12n
0479
(K12n
0479
)
A knot diagram
1
Linearized knot diagam
3 6 8 9 2 12 11 5 4 6 7 8
Solving Sequence
6,12 3,7
2 1 5 11 8 4 10 9
c
6
c
2
c
1
c
5
c
11
c
7
c
3
c
10
c
9
c
4
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h186488768414913u
49
− 290002817250832u
48
+ ··· + 308976956670931b + 23795142626938,
− 2.98208 × 10
14
u
49
+ 1.16633 × 10
15
u
48
+ ··· + 1.85386 × 10
15
a − 3.97700 × 10
15
, u
50
− 2u
49
+ ··· + 7u − 3i
I
u
2
= hb − 1, −2u
2
a + a
2
− 2au + 4u
2
− 4a + 3u + 7, u
3
+ u
2
+ 2u + 1i
I
u
3
= hb + 1, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 59 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
= h1.86×10
14
u
49
−2.90×10
14
u
48
+· · ·+3.09×10
14
b+2.38×10
13
, −2.98×
10
14
u
49
+1.17×10
15
u
48
+· · ·+1.85×10
15
a−3.98×10
15
, u
50
−2u
49
+· · ·+7u−3i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
0.160858u
49
− 0.629138u
48
+ ··· − 4.21769u + 2.14525
−0.603569u
49
+ 0.938590u
48
+ ··· + 1.19866u − 0.0770127
a
7
=
1
u
2
a
2
=
−0.442711u
49
+ 0.309453u
48
+ ··· − 3.01903u + 2.06824
−0.603569u
49
+ 0.938590u
48
+ ··· + 1.19866u − 0.0770127
a
1
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
5
=
−0.0498473u
49
− 0.638746u
48
+ ··· + 5.09518u + 0.739281
−0.316393u
49
+ 0.485397u
48
+ ··· + 2.60385u − 0.176830
a
11
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
−0.0589435u
49
− 0.198506u
48
+ ··· − 4.62549u + 2.19124
−0.738441u
49
+ 1.20164u
48
+ ··· + 1.08821u − 0.149542
a
10
=
u
3
+ 2u
u
3
+ u
a
9
=
0.660432u
49
− 0.972483u
48
+ ··· − 0.425785u + 2.52397
0.348382u
49
− 0.970681u
48
+ ··· − 2.09905u + 1.98130
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
818278759941418
308976956670931
u
49
+
1283399787362471
308976956670931
u
48
+ ··· +
3241957768122858
308976956670931
u −
3010107002943738
308976956670931
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
50
+ 18u
49
+ ··· + 4150u + 289
c
2
, c
5
u
50
+ 4u
49
+ ··· − 28u − 17
c
3
u
50
+ u
49
+ ··· + 1024u + 488
c
4
, c
8
, c
9
u
50
− u
49
+ ··· − 16u + 8
c
6
, c
7
, c
11
u
50
+ 2u
49
+ ··· − 7u − 3
c
10
, c
12
u
50
− 2u
49
+ ··· − 3995u − 2391
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
+ 38y
49
+ ··· + 3129458y + 83521
c
2
, c
5
y
50
− 18y
49
+ ··· − 4150y + 289
c
3
y
50
− 41y
49
+ ··· − 2344704y + 238144
c
4
, c
8
, c
9
y
50
+ 43y
49
+ ··· − 896y + 64
c
6
, c
7
, c
11
y
50
+ 48y
49
+ ··· − 79y + 9
c
10
, c
12
y
50
+ 16y
49
+ ··· + 33729737y + 5716881
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.548026 + 0.636865I
a = −0.141399 + 0.209810I
b = 1.031990 − 0.770119I
0.14665 + 5.50869I −5.48648 − 2.48413I
u = 0.548026 − 0.636865I
a = −0.141399 − 0.209810I
b = 1.031990 + 0.770119I
0.14665 − 5.50869I −5.48648 + 2.48413I
u = 0.747661 + 0.370902I
a = 1.27766 − 1.31418I
b = 1.119580 + 0.753217I
