12a
1204
(K12a
1204
)
A knot diagram
1
Linearized knot diagam
4 11 7 9 10 3 1 12 5 2 6 8
Solving Sequence
2,10
11
3,6
7 12 5 9 4 1 8
c
10
c
2
c
6
c
11
c
5
c
9
c
4
c
1
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h4.67618 × 10
190
u
79
+ 2.29826 × 10
191
u
78
+ ··· + 5.15330 × 10
191
b 1.47967 × 10
191
,
5.17863 × 10
194
u
79
+ 2.01367 × 10
195
u
78
+ ··· + 3.38572 × 10
194
a 3.88078 × 10
195
, u
80
+ 4u
79
+ ··· 12u + 1i
I
u
2
= h−au + b + 2a + u 1, 3a
2
+ 2au 4a 3u + 1, u
2
u + 1i
I
u
3
= hb, 3a u + 2, u
2
u + 1i
* 3 irreducible components of dim
C
= 0, with total 86 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
= h4.68 × 10
190
u
79
+ 2.30 × 10
191
u
78
+ · · · + 5.15 × 10
191
b 1.48 ×
10
191
, 5.18 × 10
194
u
79
+ 2.01 × 10
195
u
78
+ · · · + 3.39 × 10
194
a 3.88 ×
10
195
, u
80
+ 4u
79
+ · · · 12u + 1i
(i) Arc colorings
a
2
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
3
=
u
u
3
+ u
a
6
=
1.52955u
79
5.94754u
78
+ ··· + 130.269u + 11.4622
0.0907415u
79
0.445978u
78
+ ··· + 17.6286u + 0.287130
a
7
=
1.65356u
79
6.34789u
78
+ ··· + 128.810u + 11.4548
0.0338236u
79
0.258688u
78
+ ··· + 20.3603u + 0.198906
a
12
=
0.665941u
79
+ 2.23325u
78
+ ··· 127.524u 19.4828
0.155254u
79
+ 0.344909u
78
+ ··· + 1.73662u 2.15467
a
5
=
1.43881u
79
5.50156u
78
+ ··· + 112.640u + 11.1751
0.0907415u
79
0.445978u
78
+ ··· + 17.6286u + 0.287130
a
9
=
0.0923606u
79
0.0500166u
78
+ ··· + 123.650u + 20.7512
0.0594848u
79
0.0792420u
78
+ ··· 4.89863u + 2.41543
a
4
=
1.34210u
79
+ 5.18617u
78
+ ··· 149.249u 11.9533
0.0202947u
79
+ 0.0673583u
78
+ ··· 22.2316u 0.192689
a
1
=
1.65777u
79
6.13193u
78
+ ··· + 175.851u + 12.0583
0.266688u
79
0.803074u
78
+ ··· + 26.9199u + 0.143262
a
8
=
0.0702822u
79
0.631763u
78
+ ··· + 138.701u + 15.5114
0.144757u
79
+ 0.784009u
78
+ ··· 4.02021u + 2.28039
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.129037u
79
0.380541u
78
+ ··· 11.6124u + 3.37199
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
219(219u
80
+ 1298u
79
+ ··· + 2.36254 × 10
7
u 1524503)
c
2
, c
10
u
80
+ 4u
79
+ ··· 12u + 1
c
3
, c
6
u
80
+ 3u
79
+ ··· + 313u + 63
c
4
, c
5
, c
9
u
80
+ 3u
79
+ ··· + 180u + 36
c
7
, c
8
, c
12
u
80
2u
79
+ ··· 2u + 1
c
11
219(219u
80
1403u
79
+ ··· 226003u + 252193)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
47961(47961y
80
3172252y
79
+ ··· 2.97153 × 10
14
y + 2.32411 × 10
12
)
c
2
, c
10
y
80
44y
79
+ ··· 392y + 1
c
3
, c
6
y
80
69y
79
+ ··· + 7367y + 3969
c
4
, c
5
, c
9
y
80
75y
79
+ ··· + 9648y + 1296
c
7
, c
8
, c
12
y
80
+ 76y
79
+ ··· 72y + 1
c
11
47961
· (47961y
80
+ 610535y
79
+ ··· + 286076439375y + 63601309249)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.983733 + 0.200765I
a = 0.406326 1.062540I
b = 0.210455 0.410314I
