12n
0418
(K12n
0418
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 9 3 12 6 4 10 7
Solving Sequence
9,12 3,8
4 7 1 6 10 2 5 11
c
8
c
3
c
7
c
12
c
6
c
9
c
2
c
5
c
11
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.26934 × 10
56
u
30
− 1.00911 × 10
57
u
29
+ ··· + 1.14470 × 10
59
b − 5.53521 × 10
58
,
− 1.15992 × 10
59
u
30
− 2.78534 × 10
59
u
29
+ ··· + 6.06690 × 10
60
a + 1.84407 × 10
61
,
u
31
+ 2u
30
+ ··· − 374u + 53i
I
u
2
= h2288080379940u
21
− 13342880074590u
20
+ ··· + 13036173440749b + 28488698280106,
144701135614458u
21
− 482252040257618u
20
+ ··· + 91253214085243a − 23683083359794,
u
22
− 3u
21
+ ··· − u − 1i
* 2 irreducible components of dim
C
= 0, with total 53 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−3.27 × 10
56
u
30
− 1.01 × 10
57
u
29
+ · · · + 1.14 × 10
59
b − 5.54 ×
10
58
, −1.16 × 10
59
u
30
− 2.79 × 10
59
u
29
+ · · · + 6.07 × 10
60
a + 1.84 ×
10
61
, u
31
+ 2u
30
+ · · · − 374u + 53i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
3
=
0.0191188u
30
+ 0.0459104u
29
+ ··· + 8.09643u − 3.03956
0.00285607u
30
+ 0.00881553u
29
+ ··· + 0.315937u + 0.483552
a
8
=
1
−u
2
a
4
=
0.0114818u
30
+ 0.0242158u
29
+ ··· + 5.92417u − 3.11645
0.00728253u
30
+ 0.0208089u
29
+ ··· + 2.31246u + 0.143262
a
7
=
−0.0125194u
30
− 0.0332989u
29
+ ··· − 3.31812u + 2.11184
0.00904266u
30
+ 0.0208537u
29
+ ··· + 6.07142u − 1.31372
a
1
=
−0.0137586u
30
− 0.0382466u
29
+ ··· − 5.78489u + 0.627589
0.00498751u
30
+ 0.0153717u
29
+ ··· − 0.409851u + 0.438957
a
6
=
−0.0215620u
30
− 0.0541526u
29
+ ··· − 9.38954u + 3.42557
0.00904266u
30
+ 0.0208537u
29
+ ··· + 6.07142u − 1.31372
a
10
=
0.00710160u
30
+ 0.0223768u
29
+ ··· + 3.65065u + 0.846020
−0.0153838u
30
− 0.0339537u
29
+ ··· − 10.1652u + 1.84167
a
2
=
−0.00233531u
30
− 0.00869416u
29
+ ··· − 2.45300u − 0.381174
−0.00433511u
30
− 0.0145092u
29
+ ··· − 1.18936u + 0.450278
a
5
=
−0.0154553u
30
− 0.0361401u
29
+ ··· − 9.80384u + 3.74041
0.0228960u
30
+ 0.0534719u
29
+ ··· + 12.3145u − 2.52457
a
11
=
0.0170559u
30
+ 0.0494259u
29
+ ··· + 8.44345u − 0.917949
−0.0254517u
30
− 0.0597883u
29
+ ··· − 13.3489u + 2.51042
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0281078u
30
− 0.0792191u
29
+ ··· − 6.22632u − 13.3726
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ 59u
30
+ ··· − 484409u + 120409
c
2
, c
5
u
31
+ 3u
30
+ ··· + 599u + 347
c
3
, c
7
u
31
− u
30
+ ··· − 221u + 527
c
4
, c
10
u
31
− u
30
+ ··· + 5u + 13
c
6
, c
9
u
31
+ 2u
30
+ ··· + 75u
2
− 1
c
8
u
31
− 2u
30
+ ··· − 374u − 53
c
11
u
31
+ 29u
30
+ ··· + 2911u + 169
c
12
u
31
+ 2u
30