−0.80164 − 9.94223I −7.39959 + 7.60109I
u = 0.747661 − 0.370902I
a = 1.27766 + 1.31418I
b = 1.119580 − 0.753217I
−0.80164 + 9.94223I −7.39959 − 7.60109I
u = −0.701764 + 0.430117I
a = −1.00242 − 1.23319I
b = −0.971275 + 0.823552I
4.04082 + 5.32876I −2.84513 − 5.88571I
u = −0.701764 − 0.430117I
a = −1.00242 + 1.23319I
b = −0.971275 − 0.823552I
4.04082 − 5.32876I −2.84513 + 5.88571I
u = −0.613532 + 0.535693I
a = 0.370473 + 0.106254I
b = −0.839697 − 0.858575I
4.44373 − 0.93541I −1.58239 − 0.30026I
u = −0.613532 − 0.535693I
a = 0.370473 − 0.106254I
b = −0.839697 + 0.858575I
4.44373 + 0.93541I −1.58239 + 0.30026I
u = 0.680028 + 0.435043I
a = −0.548393 − 0.018507I
b = 0.600139 − 0.934400I
0.78344 − 3.70599I −5.05675 + 3.80006I
u = 0.680028 − 0.435043I
a = −0.548393 + 0.018507I
b = 0.600139 + 0.934400I
0.78344 + 3.70599I −5.05675 − 3.80006I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.609239 + 0.505071I
a = 0.659368 − 1.086520I
b = 0.728352 + 0.857268I
1.077150 − 0.581801I −4.57087 + 2.28469I
u = 0.609239 − 0.505071I
a = 0.659368 + 1.086520I
b = 0.728352 − 0.857268I
1.077150 + 0.581801I −4.57087 − 2.28469I
u = −0.314558 + 1.181770I
a = 0.755396 + 0.911108I
b = 0.883202 − 0.570553I
−1.86240 + 5.95457I 0
u = −0.314558 − 1.181770I
a = 0.755396 − 0.911108I
b = 0.883202 + 0.570553I
−1.86240 − 5.95457I 0
u = −0.754187 + 0.037133I
a = 1.177820 + 0.351943I
b = 0.791193 + 0.522358I
−5.37048 − 2.06528I −9.77366 + 3.43997I
u = −0.754187 − 0.037133I
a = 1.177820 − 0.351943I
b = 0.791193 − 0.522358I
−5.37048 + 2.06528I −9.77366 − 3.43997I
u = −0.030213 + 1.260010I
a = −0.22647 + 1.85610I
b = −1.111340 − 0.290888I
−3.90026 + 0.44346I 0
u = −0.030213 − 1.260010I
a = −0.22647 − 1.85610I
b = −1.111340 + 0.290888I
−3.90026 − 0.44346I 0
u = 0.251247 + 1.259910I
a = −0.547258 + 0.656638I
b = −0.684570 − 0.219108I
2.05074 − 3.33048I 0
u = 0.251247 − 1.259910I
a = −0.547258 − 0.656638I
b = −0.684570 + 0.219108I
2.05074 + 3.33048I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.299311 + 1.263120I
a = 0.021398 + 0.222536I
b = 0.705583 + 0.479463I
−1.35085 + 1.74111I 0
u = −0.299311 − 1.263120I
a = 0.021398 − 0.222536I
b = 0.705583 − 0.479463I
−1.35085 − 1.74111I 0
u = −0.095422 + 1.324880I
a = −0.023038 + 1.203270I
b = 1.169140 − 0.223723I
1.85552 + 1.71056I 0
u = −0.095422 − 1.324880I
a = −0.023038 − 1.203270I
b = 1.169140 + 0.223723I
1.85552 − 1.71056I 0
u = 0.667644
a = −1.23502
b = −0.589141
−1.84778 −2.14880
u = −0.179331 + 1.371620I
a = 1.20289 − 1.64393I
b = −0.538230 + 0.405630I
−1.78664 + 3.49510I 0
u = −0.179331 − 1.371620I
a = 1.20289 + 1.64393I
b = −0.538230 − 0.405630I
−1.78664 − 3.49510I 0
u = 0.523052 + 0.312664I
a = −1.58769 + 0.98505I
b = −1.278040 + 0.059074I
−5.97365 − 1.50019I −9.06126 + 4.58058I
