12n
0288
(K12n
0288
)
A knot diagram
1
Linearized knot diagam
3 6 7 9 2 5 11 5 7 12 8 10
Solving Sequence
5,8 9,11
12 4 7 3 6 2 1 10
c
8
c
11
c
4
c
7
c
3
c
6
c
2
c
1
c
10
c
5
, c
9
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h7.99341 × 10
39
u
32
− 1.73952 × 10
40
u
31
+ ··· + 6.21714 × 10
42
b − 7.27832 × 10
42
,
− 2.58634 × 10
40
u
32
+ 4.38348 × 10
40
u
31
+ ··· + 1.24343 × 10
43
a − 5.01178 × 10
42
,
u
33
− u
32
+ ··· + 1024u + 512i
I
v
1
= ha, 3v
5
+ 2v
4
+ 15v
3
+ 20v
2
+ 7b + 12v −3, v
6
+ v
5
+ 5v
4
+ 9v
3
+ 5v
2
+ v + 1i
I
v
2
= ha, b
3
− b
2
+ 1, v −1i
* 3 irreducible components of dim
C
= 0, with total 42 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
= h7.99 × 10
39
u
32
− 1.74 × 10
40
u
31
+ · · · + 6.22 × 10
42
b − 7.28 ×
10
42
, −2.59 × 10
40
u
32
+ 4.38 × 10
40
u
31
+ · · · + 1.24 × 10
43
a − 5.01 ×
10
42
, u
33
− u
32
+ · · · + 1024u + 512i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
u
2
a
11
=
0.00208001u
32
− 0.00352532u
31
+ ··· + 1.78233u + 0.403062
−0.00128571u
32
+ 0.00279794u
31
+ ··· + 1.28986u + 1.17069
a
12
=
0.000794299u
32
− 0.000727383u
31
+ ··· + 3.07219u + 1.57375
−0.00128571u
32
+ 0.00279794u
31
+ ··· + 1.28986u + 1.17069
a
4
=
u
u
3
+ u
a
7
=
−0.00110615u
32
+ 0.00221831u
31
+ ··· + 0.260315u + 0.865237
0.00241977u
32
− 0.00321235u
31
+ ··· + 4.09026u + 0.856393
a
3
=
0.00164230u
32
− 0.00102508u
31
+ ··· + 3.66559u + 0.647992
−0.000789549u
32
+ 0.00155917u
31
+ ··· + 1.76057u + 0.378455
a
6
=
−0.00110615u
32
+ 0.00221831u
31
+ ··· + 0.260315u + 0.865237
0.00119835u
32
− 0.0000262335u
31
+ ··· + 4.66276u + 1.42582
a
2
=
0.00204624u
32
− 0.0000326376u
31
+ ··· + 6.09887u + 1.29264
−0.000664888u
32
+ 0.00290411u
31
+ ··· + 4.32183u + 1.50071
a
1
=
0.00230450u
32
− 0.00224455u
31
+ ··· + 4.40244u + 0.560582
0.00119835u
32
− 0.0000262335u
31
+ ··· + 4.66276u + 1.42582
a
10
=
−0.000739170u
32
− 0.0000503781u
31
+ ··· − 1.45933u + 1.00366
−0.00132594u
32
+ 0.00245141u
31
+ ··· − 0.697988u + 1.25243
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0223829u
32
+ 0.0292513u
31
+ ··· − 14.9362u − 3.65393
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
33
+ 6u
32
+ ··· + 2u + 1
c
2
, c
5
u
33
+ 4u
32
+ ··· + 2u + 1
c
3
u
33
− 4u
32
+ ··· + 77426u + 5953
c
4
, c
8
u
33
− u
32
+ ··· + 1024u + 512
c
7
, c
11
u
33
− 4u
32
+ ··· + 2u + 1
c
9
u
33
+ 4u
32
+ ··· − 18u + 1
c
10
, c
12
u
33
− 14u
32
+ ··· + 50u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
33
+ 46y
32
+ ··· + 66y −1
c
2
, c
5
y
33
− 6y
32