+ ··· − 185350u − 50425
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
− 183y
30
+ ··· + 2147685948663y −14498327281
c
2
, c
5
y
31
− 59y
30
+ ··· − 484409y −120409
c
3
, c
7
y
31
− 57y
30
+ ··· + 1881747y −277729
c
4
, c
10
y
31
− 29y
30
+ ··· + 2911y −169
c
6
, c
9
y
31
+ 34y
30
+ ··· + 150y −1
c
8
y
31
− 10y
30
+ ··· + 84014y −2809
c
11
y
31
− 41y
30
+ ··· + 4210051y −28561
c
12
y
31
− 78y
30
+ ··· + 44563768850y −2542680625
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.703721 + 0.744561I
a = −0.131219 − 0.230843I
b = −0.150516 + 0.640112I
−0.71734 − 2.07224I −3.68384 + 1.56459I
u = 0.703721 − 0.744561I
a = −0.131219 + 0.230843I
b = −0.150516 − 0.640112I
−0.71734 + 2.07224I −3.68384 − 1.56459I
u = −0.695433 + 0.780531I
a = 0.508339 − 0.670000I
b = 0.329548 + 0.630508I
−3.81425 + 5.79719I −8.30177 − 4.14014I
u = −0.695433 − 0.780531I
a = 0.508339 + 0.670000I
b = 0.329548 − 0.630508I
−3.81425 − 5.79719I −8.30177 + 4.14014I
u = −0.884098 + 0.327223I
a = 2.72119 − 0.44116I
b = −0.58571 + 1.64877I
−9.20202 + 4.10011I −18.4887 − 4.6238I
u = −0.884098 − 0.327223I
a = 2.72119 + 0.44116I
b = −0.58571 − 1.64877I
−9.20202 − 4.10011I −18.4887 + 4.6238I
u = 1.13855
a = −1.34619
b = 0.551542
−5.55158 −15.9810
u = 0.228324 + 0.824059I
a = −0.020823 − 0.480166I
b = −0.201885 + 0.199719I
1.16898 − 1.90810I −3.82691 + 6.03216I
u = 0.228324 − 0.824059I
a = −0.020823 + 0.480166I
b = −0.201885 − 0.199719I
1.16898 + 1.90810I −3.82691 − 6.03216I
u = −1.14547
a = −1.67126
b = 0.294014
−10.8570 −1.07250
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.052704 + 0.830178I
a = 0.688824 + 1.106930I
b = 1.032010 + 0.511602I
−0.254185 + 0.523436I −8.37978 − 3.05773I
u = −0.052704 − 0.830178I
a = 0.688824 − 1.106930I
b = 1.032010 − 0.511602I
−0.254185 − 0.523436I −8.37978 + 3.05773I
u = 0.821890
a = 3.31155
b = −0.588551
−15.0143 −24.8400
u = −1.093710 + 0.585354I
a = −0.529184 − 0.132666I
b = −0.021101 + 0.605842I
−5.53724 − 1.04949I −12.01248 + 0.06352I
u = −1.093710 − 0.585354I
a = −0.529184 + 0.132666I
b = −0.021101 − 0.605842I
−5.53724 + 1.04949I −12.01248 − 0.06352I
u = 1.296560 + 0.420401I
a = −1.209060 − 0.052495I
b = 0.37149 + 1.70399I
−4.79226 − 2.17270I −10.74429 + 3.28820I
u = 1.296560 − 0.420401I
a = −1.209060 + 0.052495I
b = 0.37149 − 1.70399I
−4.79226 + 2.17270I −10.74429 − 3.28820I
u = 0.525205 + 1.267060I
a = −0.621188 + 0.802341I
b = −0.75793 + 1.60948I
−1.26769 − 5.50031I −6.94404 + 6.71659I
u = 0.525205 − 1.267060I
a = −0.621188 − 0.802341I
b = −0.75793 − 1.60948I
−1.26769 + 5.50031I −6.94404 − 6.71659I