1.68334 + 0.90111I 0
u = 0.983733 0.200765I
a = 0.406326 + 1.062540I
b = 0.210455 + 0.410314I
1.68334 0.90111I 0
u = 0.061105 + 1.004630I
a = 0.047178 0.295322I
b = 0.350818 0.747248I
9.01085 6.45760I 0. + 5.37585I
u = 0.061105 1.004630I
a = 0.047178 + 0.295322I
b = 0.350818 + 0.747248I
9.01085 + 6.45760I 0. 5.37585I
u = 0.933989 + 0.285753I
a = 0.74243 1.63544I
b = 1.22686 0.73490I
2.96990 + 3.39349I 0. 7.61793I
u = 0.933989 0.285753I
a = 0.74243 + 1.63544I
b = 1.22686 + 0.73490I
2.96990 3.39349I 0. + 7.61793I
u = 0.935699 + 0.210723I
a = 0.93109 1.46911I
b = 1.36724 0.37575I
1.85985 1.63062I 6.44657 + 8.90264I
u = 0.935699 0.210723I
a = 0.93109 + 1.46911I
b = 1.36724 + 0.37575I
1.85985 + 1.63062I 6.44657 8.90264I
u = 0.982994 + 0.345718I
a = 0.35044 + 2.66174I
b = 1.267870 + 0.058555I
3.53605 1.28537I 0
u = 0.982994 0.345718I
a = 0.35044 2.66174I
b = 1.267870 0.058555I
3.53605 + 1.28537I 0
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.623999 + 0.842208I
a = 0.557374 + 0.473399I
b = 1.44059 0.02605I
4.98872 + 2.13695I 0
u = 0.623999 0.842208I
a = 0.557374 0.473399I
b = 1.44059 + 0.02605I
4.98872 2.13695I 0
u = 0.625616 + 0.709759I
a = 0.274228 0.231688I
b = 0.446384 0.021824I
1.13446 + 2.26935I 7.02637 5.16830I
u = 0.625616 0.709759I
a = 0.274228 + 0.231688I
b = 0.446384 + 0.021824I
1.13446 2.26935I 7.02637 + 5.16830I
u = 1.016920 + 0.278841I
a = 0.10025 1.49918I
b = 0.328162 0.823029I
1.15386 3.31282I 0
u = 1.016920 0.278841I
a = 0.10025 + 1.49918I
b = 0.328162 + 0.823029I
1.15386 + 3.31282I 0
u = 1.049730 + 0.159659I
a = 1.42081 1.29437I
b = 0.033240 0.406752I
7.23462 + 0.23504I 0
u = 1.049730 0.159659I
a = 1.42081 + 1.29437I
b = 0.033240 + 0.406752I
7.23462 0.23504I 0
u = 1.079310 + 0.017861I
a = 3.67096 0.58217I
b = 1.354270 0.008617I
1.55886 + 0.00067I 0
u = 1.079310 0.017861I
a = 3.67096 + 0.58217I
b = 1.354270 + 0.008617I
1.55886 0.00067I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.340631 + 0.848794I
a = 0.477246 + 0.103415I
b = 1.44761 0.13462I
7.05350 + 2.19153I 9.52387 1.99188I
u = 0.340631 0.848794I
a = 0.477246 0.103415I
b = 1.44761 + 0.13462I
7.05350 2.19153I 9.52387 + 1.99188I
u = 1.048170 + 0.314077I
a = 0.23334 1.69617I
b = 0.177827 1.133290I
6.52325 + 5.35877I 0
u = 1.048170 0.314077I
a = 0.23334 + 1.69617I
b = 0.177827 + 1.133290I
6.52325 5.35877I 0
u = 0.106979 + 1.115510I
a = 0.042289 0.245084I
b = 0.182302 0.480029I
1.86292 + 2.79330I 0
u = 0.106979 1.115510I
a = 0.042289 + 0.245084I
b = 0.182302 + 0.480029I
1.86292 2.79330I 0
u = 0.212519 + 0.849931I
a = 0.308623 0.038482I
b = 1.43643 0.26260I
1.68255 5.75611I 4.38217 + 3.71688I
u = 0.212519 0.849931I
a = 0.308623 + 0.038482I
b = 1.43643 + 0.26260I
1.68255 + 5.75611I 4.38217 3.71688I
u = 0.138283 + 1.170680I
