12a
0813
(K12a
0813
)
A knot diagram
1
Linearized knot diagam
4 5 7 2 10 3 11 12 6 1 8 9
Solving Sequence
8,11
12 9 1
3,7
4 2 6 10 5
c
11
c
8
c
12
c
7
c
3
c
1
c
6
c
10
c
5
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−7.95449 × 10
20
u
71
− 4.31806 × 10
21
u
70
+ ··· + 1.48712 × 10
21
b − 3.47841 × 10
21
,
1.07241 × 10
22
u
71
+ 2.56114 × 10
22
u
70
+ ··· + 2.97424 × 10
21
a + 7.95838 × 10
21
, u
72
+ 4u
71
+ ··· + 4u + 1i
I
u
2
= hu
5
+ u
4
− 3u
3
− u
2
+ b + 2u − 2, u
5
+ u
4
− 3u
3
− u
2
+ a + 2u − 2, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
I
u
3
= hb − u − 2, a − u − 1, u
2
− u − 1i
I
u
4
= hb + u + 2, a + 2u, u
2
− u − 1i
* 4 irreducible components of dim
C
= 0, with total 82 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−7.95×10
20
u
71
−4.32×10
21
u
70
+· · ·+1.49×10
21
b−3.48×10
21
, 1.07×
10
22
u
71
+2.56×10
22
u
70
+· · ·+2.97×10
21
a+7.96×10
21
, u
72
+4u
71
+· · ·+4u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
9
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−3.60565u
71
− 8.61108u
70
+ ··· − 3.99235u − 2.67577
0.534891u
71
+ 2.90363u
70
+ ··· + 4.98903u + 2.33902
a
7
=
u
u
a
4
=
−11.5779u
71
− 28.0840u
70
+ ··· − 20.0416u − 7.72322
−7.43736u
71
− 16.5693u
70
+ ··· − 11.0602u − 2.70843
a
2
=
16.6166u
71
+ 39.8106u
70
+ ··· + 30.7682u + 9.88627
14.7571u
71
+ 34.3253u
70
+ ··· + 26.7496u + 6.90106
a
6
=
−2.38563u
71
− 6.49739u
70
+ ··· − 5.92951u − 3.30940
1.63521u
71
+ 4.28995u
70
+ ··· + 4.95437u + 0.667990
a
10
=
−u
6
+ 3u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
5
=
10.9945u
71
+ 25.9002u
70
+ ··· + 23.1121u + 4.39475
12.8540u
71
+ 31.3855u
70
+ ··· + 27.1307u + 7.37996
(ii) Obstruction class = −1
(iii) Cusp Shapes =
150126529301461580621605
2974244354519536997566
u
71
+
259807076562668316197598
1487122177259768498783
u
70
+ ··· +
302915952567745176733616
1487122177259768498783
u +
237828014772875129379223
2974244354519536997566
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
72
− 9u
71
+ ··· − 23u − 1
c
3
, c
6
u
72
+ 3u
71
+ ··· − 320u − 64
c
5
, c
9
u
72
+ 2u
71
+ ··· + 64u + 16
c
7
, c
8
, c
11
c
12
u
72
+ 4u
71
+ ··· + 4u + 1
c
10
u
72
− 20u
71
+ ··· − 3276u − 79
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
72
− 71y
71
+ ··· − 369y + 1
c
3
, c
6
y
72
− 45y
71
+ ··· − 241664y + 4096
c
5
, c
9
y
72
+ 30y
71
+ ··· − 3712y + 256
c
7
, c
8
, c
11
c
12
y
72
− 84y
71
+ ··· − 20y + 1
c
10
y
72
− 12y
71
+ ··· − 11660268y + 6241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.982343 + 0.346269I
a = 0.216789 − 0.337856I
b = 1.196170 + 0.510620I
−7.89851 − 4.44178I 0
u = −0.982343 − 0.346269I