u = 0.526743 + 0.289192I
a = 0.458089 − 0.578413I
b = −0.03750 − 1.47275I
2.32560 + 0.63901I −14.5403 + 2.2459I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.526743 − 0.289192I
a = 0.458089 + 0.578413I
b = −0.03750 + 1.47275I
2.32560 − 0.63901I −14.5403 − 2.2459I
u = 1.61851
a = 1.15913
b = 0.0859312
−18.4664 −13.9210
u = −1.63750 + 0.39106I
a = 0.729477 + 0.317725I
b = 0.06541 + 1.72456I
−12.19770 − 0.58193I −13.84300 + 0.10785I
u = −1.63750 − 0.39106I
a = 0.729477 − 0.317725I
b = 0.06541 − 1.72456I
−12.19770 + 0.58193I −13.84300 − 0.10785I
u = 0.196127
a = −1.56428
b = 0.421923
−0.703748 −14.3840
u = −1.36626 + 1.27176I
a = −0.916122 − 0.700221I
b = 0.39264 − 2.22764I
15.5087 + 12.5998I −12.34182 − 4.74713I
u = −1.36626 − 1.27176I
a = −0.916122 + 0.700221I
b = 0.39264 + 2.22764I
15.5087 − 12.5998I −12.34182 + 4.74713I
u = −1.23394 + 1.55331I
a = −0.498680 − 0.733814I
b = −0.09233 − 2.40682I
16.2047 − 2.4749I −8.00000 + 0.I
u = −1.23394 − 1.55331I
a = −0.498680 + 0.733814I
b = −0.09233 + 2.40682I
16.2047 + 2.4749I −8.00000 + 0.I
u = 1.36828 + 1.45922I
a = 0.696632 − 0.707290I
b = −0.22656 − 2.42636I
−19.0095 − 5.2807I −8.00000 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.36828 − 1.45922I
a = 0.696632 + 0.707290I
b = −0.22656 + 2.42636I
−19.0095 + 5.2807I −8.00000 + 0.I
8
II.
I
u
2
= h2.29 × 10
12
u
21
− 1.33 × 10
13
u
20
+ · · · + 1.30 × 10
13
b + 2.85 × 10
13
, 1.45 ×
10
14
u
21
−4.82×10
14
u
20
+· · ·+9.13×10
13
a−2.37×10
13
, u
22
−3u
21
+· · ·−u−1i
(i) Arc colorings
a
9
=
1
0
a
12
=
0
u
a
3
=
−1.58571u
21
+ 5.28477u
20
+ ··· + 8.79506u + 0.259531
−0.175518u
21
+ 1.02353u
20
+ ··· − 0.370583u − 2.18536
a
8
=
1
−u
2
a
4
=
−1.68041u
21
+ 5.28816u
20
+ ··· + 10.2237u + 1.91725
−0.144177u
21
+ 0.875198u
20
+ ··· + 0.00484553u − 1.90463
a
7
=
−0.897790u
21
+ 2.29354u
20
+ ··· + 6.23833u + 4.35533
0.179274u
21
− 0.310068u
20
+ ··· + 0.773322u + 0.158689
a
1
=
0.481602u
21
− 2.58266u
20
+ ··· − 12.9500u + 8.90752
−0.841311u
21
+ 2.70321u
20
+ ··· + 1.56148u + 1.61463
a
6
=
−1.07706u
21
+ 2.60361u
20
+ ··· + 5.46501u + 4.19664
0.179274u
21
− 0.310068u
20
+ ··· + 0.773322u + 0.158689
a
10
=
2.71177u
21
− 8.48610u
20
+ ··· − 15.1040u − 1.10776
−1.09714u
21
+ 2.80089u
20
+ ··· + 2.25750u + 1.05460
a
2
=
−4.45944u
21
+ 13.6659u
20
+ ··· + 16.9373u + 6.28405
−1.17552u
21
+ 4.02353u
20
+ ··· + 7.62942u − 1.18536
a
5
=
5.31330u
21
− 16.8601u
20
+ ··· − 26.6004u − 4.64301
1.65088u
21
− 5.79168u
20
+ ··· − 8.47517u + 4.32508
a
11
=
6.16288u
21
− 19.4046u
20
+ ··· − 29.4931u − 3.47305
−0.447926u
21
+ 0.664587u
20
+ ··· − 3.13848u + 1.76637
