12a
0076
(K12a
0076
)
A knot diagram
1
Linearized knot diagam
3 5 7 11 2 10 1 12 4 6 9 8
Solving Sequence
2,6
5 3
1,11
4 10 7 8 9 12
c
5
c
2
c
1
c
4
c
10
c
6
c
7
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h7.93101 × 10
98
u
76
+ 1.64483 × 10
99
u
75
+ ··· + 2.50573 × 10
99
b 1.01951 × 10
100
,
2.37414 × 10
100
u
76
7.33884 × 10
100
u
75
+ ··· + 6.26432 × 10
100
a 4.38701 × 10
101
,
u
77
+ 4u
76
+ ··· + 101u + 25i
I
u
2
= h−320a
2
u 190a
2
889au + 1993b + 1652a + 701u 518, 5a
3
5a
2
u 4a
2
4au a + 11u 11,
u
2
u + 1i
* 2 irreducible components of dim
C
= 0, with total 83 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
= h7.93 × 10
98
u
76
+ 1.64 × 10
99
u
75
+ · · · + 2.51 × 10
99
b 1.02 ×
10
100
, 2.37 × 10
100
u
76
7.34 × 10
100
u
75
+ · · · + 6.26 × 10
100
a 4.39 ×
10
101
, u
77
+ 4u
76
+ · · · + 101u + 25i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
0.378995u
76
+ 1.17153u
75
+ ··· + 38.9689u + 7.00317
0.316515u
76
0.656426u
75
+ ··· + 3.88281u + 4.06872
a
4
=
0.382922u
76
+ 1.34261u
75
+ ··· + 5.59826u + 1.24813
0.316632u
76
+ 1.34041u
75
+ ··· + 40.8488u + 10.7971
a
10
=
0.0624796u
76
+ 0.515104u
75
+ ··· + 42.8517u + 11.0719
0.316515u
76
0.656426u
75
+ ··· + 3.88281u + 4.06872
a
7
=
0.169032u
76
0.182910u
75
+ ··· 24.2572u 6.80526
0.289827u
76
+ 0.617219u
75
+ ··· 5.81712u 2.87335
a
8
=
0.172862u
76
0.154859u
75
+ ··· 23.2157u 6.96987
0.326324u
76
+ 0.494996u
75
+ ··· 15.9347u 6.46441
a
9
=
0.155679u
76
0.308708u
75
+ ··· + 14.0992u + 4.25438
0.0753730u
76
0.185600u
75
+ ··· + 1.65389u + 2.31494
a
12
=
0.241155u
76
+ 0.606307u
75
+ ··· 6.10719u 4.25876
0.00962114u
76
+ 0.358023u
75
+ ··· + 14.6700u + 3.86949
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1.55122u
76
3.85524u
75
+ ··· 10.1221u + 0.155354
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
+ 26u
76
+ ··· + 4801u 625
c
2
, c
5
u
77
+ 4u
76
+ ··· + 101u + 25
c
3
25(25u
77
140u
76
+ ··· 1.87152 × 10
7
u + 4199891)
c
4
25(25u
77
45u
76
+ ··· + 49984u + 52544)
c
6
, c
10
u
77
+ 3u
76
+ ··· 8u
2
+ 1
c
7
, c
8
, c
11
c
12
u
77
3u
76
+ ··· 6u + 1
c
9
u
77
+ u
76
+ ··· + 15200u + 8000
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
+ 54y
76
+ ··· + 264859601y 390625
c
2
, c
5
y
77
+ 26y
76
+ ··· + 4801y 625
c
3
625
· (625y
77
+ 32100y
76
+ ··· 165791891422930y 17639084411881)
c
4
625(625y
77
+ 30025y
76
+ ··· 4.56084 × 10
10
y 2.76087 × 10
9
)
c
6
, c
10
y
77
+ 49y
76
+ ··· + 16y 1
c
7
, c
8
, c
11
c
12
y
77
+ 93y
76
+ ··· + 16y 1
c
9
y
77
+ 35y
76
+ ··· 964480000y 64000000
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.023387 + 0.993675I
a = 1.48275 + 0.20664I
b = 0.625759 + 0.325187I
1.74432 + 2.06267I 0
u = 0.023387 0.993675I
a = 1.48275 0.20664I
b = 0.625759 0.325187I