a = 0.216789 + 0.337856I
b = 1.196170 − 0.510620I
−7.89851 + 4.44178I 0
u = 0.757927 + 0.551621I
a = −0.323743 − 0.008309I
b = −1.90119 + 0.21928I
−6.15007 − 12.15710I 0
u = 0.757927 − 0.551621I
a = −0.323743 + 0.008309I
b = −1.90119 − 0.21928I
−6.15007 + 12.15710I 0
u = −0.850217 + 0.222300I
a = −0.623196 + 0.202068I
b = −1.52408 − 0.38478I
−2.05877 − 1.35062I 0
u = −0.850217 − 0.222300I
a = −0.623196 − 0.202068I
b = −1.52408 + 0.38478I
−2.05877 + 1.35062I 0
u = 0.705422 + 0.506721I
a = 0.424505 + 0.257141I
b = 1.87330 − 0.07115I
−0.21486 − 7.76434I 0
u = 0.705422 − 0.506721I
a = 0.424505 − 0.257141I
b = 1.87330 + 0.07115I
−0.21486 + 7.76434I 0
u = −0.681164 + 0.507135I
a = −0.004024 − 0.372323I
b = −1.55030 − 0.84093I
−8.10918 + 5.48099I 0
u = −0.681164 − 0.507135I
a = −0.004024 + 0.372323I
b = −1.55030 + 0.84093I
−8.10918 − 5.48099I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.697751 + 0.460295I
a = −0.046939 − 0.942118I
b = 0.399029 + 0.513779I
−3.03405 − 5.33018I 0
u = 0.697751 − 0.460295I
a = −0.046939 + 0.942118I
b = 0.399029 − 0.513779I
−3.03405 + 5.33018I 0
u = 0.488900 + 0.673030I
a = 0.391172 − 0.358829I
b = −0.304669 + 0.448535I
0.24344 − 2.25273I 0
u = 0.488900 − 0.673030I
a = 0.391172 + 0.358829I
b = −0.304669 − 0.448535I
0.24344 + 2.25273I 0
u = −0.740284 + 0.298767I
a = 0.830320 + 1.049630I
b = 1.257810 − 0.028274I
−4.10061 + 0.49792I −17.6259 + 0.I
u = −0.740284 − 0.298767I
a = 0.830320 − 1.049630I
b = 1.257810 + 0.028274I
−4.10061 − 0.49792I −17.6259 + 0.I
u = 0.653152 + 0.419191I
a = −0.268386 − 0.707920I
b = −1.66871 − 0.10927I
−1.67645 − 2.50037I −15.9818 + 5.1399I
u = 0.653152 − 0.419191I
a = −0.268386 + 0.707920I
b = −1.66871 + 0.10927I
−1.67645 + 2.50037I −15.9818 − 5.1399I
u = 0.566256 + 0.518532I
a = 0.135073 + 0.566520I
b = −0.255171 − 0.370268I
2.61662 − 3.02816I −7.67475 + 5.37656I
u = 0.566256 − 0.518532I
a = 0.135073 − 0.566520I
b = −0.255171 + 0.370268I
2.61662 + 3.02816I −7.67475 − 5.37656I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.654003 + 0.367302I
a = 0.354913 + 0.490782I
b = 1.63048 + 0.78250I
−2.04063 + 2.41804I −16.4783 − 6.4550I
u = −0.654003 − 0.367302I
a = 0.354913 − 0.490782I
b = 1.63048 − 0.78250I
−2.04063 − 2.41804I −16.4783 + 6.4550I
u = 0.706946 + 0.176779I
a = −0.682322 + 0.627956I
b = 1.382590 − 0.098280I
−10.18240 − 0.21970I −23.0944 + 10.0861I
u = 0.706946 − 0.176779I
a = −0.682322 − 0.627956I
b = 1.382590 + 0.098280I
−10.18240 + 0.21970I −23.0944 − 10.0861I
u = 0.148844 + 0.693249I
a = −0.16677 − 1.81670I
b = 0.330588 + 0.107064I
−4.33570 + 7.98491I −14.0293 − 4.5706I
u = 0.148844 − 0.693249I
a = −0.16677 + 1.81670I