+ ··· + 2y −1
c
3
y
33
+ 130y
32
+ ··· + 1530880802y −35438209
c
4
, c
8
y
33
+ 49y
32
+ ··· − 917504y −262144
c
7
, c
11
y
33
− 14y
32
+ ··· + 50y −1
c
9
y
33
− 70y
32
+ ··· + 290y −1
c
10
, c
12
y
33
+ 14y
32
+ ··· + 1938y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.259194 + 0.938083I
a = 1.296390 − 0.418631I
b = −0.842802 + 0.497518I
−1.68399 − 2.04132I −4.24848 + 3.69259I
u = −0.259194 − 0.938083I
a = 1.296390 + 0.418631I
b = −0.842802 − 0.497518I
−1.68399 + 2.04132I −4.24848 − 3.69259I
u = −0.299553 + 0.982584I
a = 0.491758 − 0.071067I
b = −0.276643 − 0.578301I
1.95211 + 1.67358I −0.85105 − 3.68739I
u = −0.299553 − 0.982584I
a = 0.491758 + 0.071067I
b = −0.276643 + 0.578301I
1.95211 − 1.67358I −0.85105 + 3.68739I
u = −0.819751 + 0.642390I
a = −1.19497 + 1.76483I
b = 0.940469 + 0.288411I
4.57287 − 1.92834I 2.42456 − 1.90294I
u = −0.819751 − 0.642390I
a = −1.19497 − 1.76483I
b = 0.940469 − 0.288411I
4.57287 + 1.92834I 2.42456 + 1.90294I
u = 0.906320 + 0.161254I
a = −0.342325 + 1.004680I
b = 0.936395 + 0.663389I
−1.64047 + 4.33466I −2.39244 − 5.76520I
u = 0.906320 − 0.161254I
a = −0.342325 − 1.004680I
b = 0.936395 − 0.663389I
−1.64047 − 4.33466I −2.39244 + 5.76520I
u = −0.138715 + 1.076100I
a = 0.343138 − 0.314662I
b = −0.540873 + 0.646097I
0.99056 + 3.01055I −2.29192 − 3.36152I
u = −0.138715 − 1.076100I
a = 0.343138 + 0.314662I
b = −0.540873 − 0.646097I
0.99056 − 3.01055I −2.29192 + 3.36152I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.820423 + 0.241734I
a = −0.127283 + 1.097200I
b = 0.790989 + 0.648302I
−2.09854 + 0.79204I −4.42932 + 0.29217I
u = −0.820423 − 0.241734I
a = −0.127283 − 1.097200I
b = 0.790989 − 0.648302I
−2.09854 − 0.79204I −4.42932 − 0.29217I
u = 0.588887 + 0.452734I
a = 1.005150 + 0.039063I
b = −0.876518 − 0.152706I
1.49526 + 0.33133I 5.50598 − 0.36289I
u = 0.588887 − 0.452734I
a = 1.005150 − 0.039063I
b = −0.876518 + 0.152706I
1.49526 − 0.33133I 5.50598 + 0.36289I
u = 1.103600 + 0.681610I
a = −1.01014 − 1.30375I
b = 1.017310 − 0.360748I
5.11059 − 4.16082I 2.72191 + 5.85960I
u = 1.103600 − 0.681610I
a = −1.01014 + 1.30375I
b = 1.017310 + 0.360748I
5.11059 + 4.16082I 2.72191 − 5.85960I
u = −0.020434 + 1.399020I
a = 1.58993 + 0.37908I
b = −1.035370 + 0.580512I
2.46612 − 7.83728I 0.08663 + 7.57867I
u = −0.020434 − 1.399020I
a = 1.58993 − 0.37908I
b = −1.035370 − 0.580512I
2.46612 + 7.83728I 0.08663 − 7.57867I
u = −0.023074 + 0.498558I
a = −0.216617 + 0.905947I
b = 0.878924 + 0.769382I
−3.74171 + 2.90167I 6.31914 − 4.62545I
u = −0.023074 − 0.498558I