1.74432 2.06267I 0
u = 0.689051 + 0.710247I
a = 0.672174 + 0.847004I
b = 1.093650 0.218602I
3.26103 + 2.04999I 0
u = 0.689051 0.710247I
a = 0.672174 0.847004I
b = 1.093650 + 0.218602I
3.26103 2.04999I 0
u = 0.437005 + 0.886797I
a = 0.617746 0.137414I
b = 0.200968 + 0.136308I
0.31514 + 1.81008I 0
u = 0.437005 0.886797I
a = 0.617746 + 0.137414I
b = 0.200968 0.136308I
0.31514 1.81008I 0
u = 0.802987 + 0.670328I
a = 0.132409 + 0.135406I
b = 0.43177 + 1.42400I
5.18414 + 3.21854I 0
u = 0.802987 0.670328I
a = 0.132409 0.135406I
b = 0.43177 1.42400I
5.18414 3.21854I 0
u = 0.580300 + 0.745312I
a = 0.01473 + 1.95275I
b = 0.032548 + 1.130350I
2.99487 + 1.53571I 8.00000 + 0.I
u = 0.580300 0.745312I
a = 0.01473 1.95275I
b = 0.032548 1.130350I
2.99487 1.53571I 8.00000 + 0.I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.850071 + 0.645897I
a = 0.687278 0.617056I
b = 1.031170 + 0.139364I
12.61110 + 4.44495I 0
u = 0.850071 0.645897I
a = 0.687278 + 0.617056I
b = 1.031170 0.139364I
12.61110 4.44495I 0
u = 0.107724 + 1.076330I
a = 0.83445 1.21670I
b = 0.391468 + 0.997418I
1.08919 + 2.96820I 0
u = 0.107724 1.076330I
a = 0.83445 + 1.21670I
b = 0.391468 0.997418I
1.08919 2.96820I 0
u = 0.645982 + 0.868158I
a = 0.960269 0.964614I
b = 1.243670 + 0.117565I
0.13971 2.51501I 0
u = 0.645982 0.868158I
a = 0.960269 + 0.964614I
b = 1.243670 0.117565I
0.13971 + 2.51501I 0
u = 0.756836 + 0.799522I
a = 0.201274 + 0.141714I
b = 0.47634 1.45900I
7.35750 1.25503I 0
u = 0.756836 0.799522I
a = 0.201274 0.141714I
b = 0.47634 + 1.45900I
7.35750 + 1.25503I 0
u = 0.925906 + 0.617713I
a = 0.094308 0.190665I
b = 0.44275 1.38890I
8.30126 + 7.27195I 0
u = 0.925906 0.617713I
a = 0.094308 + 0.190665I
b = 0.44275 + 1.38890I
8.30126 7.27195I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.171129 + 0.864991I
a = 1.77593 0.38376I
b = 0.748125 0.526560I
2.60922 1.38173I 13.51813 + 2.09755I
u = 0.171129 0.864991I
a = 1.77593 + 0.38376I
b = 0.748125 + 0.526560I
2.60922 + 1.38173I 13.51813 2.09755I
u = 0.564948 + 0.667315I
a = 1.52137 2.48650I
b = 0.111660 + 0.733444I
10.81200 + 1.40949I 6.43106 2.48150I
u = 0.564948 0.667315I
a = 1.52137 + 2.48650I
b = 0.111660 0.733444I
10.81200 1.40949I 6.43106 + 2.48150I
u = 0.582271 + 0.971594I
a = 0.641231 0.469572I
b = 0.301785 + 0.108520I
1.27808 + 3.12805I 0
u = 0.582271 0.971594I
a = 0.641231 + 0.469572I
b = 0.301785 0.108520I
1.27808 3.12805I 0
u = 0.378177 + 0.760297I
a = 1.97319 + 0.66535I
b = 0.893170 + 0.851679I
2.80627 4.33786I 7.45487 3.06969I
u = 0.378177 0.760297I
a = 1.97319 0.66535I
b = 0.893170 0.851679I
2.80627 + 4.33786I 7.45487 + 3.06969I
u = 0.790859 + 0.836843I
a = 1.77041 0.38931I
b = 0.62234 1.33323I
16.1641 1.5411I 0
u = 0.790859 0.836843I
a = 1.77041 + 0.38931I