b = 0.330588 − 0.107064I
−4.33570 − 7.98491I −14.0293 + 4.5706I
u = 0.362499 + 0.542365I
a = −0.703035 − 0.020137I
b = 0.567304 + 0.021974I
3.20652 − 0.63611I −6.08573 + 2.74041I
u = 0.362499 − 0.542365I
a = −0.703035 + 0.020137I
b = 0.567304 − 0.021974I
3.20652 + 0.63611I −6.08573 − 2.74041I
u = 0.179620 + 0.596705I
a = 0.16130 + 1.98572I
b = −0.121937 + 0.128533I
1.32458 + 4.00559I −9.89823 − 4.05878I
u = 0.179620 − 0.596705I
a = 0.16130 − 1.98572I
b = −0.121937 − 0.128533I
1.32458 − 4.00559I −9.89823 + 4.05878I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.224967 + 0.575498I
a = 0.70393 + 1.64159I
b = 0.429947 − 0.451121I
−6.77156 − 1.76410I −16.4390 − 0.3709I
u = −0.224967 − 0.575498I
a = 0.70393 − 1.64159I
b = 0.429947 + 0.451121I
−6.77156 + 1.76410I −16.4390 + 0.3709I
u = 1.41016
a = −0.565928
b = 0.219603
−11.4382 0
u = −0.548767
a = −3.83647
b = −4.23596
−2.45821 −112.620
u = −1.45092 + 0.07467I
a = −0.908730 − 0.317137I
b = −1.41622 + 0.17108I
−2.53260 + 2.67846I 0
u = −1.45092 − 0.07467I
a = −0.908730 + 0.317137I
b = −1.41622 − 0.17108I
−2.53260 − 2.67846I 0
u = 0.147964 + 0.516203I
a = 1.105020 − 0.315921I
b = −0.893399 − 0.180647I
−1.46043 + 1.94339I −11.45163 − 1.22090I
u = 0.147964 − 0.516203I
a = 1.105020 + 0.315921I
b = −0.893399 + 0.180647I
−1.46043 − 1.94339I −11.45163 + 1.22090I
u = −1.46952 + 0.20603I
a = 0.346174 + 0.478606I
b = 0.971727 + 0.391726I
−6.09783 + 5.43700I 0
u = −1.46952 − 0.20603I
a = 0.346174 − 0.478606I
b = 0.971727 − 0.391726I
−6.09783 − 5.43700I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.49411 + 0.02315I
a = 1.74011 − 0.37479I
b = 2.31872 + 0.15589I
−6.25312 + 1.44485I 0
u = −1.49411 − 0.02315I
a = 1.74011 + 0.37479I
b = 2.31872 − 0.15589I
−6.25312 − 1.44485I 0
u = 0.253261 + 0.393389I
a = −0.05262 − 2.24609I
b = −0.451196 − 0.277085I
−0.487985 − 0.461323I −11.73637 + 1.56029I
u = 0.253261 − 0.393389I
a = −0.05262 + 2.24609I
b = −0.451196 + 0.277085I
−0.487985 + 0.461323I −11.73637 − 1.56029I
u = 1.54992 + 0.04257I
a = 0.513560 − 0.344106I
b = 0.309960 − 0.008693I
−7.50903 − 0.53436I 0
u = 1.54992 − 0.04257I
a = 0.513560 + 0.344106I
b = 0.309960 + 0.008693I
−7.50903 + 0.53436I 0
u = −1.55015 + 0.14465I
a = 0.338834 − 0.369514I
b = 0.302206 − 0.861493I
−4.45615 + 5.40578I 0
u = −1.55015 − 0.14465I
a = 0.338834 + 0.369514I
b = 0.302206 + 0.861493I
−4.45615 − 5.40578I 0
u = −0.433430
a = −0.914990
b = −0.390164
−0.700979 −13.7250
u = 1.59454 + 0.10539I
a = −2.49347 + 1.65768I
b = −3.18246 + 1.46944I
−9.72702 − 4.16869I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59454 − 0.10539I
a = −2.49347 − 1.65768I
