17y + 4)
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.351808 + 0.720342I
a = 0.195047 + 0.703062I
b = 1.00000
1.85594 1.41510I 6.55007 + 4.61446I
u = 0.351808 0.720342I
a = 0.195047 0.703062I
b = 1.00000
1.85594 + 1.41510I 6.55007 4.61446I
u = 0.851808 + 0.911292I
a = 0.136224 0.449937I
b = 1.00000
5.14581 + 3.16396I 1.25097 + 11.86905I
u = 0.851808 0.911292I
a = 0.136224 + 0.449937I
b = 1.00000
5.14581 3.16396I 1.25097 11.86905I
17
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u 1)
4
)(u
83
5u
82
+ ··· + 1900u + 289)
c
2
u
4
(u
83
7u
82
+ ··· 9656u 4624)
c
3
((u + 1)
4
)(u
83
5u
82
+ ··· + 1900u + 289)
c
4
, c
5
(u
4
u
3
+ u
2
+ 1)(u
83
2u
82
+ ··· + 2u 1)
c
6
(u
4
+ u
3
+ 5u
2
u + 2)(u
83
2u
82
+ ··· 220u + 740)
c
7
(u
4
u
3
+ 3u
2
2u + 1)(u
83
+ 2u
82
+ ··· + 4u + 1)
c
8
289(17u
4
3u
3
+ 11u
2
+ 1)
· (17u
83
+ 146u
82
+ ··· 1099060u 237379)
c
9
(u
4
+ u
3
+ u
2
+ 1)(u
83
2u
82
+ ··· + 2u 1)
c
10
289(17u
4
+ 3u
3
4u
2
+ u + 2)
· (17u
83
44u
82
+ ··· 58491986u 15121498)
c
11
, c
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
83
+ 2u
82
+ ··· + 4u + 1)
18
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
((y 1)
4
)(y
83
69y
82
+ ··· + 2397356y 83521)
c
2
y
4
(y
83
+ 27y
82
+ ··· 5.56859 × 10
8
y 2.13814 × 10
7
)
c
4
, c
5
, c
9
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
83
+ 84y
82
+ ··· 10y 1)
c
6
(y
4
+ 9y
3
+ 31y
2
+ 19y + 4)
· (y
83
24y
82
+ ··· 10786680y 547600)
c
7
, c
11
, c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
83
+ 72y
82
+ ··· 10y 1)
c
8
83521(289y
4
+ 365y
3
+ 155y
2
+ 22y + 1)
· (289y
83
5404y
82
+ ··· 206281469138y 56348789641)
c
10
83521(289y
4
145y
3
+ 78y
2
17y + 4)
· (289y
83
33114y
82
+ ··· + 5536442937181744y 228659701764004)
19