b = 0.62234 + 1.33323I
16.1641 + 1.5411I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.639240 + 0.976315I
a = 1.65830 0.49768I
b = 0.125080 1.109880I
2.18376 + 3.33368I 0
u = 0.639240 0.976315I
a = 1.65830 + 0.49768I
b = 0.125080 + 1.109880I
2.18376 3.33368I 0
u = 0.283439 + 0.778804I
a = 2.33704 1.18812I
b = 0.062296 1.174070I
9.98727 + 1.50639I 0.66145 3.42901I
u = 0.283439 0.778804I
a = 2.33704 + 1.18812I
b = 0.062296 + 1.174070I
9.98727 1.50639I 0.66145 + 3.42901I
u = 0.117920 + 1.168920I
a = 1.291680 0.300778I
b = 0.628830 0.167135I
5.79410 + 3.63952I 0
u = 0.117920 1.168920I
a = 1.291680 + 0.300778I
b = 0.628830 + 0.167135I
5.79410 3.63952I 0
u = 0.723744 + 0.928946I
a = 1.85578 + 0.31129I
b = 0.61575 + 1.38912I
6.95838 4.36192I 0
u = 0.723744 0.928946I
a = 1.85578 0.31129I
b = 0.61575 1.38912I
6.95838 + 4.36192I 0
u = 1.082260 + 0.468850I
a = 0.123493 0.256538I
b = 0.044273 1.217200I
6.73924 + 1.85246I 0
u = 1.082260 0.468850I
a = 0.123493 + 0.256538I
b = 0.044273 + 1.217200I
6.73924 1.85246I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.676567 + 0.972926I
a = 1.098660 + 0.822983I
b = 1.181550 0.009799I
2.47138 7.34623I 0
u = 0.676567 0.972926I
a = 1.098660 0.822983I
b = 1.181550 + 0.009799I
2.47138 + 7.34623I 0
u = 1.025320 + 0.614382I
a = 0.228092 + 0.157777I
b = 0.45532 + 1.37631I
17.3658 + 9.6655I 0
u = 1.025320 0.614382I
a = 0.228092 0.157777I
b = 0.45532 1.37631I
17.3658 9.6655I 0
u = 0.769678 + 0.915176I
a = 0.069711 0.333527I
b = 0.52438 + 1.43530I
15.9240 4.3215I 0
u = 0.769678 0.915176I
a = 0.069711 + 0.333527I
b = 0.52438 1.43530I
15.9240 + 4.3215I 0
u = 0.457284 + 0.657961I
a = 0.61765 + 1.70350I
b = 0.013064 0.547144I
2.28018 + 1.37290I 3.34311 4.48860I
u = 0.457284 0.657961I
a = 0.61765 1.70350I
b = 0.013064 + 0.547144I
2.28018 1.37290I 3.34311 + 4.48860I
u = 0.271251 + 0.735692I
a = 0.256281 + 1.284760I
b = 0.764229 0.712502I
2.74924 + 1.47081I 7.37057 5.74659I
u = 0.271251 0.735692I
a = 0.256281 1.284760I
b = 0.764229 + 0.712502I
2.74924 1.47081I 7.37057 + 5.74659I
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.672668 + 1.026560I
a = 0.772233 + 0.609784I
b = 0.372498 0.168400I
9.55875 + 3.71126I 0
u = 0.672668 1.026560I
a = 0.772233 0.609784I
b = 0.372498 + 0.168400I
9.55875 3.71126I 0
u = 0.712145 + 1.018770I
a = 1.86345 0.22946I
b = 0.57025 1.40468I
4.13125 8.92679I 0
u = 0.712145 1.018770I
a = 1.86345 + 0.22946I
b = 0.57025 + 1.40468I
4.13125 + 8.92679I 0
u = 0.640073 + 0.401249I
a = 0.61346 1.74507I
b = 0.242727 + 0.508756I
10.92250 + 1.41966I 3.27349 3.63147I
u = 0.640073 0.401249I
a = 0.61346 + 1.74507I
b = 0.242727 0.508756I
10.92250 1.41966I 3.27349 + 3.63147I
u = 0.725026 + 1.045960I
a = 1.119890 0.723073I
b = 1.123130 0.004421I