b = −3.18246 − 1.46944I
−9.72702 + 4.16869I 0
u = −1.59357 + 0.11931I
a = 3.10005 + 0.57745I
b = 3.92954 + 0.54344I
−9.33167 + 4.48353I 0
u = −1.59357 − 0.11931I
a = 3.10005 − 0.57745I
b = 3.92954 − 0.54344I
−9.33167 − 4.48353I 0
u = 1.60524
a = 4.54320
b = 4.85745
−10.0666 0
u = 1.59950 + 0.14775I
a = 2.05789 − 1.61299I
b = 2.91237 − 1.33358I
−15.8332 − 7.9107I 0
u = 1.59950 − 0.14775I
a = 2.05789 + 1.61299I
b = 2.91237 + 1.33358I
−15.8332 + 7.9107I 0
u = −1.60538 + 0.06802I
a = −2.79656 − 0.42280I
b = −3.85842 − 0.63401I
−18.1236 + 1.2636I 0
u = −1.60538 − 0.06802I
a = −2.79656 + 0.42280I
b = −3.85842 + 0.63401I
−18.1236 − 1.2636I 0
u = −1.60487 + 0.13290I
a = −0.380165 + 0.730302I
b = −0.24001 + 1.58204I
−10.86460 + 7.53927I 0
u = −1.60487 − 0.13290I
a = −0.380165 − 0.730302I
b = −0.24001 − 1.58204I
−10.86460 − 7.53927I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60661 + 0.14847I
a = −2.97807 − 0.93378I
b = −3.79856 − 0.70427I
−8.05272 + 10.21100I 0
u = −1.60661 − 0.14847I
a = −2.97807 + 0.93378I
b = −3.79856 + 0.70427I
−8.05272 − 10.21100I 0
u = 1.61319 + 0.08752I
a = −1.025740 + 0.290343I
b = −0.954538 − 0.378372I
−12.16050 − 1.96894I 0
u = 1.61319 − 0.08752I
a = −1.025740 − 0.290343I
b = −0.954538 + 0.378372I
−12.16050 + 1.96894I 0
u = 1.62747 + 0.05876I
a = 2.88948 − 0.85424I
b = 3.47835 − 0.91637I
−10.52250 + 0.30794I 0
u = 1.62747 − 0.05876I
a = 2.88948 + 0.85424I
b = 3.47835 + 0.91637I
−10.52250 − 0.30794I 0
u = −1.62590 + 0.16520I
a = 2.71253 + 1.00812I
b = 3.59859 + 0.64474I
−14.2359 + 14.8752I 0
u = −1.62590 − 0.16520I
a = 2.71253 − 1.00812I
b = 3.59859 − 0.64474I
−14.2359 − 14.8752I 0
u = 1.68204 + 0.06795I
a = −2.19107 + 0.66703I
b = −2.98376 + 0.93026I
−17.1989 + 2.9520I 0
u = 1.68204 − 0.06795I
a = −2.19107 − 0.66703I
b = −2.98376 − 0.93026I
−17.1989 − 2.9520I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.217797 + 0.169704I
a = −1.98973 − 1.50144I
b = −0.509511 + 0.059295I
−0.769880 − 0.033097I −11.72378 − 0.92219I
u = −0.217797 − 0.169704I
a = −1.98973 + 1.50144I
b = −0.509511 − 0.059295I
−0.769880 + 0.033097I −11.72378 + 0.92219I
12
II. I
u
2
= hu
5
+ u
4
− 3u
3
− u
2
+ b + 2u − 2, u
5
+ u
4
− 3u
3
− u
2
+ a + 2u −
2, u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
9
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
−u
5
− u
4
+ 3u
3
+ u
2
− 2u + 2
−u
5
− u
4
+ 3u
3
+ u
2
− 2u + 2
a
7
=
u
u
a
4
=
−u
5
− u
4
+ 3u
3
+ u
2
− 2u + 2
−u
5
− u
4
+ 3u
3
+ u
2
− 2u + 2
a
2
=
−u
5
− u
4
+ 3u
3
− 2u + 3
−u
5
− 2u
4
+ 3u
3
+ 3u
2
− 2u + 2
a
6
=
u
u
a
10
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
a
5
=
u
2
− 1
u
4