a = 0.583637 + 0.306881I
b = 1.44697 + 0.29238I
3.25272 10.24640I 0
u = 0.138283 1.170680I
a = 0.583637 0.306881I
b = 1.44697 0.29238I
3.25272 + 10.24640I 0
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.048580 + 0.539589I
a = 0.03548 + 1.55272I
b = 1.399330 + 0.163222I
3.52510 + 3.03832I 0
u = 1.048580 0.539589I
a = 0.03548 1.55272I
b = 1.399330 0.163222I
3.52510 3.03832I 0
u = 0.818925
a = 0.650075
b = 1.65973
2.81430 14.1920
u = 0.777268 + 0.158021I
a = 1.28789 1.00859I
b = 1.77876 0.23396I
1.23750 + 1.13200I 5.16037 4.27670I
u = 0.777268 0.158021I
a = 1.28789 + 1.00859I
b = 1.77876 + 0.23396I
1.23750 1.13200I 5.16037 + 4.27670I
u = 1.222600 + 0.255392I
a = 0.298898 1.012200I
b = 0.675657 0.690427I
5.60593 3.18248I 0
u = 1.222600 0.255392I
a = 0.298898 + 1.012200I
b = 0.675657 + 0.690427I
5.60593 + 3.18248I 0
u = 1.142820 + 0.531044I
a = 0.29895 + 1.56428I
b = 1.44537 + 0.29546I
4.55144 7.27382I 0
u = 1.142820 0.531044I
a = 0.29895 1.56428I
b = 1.44537 0.29546I
4.55144 + 7.27382I 0
u = 1.248980 + 0.228822I
a = 1.50489 0.50878I
b = 1.290870 + 0.128288I
3.14500 + 2.19857I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.248980 0.228822I
a = 1.50489 + 0.50878I
b = 1.290870 0.128288I
3.14500 2.19857I 0
u = 1.231060 + 0.327570I
a = 0.650637 0.984088I
b = 0.871372 0.916770I
12.18400 + 5.43510I 0
u = 1.231060 0.327570I
a = 0.650637 + 0.984088I
b = 0.871372 + 0.916770I
12.18400 5.43510I 0
u = 1.27404
a = 0.523112
b = 0.645940
4.24711 0
u = 1.183130 + 0.512946I
a = 0.41862 + 1.63827I
b = 1.44596 + 0.42331I
1.27215 + 10.73830I 0
u = 1.183130 0.512946I
a = 0.41862 1.63827I
b = 1.44596 0.42331I
1.27215 10.73830I 0
u = 1.093750 + 0.738943I
a = 0.748613 1.122850I
b = 1.166760 0.270892I
9.55293 2.80719I 0
u = 1.093750 0.738943I
a = 0.748613 + 1.122850I
b = 1.166760 + 0.270892I
9.55293 + 2.80719I 0
u = 0.261215 + 1.302270I
a = 0.565935 + 0.149777I
b = 1.377250 + 0.194353I
3.14084 + 5.32909I 0
u = 0.261215 1.302270I
a = 0.565935 0.149777I
b = 1.377250 0.194353I
3.14084 5.32909I 0
9
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.223054 + 0.595115I
a = 1.49321 + 0.64074I
b = 0.615226 + 0.539891I
8.01703 2.08920I 1.364316 + 0.139969I
u = 0.223054 0.595115I
a = 1.49321 0.64074I
b = 0.615226 0.539891I
8.01703 + 2.08920I 1.364316 0.139969I
u = 1.327730 + 0.475279I
a = 0.230483 + 1.372100I
b = 0.440531 + 0.965989I
13.3328 + 11.6550I 0
u = 1.327730 0.475279I
a = 0.230483 1.372100I
b = 0.440531 0.965989I
13.3328 11.6550I 0
u = 1.34532 + 0.46601I
a = 0.125579 + 1.193110I
b = 0.396012 + 0.794879I
6.48026 8.12212I 0
u = 1.34532 0.46601I
a = 0.125579 1.193110I
b = 0.396012 0.794879I
6.48026 + 8.12212I 0
u = 0.60690 + 1.30455I
a = 0.608740 0.107378I
b = 1.278700 + 0.099548I
1.48332 + 1.01891I 0