11.3969 10.3217I 0
u = 0.725026 1.045960I
a = 1.119890 + 0.723073I
b = 1.123130 + 0.004421I
11.3969 + 10.3217I 0
u = 0.201201 + 1.271660I
a = 0.929381 + 0.895259I
b = 0.346853 1.094610I
0.58610 + 5.84122I 0
u = 0.201201 1.271660I
a = 0.929381 0.895259I
b = 0.346853 + 1.094610I
0.58610 5.84122I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.740013 + 1.082960I
a = 1.83895 + 0.18377I
b = 0.54663 + 1.38812I
6.8662 13.3948I 0
u = 0.740013 1.082960I
a = 1.83895 0.18377I
b = 0.54663 1.38812I
6.8662 + 13.3948I 0
u = 0.771024 + 1.128770I
a = 1.81769 0.15434I
b = 0.53700 1.37405I
15.7376 16.1737I 0
u = 0.771024 1.128770I
a = 1.81769 + 0.15434I
b = 0.53700 + 1.37405I
15.7376 + 16.1737I 0
u = 0.320237 + 0.541394I
a = 0.18136 + 2.01696I
b = 0.231553 0.595039I
2.26536 + 1.35585I 3.06700 4.58945I
u = 0.320237 0.541394I
a = 0.18136 2.01696I
b = 0.231553 + 0.595039I
2.26536 1.35585I 3.06700 + 4.58945I
u = 1.296830 + 0.495291I
a = 0.176059 + 0.133103I
b = 0.049062 + 1.240290I
15.6374 + 2.0891I 0
u = 1.296830 0.495291I
a = 0.176059 0.133103I
b = 0.049062 1.240290I
15.6374 2.0891I 0
u = 0.825265 + 1.129010I
a = 0.971647 + 0.072412I
b = 0.154594 + 1.175390I
4.80654 + 4.92929I 0
u = 0.825265 1.129010I
a = 0.971647 0.072412I
b = 0.154594 1.175390I
4.80654 4.92929I 0
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.512499 + 0.280972I
a = 0.726334 + 0.007761I
b = 0.013821 + 1.181210I
3.20881 + 1.14210I 4.80285 5.42907I
u = 0.512499 0.280972I
a = 0.726334 0.007761I
b = 0.013821 1.181210I
3.20881 1.14210I 4.80285 + 5.42907I
u = 0.23954 + 1.42224I
a = 0.869717 0.736081I
b = 0.336774 + 1.148260I
8.71669 + 7.31926I 0
u = 0.23954 1.42224I
a = 0.869717 + 0.736081I
b = 0.336774 1.148260I
8.71669 7.31926I 0
u = 0.93837 + 1.22898I
a = 0.807522 + 0.046238I
b = 0.163263 1.205750I
13.4511 + 5.6875I 0
u = 0.93837 1.22898I
a = 0.807522 0.046238I
b = 0.163263 + 1.205750I
13.4511 5.6875I 0
u = 0.193384
a = 1.47995
b = 0.443692
0.677358 14.5420
12
II. I
u
2
= h−320a
2
u 889au + · · · + 1652a 518, 5a
3
5a
2
u 4a
2
4au
a + 11u 11, u
2
u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u 1
a
3
=
u
u 1
a
1
=
1
0
a
11
=
a
0.160562a
2
u + 0.446061au + ··· 0.828901a + 0.259910
a
4
=
0.169594a
2
u + 0.114902au + ··· 0.150527a + 0.437030
0.0326141a
2
u 0.137481au + ··· + 0.105871a 0.584044
a
10
=
0.160562a
2
u + 0.446061au + ··· + 0.171099a + 0.259910
0.160562a
2
u + 0.446061au + ··· 0.828901a + 0.259910
a
7
=
0.0501756a
2
u + 0.173106au + ··· + 0.00903161a + 0.793778
0.880582a
2
u + 0.288008au + ··· 0.141495a 0.769192
a
8
=
0.830406a
2
u 0.114902au + ··· + 0.150527a + 1.56297
0.880582a
2
u + 0.288008au + ··· 0.141495a 0.769192
a
9
=
0.160562a
2
u + 0.446061au + ··· + 0.171099a + 0.259910
0.160562a
2