u = 0.523052 − 0.312664I
a = −1.58769 − 0.98505I
b = −1.278040 − 0.059074I
−5.97365 + 1.50019I −9.06126 − 4.58058I
u = 0.062298 + 1.409670I
a = −0.212165 − 1.347970I
b = 0.181198 + 0.793511I
5.34369 − 2.04364I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.062298 − 1.409670I
a = −0.212165 + 1.347970I
b = 0.181198 − 0.793511I
5.34369 + 2.04364I 0
u = 0.20226 + 1.41029I
a = 0.244900 + 0.806956I
b = −1.348940 + 0.042324I
−0.46882 − 4.20038I 0
u = 0.20226 − 1.41029I
a = 0.244900 − 0.806956I
b = −1.348940 − 0.042324I
−0.46882 + 4.20038I 0
u = −0.478945 + 0.205762I
a = 1.01707 − 2.37277I
b = −0.767299 + 0.234309I
−6.81379 + 1.04376I −7.43326 − 6.78776I
u = −0.478945 − 0.205762I
a = 1.01707 + 2.37277I
b = −0.767299 − 0.234309I
−6.81379 − 1.04376I −7.43326 + 6.78776I
u = 0.28571 + 1.46065I
a = 0.22222 − 2.14370I
b = 1.175840 + 0.774815I
5.0883 − 13.7071I 0
u = 0.28571 − 1.46065I
a = 0.22222 + 2.14370I
b = 1.175840 − 0.774815I
5.0883 + 13.7071I 0
u = 0.24689 + 1.47668I
a = −1.12288 + 0.98727I
b = 0.577120 − 1.045150I
6.96288 − 7.09069I 0
u = 0.24689 − 1.47668I
a = −1.12288 − 0.98727I
b = 0.577120 + 1.045150I
6.96288 + 7.09069I 0
u = 0.21123 + 1.48331I
a = −0.10979 − 1.94214I
b = 0.854567 + 0.927257I
7.49634 − 3.56090I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21123 − 1.48331I
a = −0.10979 + 1.94214I
b = 0.854567 − 0.927257I
7.49634 + 3.56090I 0
u = −0.25705 + 1.47829I
a = −0.06564 − 2.05483I
b = −1.058610 + 0.870913I
10.20760 + 8.82997I 0
u = −0.25705 − 1.47829I
a = −0.06564 + 2.05483I
b = −1.058610 − 0.870913I
10.20760 − 8.82997I 0
u = 0.15233 + 1.49913I
a = −1.01986 + 1.15371I
b = 0.992952 − 0.891101I
7.08236 + 3.11695I 0
u = 0.15233 − 1.49913I
a = −1.01986 − 1.15371I
b = 0.992952 + 0.891101I
7.08236 − 3.11695I 0
u = −0.20291 + 1.49495I
a = 1.08852 + 1.06865I
b = −0.799853 − 0.997275I
11.03000 + 2.01018I 0
u = −0.20291 − 1.49495I
a = 1.08852 − 1.06865I
b = −0.799853 + 0.997275I
11.03000 − 2.01018I 0
u = 0.275380 + 0.327909I
a = −0.267865 − 0.801075I
b = 0.330232 + 0.361285I
−0.199328 − 0.932041I −3.89641 + 7.43641I
u = 0.275380 − 0.327909I
a = −0.267865 + 0.801075I
b = 0.330232 − 0.361285I
−0.199328 + 0.932041I −3.89641 − 7.43641I
u = −0.403899
a = 2.57601
b = 1.10270
−2.29285 3.34720
9
II. I
u
2
= hb − 1, −2u
2
a + a
2
− 2au + 4u
2
− 4a + 3u + 7, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
a
1
a
7
=
1
u
2
a
2
=
a + 1
1
a
1
=
1
0
a
5
=
−a
−1
a
11
=
u
−u
2
− u − 1
a
8
=
u
2
+ 1
u
2
+ u + 1
a
4
=
u
2
+ u + 2
au + 2
a
10
=
−u
2
− 1
−u
2
− u − 1
a
9
=
u
2
a − 2u
2
+ a − 3
u
2
a + au + a + u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
− 4u − 16
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
(u − 1)
6
c
2
(u + 1)
6
c
3
, c
4
, c
8
c
9
(u
2
+ 2)
3
c
6
, c
7
(u
3
+ u
2
+ 2u + 1)
2
c
10