u = 0.60690 1.30455I
a = 0.608740 + 0.107378I
b = 1.278700 0.099548I
1.48332 1.01891I 0
u = 1.34808 + 0.53347I
a = 0.486605 + 0.764340I
b = 0.045270 + 0.726049I
12.96030 + 0.84938I 0
u = 1.34808 0.53347I
a = 0.486605 0.764340I
b = 0.045270 0.726049I
12.96030 0.84938I 0
10
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 1.38093 + 0.48836I
a = 0.173702 + 0.905038I
b = 0.212560 + 0.657694I
6.22030 + 3.10276I 0
u = 1.38093 0.48836I
a = 0.173702 0.905038I
b = 0.212560 0.657694I
6.22030 3.10276I 0
u = 1.34090 + 0.60045I
a = 0.12043 1.56951I
b = 1.51716 0.36747I
7.0624 + 16.4733I 0
u = 1.34090 0.60045I
a = 0.12043 + 1.56951I
b = 1.51716 + 0.36747I
7.0624 16.4733I 0
u = 1.48152
a = 0.0914854
b = 1.00347
4.17379 0
u = 1.35642 + 0.64883I
a = 0.061175 1.364930I
b = 1.47058 0.30512I
0.49201 12.12130I 0
u = 1.35642 0.64883I
a = 0.061175 + 1.364930I
b = 1.47058 + 0.30512I
0.49201 + 12.12130I 0
u = 1.32963 + 0.74793I
a = 0.144785 1.138680I
b = 1.381900 0.250810I
1.15043 + 6.39677I 0
u = 1.32963 0.74793I
a = 0.144785 + 1.138680I
b = 1.381900 + 0.250810I
1.15043 6.39677I 0
u = 0.135498 + 0.451659I
a = 1.052310 + 0.225740I
b = 0.388744 + 0.698459I
4.10847 2.26740I 1.42053 + 3.16015I
11
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.135498 0.451659I
a = 1.052310 0.225740I
b = 0.388744 0.698459I
4.10847 + 2.26740I 1.42053 3.16015I
u = 0.234414 + 0.396606I
a = 0.549751 0.088710I
b = 0.468548 + 0.287683I
0.918234 + 0.452351I 9.16608 2.88117I
u = 0.234414 0.396606I
a = 0.549751 + 0.088710I
b = 0.468548 0.287683I
0.918234 0.452351I 9.16608 + 2.88117I
u = 1.51980 + 0.33755I
a = 0.427503 0.115599I
b = 1.254650 0.289980I
8.94217 + 4.52912I 0
u = 1.51980 0.33755I
a = 0.427503 + 0.115599I
b = 1.254650 + 0.289980I
8.94217 4.52912I 0
u = 0.145928 + 0.335228I
a = 1.74460 + 1.61934I
b = 0.225695 + 0.345536I
1.68024 + 0.84062I 2.79003 + 2.56570I
u = 0.145928 0.335228I
a = 1.74460 1.61934I
b = 0.225695 0.345536I
1.68024 0.84062I 2.79003 2.56570I
u = 0.179903 + 0.241663I
a = 2.40130 2.21797I
b = 1.46662 + 0.24782I
1.32557 0.73674I 2.49863 0.34688I
u = 0.179903 0.241663I
a = 2.40130 + 2.21797I
b = 1.46662 0.24782I
1.32557 + 0.73674I 2.49863 + 0.34688I
u = 0.0496730
a = 20.2292
b = 1.44197
3.34378 2.52060
12
II. I
u
2
= h−au + b + 2a + u 1, 3a
2
+ 2au 4a 3u + 1, u
2
u + 1i
(i) Arc colorings
a
2
=
0
u
a
10
=
1
0
a
11
=
1
u 1
a
3
=
u
u + 1
a
6
=
a
au 2a u + 1
a
7
=
a u
au 2a + 2
a
12
=
1
3
au +
1
3
a + u +
2
3
au +
2
3
u
4
3
a
5
=
au + 3a + u 1
au 2a u + 1
a
9
=
au a
4
3
u
4
3
2
a
4
=
a
au + 2a + u 1
a
1
=
2
3
au +
2
3
a +
2
3
u 1
a
2
3
u +
4
3
a
8
=
2
3
au
1
3
a 2u +
1
3
a +
4
3
u +
4
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
9(9u
4
18u
3
+ 27u
2
18u + 7)
c
2
, c
12
(u
2
+ u + 1)
2
c
3
(u + 1)
4
c
4