u + 0.446061au + ··· 0.828901a + 0.259910
a
12
=
0.158053a
2
u + 0.204717au + ··· + 0.871550a 0.400401
0.720020a
2
u + 0.734069au + ··· 0.970396a 1.50928
(ii) Obstruction class = 1
(iii) Cusp Shapes =
402
1993
a
2
u
135
1993
a
2
8761
1993
au +
8936
1993
a
10883
1993
u
9389
1993
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
2
u + 1)
3
c
2
(u
2
+ u + 1)
3
c
3
25(25u
6
35u
5
+ 29u
4
18u
3
+ 9u
2
4u + 1)
c
4
25(25u
6
20u
5
+ 21u
4
6u
3
+ 5u
2
u + 1)
c
6
(u
3
+ u
2
1)
2
c
7
, c
8
(u
3
u
2
+ 2u 1)
2
c
9
u
6
c
10
(u
3
u
2
+ 1)
2
c
11
, c
12
(u
3
+ u
2
+ 2u + 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y
2
+ y + 1)
3
c
3
625(625y
6
+ 225y
5
+ 31y
4
32y
3
5y
2
+ 2y + 1)
c
4
625(625y
6
+ 650y
5
+ 451y
4
+ 184y
3
+ 55y
2
+ 9y + 1)
c
6
, c
10
(y
3
y
2
+ 2y 1)
2
c
7
, c
8
, c
11
c
12
(y
3
+ 3y
2
+ 2y 1)
2
c
9
y
6
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.858302 0.653743I
b = 0.754878
1.11345 + 2.02988I 12.07771 2.86462I
u = 0.500000 + 0.866025I
a = 0.434082 + 1.056380I
b = 0.877439 0.744862I
3.02413 0.79824I 2.61844 4.09859I
u = 0.500000 + 0.866025I
a = 1.72422 + 0.46339I
b = 0.877439 + 0.744862I
3.02413 + 4.85801I 1.92384 9.69912I
u = 0.500000 0.866025I
a = 0.858302 + 0.653743I
b = 0.754878
1.11345 2.02988I 12.07771 + 2.86462I
u = 0.500000 0.866025I
a = 0.434082 1.056380I
b = 0.877439 + 0.744862I
3.02413 + 0.79824I 2.61844 + 4.09859I
u = 0.500000 0.866025I
a = 1.72422 0.46339I
b = 0.877439 0.744862I
3.02413 4.85801I 1.92384 + 9.69912I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
u + 1)
3
)(u
77
+ 26u
76
+ ··· + 4801u 625)
c
2
((u
2
+ u + 1)
3
)(u
77
+ 4u
76
+ ··· + 101u + 25)
c
3
625(25u
6
35u
5
+ 29u
4
18u
3
+ 9u
2
4u + 1)
· (25u
77
140u
76
+ ··· 18715176u + 4199891)
c
4
625(25u
6
20u
5
+ 21u
4
6u
3
+ 5u
2
u + 1)
· (25u
77
45u
76
+ ··· + 49984u + 52544)
c
5
((u
2
u + 1)
3
)(u
77
+ 4u
76
+ ··· + 101u + 25)
c
6
((u
3
+ u
2
1)
2
)(u
77
+ 3u
76
+ ··· 8u
2
+ 1)
c
7
, c
8
((u
3
u
2
+ 2u 1)
2
)(u
77
3u
76
+ ··· 6u + 1)
c
9
u
6
(u
77
+ u
76
+ ··· + 15200u + 8000)
c
10
((u
3
u
2
+ 1)
2
)(u
77
+ 3u
76
+ ··· 8u
2
+ 1)
c
11
, c
12
((u
3
+ u
2
+ 2u + 1)
2
)(u
77
3u
76
+ ··· 6u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
3
)(y
77
+ 54y
76
+ ··· + 2.64860 × 10
8
y 390625)
c
2
, c
5
((y
2
+ y + 1)
3
)(y
77
+ 26y
76
+ ··· + 4801y 625)
c
3
390625(625y
6
+ 225y
5
+ 31y
4
32y
3
5y
2
+ 2y + 1)
· (625y
77
+ 32100y
76
+ ··· 165791891422930y 17639084411881)
c
4
390625(625y
6
+ 650y
5
+ 451y
4
+ 184y
3
+ 55y
2
+ 9y + 1)
· (625y
77
+ 30025y
76
+ ··· 45608364032y 2760871936)
c
6
, c
10
((y
3
y
2
+ 2y 1)
2
)(y
77
+ 49y
76
+ ··· + 16y 1)
c
7
, c
8
, c
11
c
12
((y
3
+ 3y
2
+ 2y 1)
2
)(y
77
+ 93y
76
+ ··· + 16y 1)
c
9
y
6
(y
77
+ 35y
76
+ ··· 9.64480 × 10
8
y 6.40000 × 10
7
)
18