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
358582400273224
91253214085243
u
21
−
1126227269963647
91253214085243
u
20
+ ··· −
215672464858020
91253214085243
u −
410928767453229
91253214085243
9
(iv) u-Polynomials at the component
10
Crossings u-Polynomials at each crossing
c
1
u
22
− 18u
21
+ ··· − 10u + 1
c
2
u
22
+ 2u
21
+ ··· − 2u − 1
c
3
u
22
− 10u
20
+ ··· + 4u − 1
c
4
u
22
− 8u
20
+ ··· + 2u + 1
c
5
u
22
− 2u
21
+ ··· + 2u − 1
c
6
u
22
+ 3u
21
+ ··· − u + 1
c
7
u
22
− 10u
20
+ ··· − 4u − 1
c
8
u
22
− 3u
21
+ ··· − u − 1
c
9
u
22
− 3u
21
+ ··· + u + 1
c
10
u
22
− 8u
20
+ ··· − 2u + 1
c
11
u
22
+ 16u
21
+ ··· + 6u + 1
c
12
u
22
− u
21
+ ··· + 265u − 325
11
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
− 38y
21
+ ··· + 22y + 1
c
2
, c
5
y
22
− 18y
21
+ ··· − 10y + 1
c
3
, c
7
y
22
− 20y
21
+ ··· − 22y + 1
c
4
, c
10
y
22
− 16y
21
+ ··· − 6y + 1
c
6
, c
9
y
22
+ 7y
21
+ ··· + 11y + 1
c
8
y
22
+ 3y
21
+ ··· + 15y + 1
c
11
y
22
− 8y
21
+ ··· + 18y + 1
c
12
y
22
− 13y
21
+ ··· + 178075y + 105625
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.675462 + 0.838319I
a = −0.008572 + 0.690284I
b = 0.049974 − 0.146584I
−4.45633 + 6.34458I −15.5915 − 9.5884I
u = −0.675462 − 0.838319I
a = −0.008572 − 0.690284I
b = 0.049974 + 0.146584I
−4.45633 − 6.34458I −15.5915 + 9.5884I
u = 0.633475 + 0.887297I
a = −0.292441 + 0.485808I
b = 0.017991 + 0.544505I
−1.45417 − 2.44146I −12.83139 + 5.34000I
u = 0.633475 − 0.887297I
a = −0.292441 − 0.485808I
b = 0.017991 − 0.544505I
−1.45417 + 2.44146I −12.83139 − 5.34000I
u = −0.042940 + 1.104590I
a = 0.39566 + 1.44174I
b = 1.03092 + 1.63134I
−1.065930 − 0.329159I −13.19387 + 1.39425I
u = −0.042940 − 1.104590I
a = 0.39566 − 1.44174I
b = 1.03092 − 1.63134I
−1.065930 + 0.329159I −13.19387 − 1.39425I
u = −0.252383 + 1.147210I
a = −0.301449 − 0.369158I
b = 1.053220 − 0.343716I
−3.17115 − 2.28573I −13.14996 + 1.17177I
u = −0.252383 − 1.147210I
a = −0.301449 + 0.369158I
b = 1.053220 + 0.343716I
−3.17115 + 2.28573I −13.14996 − 1.17177I
u = −1.188140 + 0.190133I
a = 1.38990 − 0.30485I
b = −0.372214 + 1.249320I
−6.70637 + 3.83944I −14.0398 − 3.8960I
u = −1.188140 − 0.190133I
a = 1.38990 + 0.30485I
b = −0.372214 − 1.249320I
−6.70637 − 3.83944I −14.0398 + 3.8960I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24876
a = 1.55789
b = −0.564169
−11.2120 −24.0840
u = 0.724135 + 1.064440I
a = −0.151217 − 0.018235I
b = −0.878909 + 0.636056I
−1.25661 − 2.81754I −11.73737 + 2.98648I
u = 0.724135 − 1.064440I
a = −0.151217 + 0.018235I
b = −0.878909 − 0.636056I
−1.25661 + 2.81754I −11.73737 − 2.98648I