, c
5
, c
9
(u
2
2)
2
c
6
(u 1)
4
c
7
, c
8
, c
10
(u
2
u + 1)
2
c
11
9(9u
4
12u + 7)
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
81(81y
4
+ 162y
3
+ 207y
2
+ 54y + 49)
c
2
, c
7
, c
8
c
10
, c
12
(y
2
+ y + 1)
2
c
3
, c
6
(y 1)
4
c
4
, c
5
, c
9
(y 2)
4
c
11
81(81y
4
+ 126y
2
144y + 49)
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.207110 + 0.119573I
b = 1.41421
3.28987 2.02988I 2.00000 + 3.46410I
u = 0.500000 + 0.866025I
a = 0.207107 0.696923I
b = 1.41421
3.28987 2.02988I 2.00000 + 3.46410I
u = 0.500000 0.866025I
a = 1.207110 0.119573I
b = 1.41421
3.28987 + 2.02988I 2.00000 3.46410I
u = 0.500000 0.866025I
a = 0.207107 + 0.696923I
b = 1.41421
3.28987 + 2.02988I 2.00000 3.46410I
16
III. I
u
3
= hb, 3a u + 2, u
2
u + 1i
(i) Arc colorings
a
2
=
0
u
a
10
=
1
0
a
11
=
1
u 1
a
3
=
u
u + 1
a
6
=
1
3
u
2
3
0
a
7
=
4
3
u
2
3
u 1
a
12
=
1
3
u + 1
u 1
a
5
=
1
3
u
2
3
0
a
9
=
1
0
a
4
=
1
3
u
2
3
0
a
1
=
0.333333
u
a
8
=
u
1
3
u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
4
3
u
14
3
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
3(3u
2
3u + 1)
c
2
, c
7
, c
8
u
2
+ u + 1
c
3
(u 1)
2
c
4
, c
5
, c
9
u
2
c
6
(u + 1)
2
c
10
, c
12
u
2
u + 1
c
11
3(3u
2
+ 1)
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
9(9y
2
3y + 1)
c
2
, c
7
, c
8
c
10
, c
12
y
2
+ y + 1
c
3
, c
6
(y 1)
2
c
4
, c
5
, c
9
y
2
c
11
9(3y + 1)
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.500000 + 0.288675I
b = 0
1.64493 2.02988I 5.33333 1.15470I
u = 0.500000 0.866025I
a = 0.500000 0.288675I
b = 0
1.64493 + 2.02988I 5.33333 + 1.15470I
20
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
5913(3u
2
3u + 1)(9u
4
18u
3
+ 27u
2
18u + 7)
· (219u
80
+ 1298u
79
+ ··· + 23625360u 1524503)
c
2
((u
2
+ u + 1)
3
)(u
80
+ 4u
79
+ ··· 12u + 1)
c
3
((u 1)
2
)(u + 1)
4
(u
80
+ 3u
79
+ ··· + 313u + 63)
c
4
, c
5
, c
9
u
2
(u
2
2)
2
(u
80
+ 3u
79
+ ··· + 180u + 36)
c
6
((u 1)
4
)(u + 1)
2
(u
80
+ 3u
79
+ ··· + 313u + 63)
c
7
, c
8
((u
2
u + 1)
2
)(u
2
+ u + 1)(u
80
2u
79
+ ··· 2u + 1)
c
10
((u
2
u + 1)
3
)(u
80
+ 4u
79
+ ··· 12u + 1)
c
11
5913(3u
2
+ 1)(9u
4
12u + 7)
· (219u
80
1403u
79
+ ··· 226003u + 252193)
c
12
(u
2
u + 1)(u
2
+ u + 1)
2
(u
80
2u
79
+ ··· 2u + 1)
21
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
34963569(9y
2
3y + 1)(81y
4
+ 162y
3
+ 207y
2
+ 54y + 49)
· (4.80 × 10
4
y
80
3.17 × 10
6
y
79
+ ··· 2.97 × 10
14
y + 2.32 × 10
12
)
c
2
, c
10
((y
2
+ y + 1)
3
)(y
80
44y
79
+ ··· 392y + 1)
c
3
, c
6
((y 1)
6
)(y
80
69y
79
+ ··· + 7367y + 3969)
c
4
, c
5
, c
9
y
2
(y 2)
4
(y
80
75y
79
+ ··· + 9648y + 1296)
c
7
, c
8
, c
12
((y
2
+ y + 1)
3
)(y
80
+ 76y
79
+ ··· 72y + 1)
c
11
34963569(3y + 1)
2
(81y
4
+ 126y
2
144y + 49)
· (47961y
80
+ 610535y
79
+ ··· + 286076439375y + 63601309249)
22