, c
12
(u
3
+ u
2
− 1)
2
c
11
(u
3
− u
2
+ 2u − 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
6
c
3
, c
4
, c
8
c
9
(y + 2)
6
c
6
, c
7
, c
11
(y
3
+ 3y
2
+ 2y −1)
2
c
10
, c
12
(y
3
− y
2
+ 2y −1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.917744 − 0.191855I
b = 1.00000
−3.55561 + 2.82812I −8.49024 − 2.97945I
u = −0.215080 + 1.307140I
a = −0.67262 + 1.68158I
b = 1.00000
−3.55561 + 2.82812I −8.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 0.917744 + 0.191855I
b = 1.00000
−3.55561 − 2.82812I −8.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = −0.67262 − 1.68158I
b = 1.00000
−3.55561 − 2.82812I −8.49024 + 2.97945I
u = −0.569840
a = 1.75488 + 1.87343I
b = 1.00000
−7.69319 −15.0200
u = −0.569840
a = 1.75488 − 1.87343I
b = 1.00000
−7.69319 −15.0200
13
III. I
u
3
= hb + 1, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
3
=
−u
2
+ u − 2
−1
a
7
=
1
u
2
a
2
=
−u
2
+ u − 3
−1
a
1
=
−1
0
a
5
=
−u
2
+ u − 2
−1
a
11
=
u
u
2
− u + 1
a
8
=
u
2
+ 1
u
2
− u + 1
a
4
=
−u
2
+ u − 2
−1
a
10
=
u
2
+ 1
u
2
− u + 1
a
9
=
u
2
+ 1
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −6u
2
+ 4u − 16
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
4
, c
8
c
9
u
3
c
5
(u + 1)
3
c
6
, c
7
u
3
− u
2
+ 2u − 1
c
10
, c
12
u
3
− u
2
+ 1
c
11
u
3
+ u
2
+ 2u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
3
c
3
, c
4
, c
8
c
9
y
3
c
6
, c
7
, c
11
y
3
+ 3y
2
+ 2y −1
c
10
, c
12
y
3
− y
2
+ 2y −1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.122561 + 0.744862I
b = −1.00000
1.37919 − 2.82812I −5.16553 + 1.85489I
u = 0.215080 − 1.307140I
a = −0.122561 − 0.744862I
b = −1.00000
1.37919 + 2.82812I −5.16553 − 1.85489I
u = 0.569840
a = −1.75488
b = −1.00000
−2.75839 −15.6690
17
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
9
)(u
50
+ 18u
49
+ ··· + 4150u + 289)
c
2
((u − 1)
3
)(u + 1)
6
(u
50
+ 4u
49
+ ··· − 28u − 17)
c
3
u
3
(u
2
+ 2)
3
(u
50
+ u
49
+ ··· + 1024u + 488)
c
4
, c
8
, c
9
u
3
(u
2
+ 2)
3
(u
50
− u
49
+ ··· − 16u + 8)
c
5
((u − 1)
6
)(u + 1)
3
(u
50
+ 4u
49
+ ··· − 28u − 17)
c
6
, c
7
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
50
+ 2u
49
+ ··· − 7u − 3)
c
10
, c
12
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
50
− 2u
49
+ ··· − 3995u − 2391)
c
11
((u
3
− u
2
+ 2u − 1)
2
)(u
3
+ u
2
+ 2u + 1)(u
50
+ 2u
49
+ ··· − 7u − 3)
18
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
9
)(y
50
+ 38y
49
+ ··· + 3129458y + 83521)
c
2
, c
5
((y −1)
9
)(y
50
− 18y
49
+ ··· − 4150y + 289)
c
3
y
3
(y + 2)
6
(y
50
− 41y
49
+ ··· − 2344704y + 238144)
c
4
, c
8
, c
9
y
3
(y + 2)
6
(y
50
+ 43y
49
+ ··· − 896y + 64)
c
6
, c
7
, c
11
((y
3
+ 3y
2
+ 2y −1)
3
)(y
50
+ 48y
49
+ ··· − 79y + 9)
c
10
, c
12
((y
3
− y
2
+ 2y −1)
3
)(y
50
+ 16y
49
+ ··· + 3.37297 × 10
7
y + 5716881)
19