a = −0.216617 − 0.905947I
b = 0.878924 − 0.769382I
−3.74171 − 2.90167I 6.31914 + 4.62545I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.38369 + 1.47441I
a = 1.321050 − 0.219840I
b = −1.068020 − 0.492605I
4.14146 + 2.52091I 3.12902 − 2.10165I
u = 0.38369 − 1.47441I
a = 1.321050 + 0.219840I
b = −1.068020 + 0.492605I
4.14146 − 2.52091I 3.12902 + 2.10165I
u = −0.379202
a = 1.20462
b = 0.150542
−0.908337 −11.6530
u = −0.43213 + 1.91828I
a = −0.064840 + 0.127886I
b = −0.511933 + 0.957121I
11.27410 + 6.04297I 0
u = −0.43213 − 1.91828I
a = −0.064840 − 0.127886I
b = −0.511933 − 0.957121I
11.27410 − 6.04297I 0
u = 0.27574 + 1.97448I
a = −0.016267 − 0.141101I
b = −0.473285 − 0.959466I
11.52690 + 0.81316I 0
u = 0.27574 − 1.97448I
a = −0.016267 + 0.141101I
b = −0.473285 + 0.959466I
11.52690 − 0.81316I 0
u = 0.66557 + 1.97108I
a = 1.118020 + 0.848015I
b = −1.143380 + 0.700941I
13.2296 − 12.1129I 0
u = 0.66557 − 1.97108I
a = 1.118020 − 0.848015I
b = −1.143380 − 0.700941I
13.2296 + 12.1129I 0
u = −0.53201 + 2.07441I
a = 1.114790 − 0.764503I
b = −1.158540 − 0.681377I
13.6520 + 5.1893I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.53201 − 2.07441I
a = 1.114790 + 0.764503I
b = −1.158540 + 0.681377I
13.6520 − 5.1893I 0
u = 0.11108 + 2.30479I
a = −1.410100 − 0.047794I
b = 1.288010 − 0.018877I
18.1642 − 3.5486I 0
u = 0.11108 − 2.30479I
a = −1.410100 + 0.047794I
b = 1.288010 + 0.018877I
18.1642 + 3.5486I 0
8
II.
I
v
1
= ha, 3v
5
+2v
4
+15v
3
+20v
2
+7b+12v −3, v
6
+v
5
+5v
4
+9v
3
+5v
2
+v +1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
9
=
1
0
a
11
=
0
−
3
7
v
5
−
2
7
v
4
+ ··· −
12
7
v +
3
7
a
12
=
−
3
7
v
5
−
2
7
v
4
+ ··· −
12
7
v +
3
7
−
3
7
v
5
−
2
7
v
4
+ ··· −
12
7
v +
3
7
a
4
=
v
0
a
7
=
1
−
5
7
v
5
−
3
7
v
4
+ ··· − 3v −
4
7
a
3
=
−
2
7
v
5
+
1
7
v
4
+ ··· +
6
7
v −
5
7
−
1
7
v
5
+
1
7
v
4
+ ··· +
12
7
v −
2
7
a
6
=
−
3
7
v
5
− 2v
3
+ ··· +
3
7
v +
5
7
−
5
7
v
5
−
3
7
v
4
+ ··· − 3v −
4
7
a
2
=
−
1
7
v
5
+
2
7
v
4
+ ··· +
2
7
v −
8
7
1
7
v
5
+
5
7
v
4
+ ··· +
26
7
v +
1
7
a
1
=
−1
5
7
v
5
+
3
7
v
4
+ ··· + 3v +
4
7
a
10
=
5
7
v
5
+
3
7
v
4
+ ··· + 3v +
11
7
2
7
v
5
+
1
7
v
4
+ ··· +
9
7
v + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 5v
5
+
12
7
v
4
+
160
7
v
3
+
199
7
v
2
+
20
7
v −
58
7
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
9
c
12
(u
3
− u
2
+ 2u − 1)
2
c
2
, c
11
(u
3
+ u
2
− 1)
2
c
4
, c
8
u
6
c
5
, c
7
(u
3
− u
2
+ 1)
2
c
6
, c
10
(u
3
+ u
2
+ 2u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
5
, c
7
c
11
(y
3
− y