u = −0.611081
a = −3.95557
b = −0.264471
−14.5437 −7.25840
u = 0.56540 + 1.38339I
a = −0.809415 + 0.937201I
b = −0.85679 + 2.47579I
−2.03475 − 5.46840I −17.4047 + 5.9669I
u = 0.56540 − 1.38339I
a = −0.809415 − 0.937201I
b = −0.85679 − 2.47579I
−2.03475 + 5.46840I −17.4047 − 5.9669I
u = 0.124853 + 0.474502I
a = 0.797687 − 0.440440I
b = 0.128382 − 1.329670I
2.74060 − 1.00097I −1.72317 + 7.63275I
u = 0.124853 − 0.474502I
a = 0.797687 + 0.440440I
b = 0.128382 + 1.329670I
2.74060 + 1.00097I −1.72317 − 7.63275I
u = 1.44364 + 0.52025I
a = −1.170920 + 0.077131I
b = 0.77946 + 1.66077I
−5.74006 − 1.77370I −18.0387 + 1.9713I
u = 1.44364 − 0.52025I
a = −1.170920 − 0.077131I
b = 0.77946 − 1.66077I
−5.74006 + 1.77370I −18.0387 − 1.9713I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.151420 + 0.403445I
a = 3.34960 + 3.75605I
b = −0.53770 + 1.48620I
−8.39060 + 3.39579I −12.11834 − 0.09038I
u = −0.151420 − 0.403445I
a = 3.34960 − 3.75605I
b = −0.53770 − 1.48620I
−8.39060 − 3.39579I −12.11834 + 0.09038I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 18u
21
+ ··· − 10u + 1)(u
31
+ 59u
30
+ ··· − 484409u + 120409)
c
2
(u
22
+ 2u
21
+ ··· − 2u − 1)(u
31
+ 3u
30
+ ··· + 599u + 347)
c
3
(u
22
− 10u
20
+ ··· + 4u − 1)(u
31
− u
30
+ ··· − 221u + 527)
c
4
(u
22
− 8u
20
+ ··· + 2u + 1)(u
31
− u
30
+ ··· + 5u + 13)
c
5
(u
22
− 2u
21
+ ··· + 2u − 1)(u
31
+ 3u
30
+ ··· + 599u + 347)
c
6
(u
22
+ 3u
21
+ ··· − u + 1)(u
31
+ 2u
30
+ ··· + 75u
2
− 1)
c
7
(u
22
− 10u
20
+ ··· − 4u − 1)(u
31
− u
30
+ ··· − 221u + 527)
c
8
(u
22
− 3u
21
+ ··· − u − 1)(u
31
− 2u
30
+ ··· − 374u − 53)
c
9
(u
22
− 3u
21
+ ··· + u + 1)(u
31
+ 2u
30
+ ··· + 75u
2
− 1)
c
10
(u
22
− 8u
20
+ ··· − 2u + 1)(u
31
− u
30
+ ··· + 5u + 13)
c
11
(u
22
+ 16u
21
+ ··· + 6u + 1)(u
31
+ 29u
30
+ ··· + 2911u + 169)
c
12
(u
22
− u
21
+ ··· + 265u − 325)(u
31
+ 2u
30
+ ··· − 185350u − 50425)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
− 38y
21
+ ··· + 22y + 1)
· (y
31
− 183y
30
+ ··· + 2147685948663y −14498327281)
c
2
, c
5
(y
22
− 18y
21
+ ··· − 10y + 1)(y
31
− 59y
30
+ ··· − 484409y −120409)
c
3
, c
7
(y
22
− 20y
21
+ ··· − 22y + 1)
· (y
31
− 57y
30
+ ··· + 1881747y −277729)
c
4
, c
10
(y
22
− 16y
21
+ ··· − 6y + 1)(y
31
− 29y
30
+ ··· + 2911y −169)
c
6
, c
9
(y
22
+ 7y
21
+ ··· + 11y + 1)(y
31
+ 34y
30
+ ··· + 150y −1)
c
8
(y
22
+ 3y
21
+ ··· + 15y + 1)(y
31
− 10y
30
+ ··· + 84014y −2809)
c
11
(y
22
− 8y
21
+ ··· + 18y + 1)(y
31
− 41y
30
+ ··· + 4210051y −28561)
c
12
(y
22
− 13y
21
+ ··· + 178075y + 105625)
· (y
31
− 78y
30
+ ··· + 44563768850y −2542680625)
18