2
+ 2y −1)
2
c
4
, c
8
y
6
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.947279 + 0.320410I
a = 0
b = 0.877439 − 0.744862I
− 5.65624I −0.41065 + 5.95889I
v = −0.947279 − 0.320410I
a = 0
b = 0.877439 + 0.744862I
5.65624I −0.41065 − 5.95889I
v = 0.069840 + 0.424452I
a = 0
b = 0.877439 − 0.744862I
−4.13758 − 2.82812I −13.82394 + 1.30714I
v = 0.069840 − 0.424452I
a = 0
b = 0.877439 + 0.744862I
−4.13758 + 2.82812I −13.82394 − 1.30714I
v = 0.37744 + 2.29387I
a = 0
b = −0.754878
4.13758 − 2.82812I −0.76541 + 4.65175I
v = 0.37744 − 2.29387I
a = 0
b = −0.754878
4.13758 + 2.82812I −0.76541 − 4.65175I
12
III. I
v
2
= ha, b
3
− b
2
+ 1, v − 1i
(i) Arc colorings
a
5
=
1
0
a
8
=
1
0
a
9
=
1
0
a
11
=
0
b
a
12
=
b
b
a
4
=
1
0
a
7
=
1
b
2
a
3
=
−b
2
+ 1
−b
2
+ b + 1
a
6
=
b
2
+ 1
b
2
a
2
=
b
b
a
1
=
−1
−b
2
a
10
=
−b
2
+ 1
−b
2
+ b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
9
c
12
u
3
− u
2
+ 2u − 1
c
2
, c
11
u
3
+ u
2
− 1
c
4
, c
8
u
3
c
5
, c
7
u
3
− u
2
+ 1
c
6
, c
10
u
3
+ u
2
+ 2u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
6
c
9
, c
10
, c
12
y
3
+ 3y
2
+ 2y − 1
c
2
, c
5
, c
7
c
11
y
3
− y
2
+ 2y − 1
c
4
, c
8
y
3
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = 0.877439 + 0.744862I
0 0
v = 1.00000
a = 0
b = 0.877439 − 0.744862I
0 0
v = 1.00000
a = 0
b = −0.754878
0 0
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
3
)(u
33
+ 6u
32
+ ··· + 2u + 1)
c
2
((u
3
+ u
2
− 1)
3
)(u
33
+ 4u
32
+ ··· + 2u + 1)
c
3
((u
3
− u
2
+ 2u − 1)
3
)(u
33
− 4u
32
+ ··· + 77426u + 5953)
c
4
, c
8
u
9
(u
33
− u
32
+ ··· + 1024u + 512)
c
5
((u
3
− u
2
+ 1)
3
)(u
33
+ 4u
32
+ ··· + 2u + 1)
c
6
((u
3
+ u
2
+ 2u + 1)
3
)(u
33
+ 6u
32
+ ··· + 2u + 1)
c
7
((u
3
− u
2
+ 1)
3
)(u
33
− 4u
32
+ ··· + 2u + 1)
c
9
((u
3
− u
2
+ 2u − 1)
3
)(u
33
+ 4u
32
+ ··· − 18u + 1)
c
10
((u
3
+ u
2
+ 2u + 1)
3
)(u
33
− 14u
32
+ ··· + 50u − 1)
c
11
((u
3
+ u
2
− 1)
3
)(u
33
− 4u
32
+ ··· + 2u + 1)
c
12
((u
3
− u
2
+ 2u − 1)
3
)(u
33
− 14u
32
+ ··· + 50u − 1)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
33
+ 46y
32
+ ··· + 66y − 1)
c
2
, c
5
((y
3
− y
2
+ 2y − 1)
3
)(y
33
− 6y
32
+ ··· + 2y − 1)
c
3
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
33
+ 130y
32
+ ··· + 1530880802y − 35438209)
c
4
, c
8
y
9
(y
33
+ 49y
32
+ ··· − 917504y − 262144)
c
7
, c
11
((y
3
− y
2
+ 2y − 1)
3
)(y
33
− 14y
32
+ ··· + 50y − 1)
c
9
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
33
− 70y
32
+ ··· + 290y − 1)
c
10
, c
12
((y
3
+ 3y
2
+ 2y − 1)
3
)(y
33
+ 14y
32
+ ··· + 1938y − 1)
18