− 2u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = −10u
5
− 6u
4
+ 30u
3
+ 5u
2
− 17u + 7
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
6
u
6
c
4
(u + 1)
6
c
5
, c
10
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
7
, c
8
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
9
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
c
11
, c
12
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
, c
9
, c
10
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
c
7
, c
8
, c
11
c
12
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.493180 + 0.575288I
a = 0.228804 + 0.434483I
b = 0.228804 + 0.434483I
1.31531 − 1.97241I −10.05095 + 2.83524I
u = 0.493180 − 0.575288I
a = 0.228804 − 0.434483I
b = 0.228804 − 0.434483I
1.31531 + 1.97241I −10.05095 − 2.83524I
u = −0.483672
a = 2.83358
b = 2.83358
−2.38379 12.9340
u = −1.52087 + 0.16310I
a = −0.636388 + 0.565801I
b = −0.636388 + 0.565801I
−5.34051 + 4.59213I −15.4320 − 0.4465I
u = −1.52087 − 0.16310I
a = −0.636388 − 0.565801I
b = −0.636388 − 0.565801I
−5.34051 − 4.59213I −15.4320 + 0.4465I
u = 1.53904
a = −2.01841
b = −2.01841
−9.30502 −17.9680
16
III. I
u
3
= hb − u − 2, a − u − 1, u
2
− u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u + 1
a
9
=
−u
−u − 1
a
1
=
−u
−u
a
3
=
u + 1
u + 2
a
7
=
u
u
a
4
=
0
1
a
2
=
−u
−2u
a
6
=
−u − 1
−2u − 1
a
10
=
−u
−u − 1
a
5
=
−u − 1
−2u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −19
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
10
u
2
+ u − 1
c
4
, c
6
, c
11
c
12
u
2
− u − 1
c
5
, c
9
u
2
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
10
, c
11
c
12
y
2
− 3y + 1
c
5
, c
9
y
2
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 0.381966
b = 1.38197
−1.97392 −19.0000
u = 1.61803
a = 2.61803
b = 3.61803
−17.7653 −19.0000
20
IV. I
u
4
= hb + u + 2, a + 2u, u
2
− u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
u + 1
a
9
=
−u
−u − 1
a
1
=
−u
−u
a
3
=
−2u
−u − 2
a
7
=
u
u
a
4
=
−2u + 1
−u − 1
a
2
=
−3
−2u
a
6
=
u − 2
−u + 1
a
10
=
−u
−u − 1
a
5
=
u − 2
−u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
7
, c
8
, c
10
u
2
+ u − 1
c
4
, c
6
, c
11
c
12
u
2
− u − 1
c
5
, c
9
u
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
c
8
, c
10
, c
11
c
12
y
2
− 3y + 1
c
5
, c
9
y
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618034
a = 1.23607
b = −1.38197
−9.86960 −4.00000
u = 1.61803
a = −3.23607
b = −3.61803
−9.86960 −4.00000
24
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
((u − 1)
6
)(u
2
+ u − 1)
2
(u
72
− 9u
71
+ ··· − 23u − 1)
c
3
u
6
(u
2
+ u − 1)
2
(u
72
+ 3u
71
+ ··· − 320u − 64)
c
4
((u + 1)
6
)(u
2
− u − 1)
2
(u
72
− 9u
71
+ ··· − 23u − 1)
c
5
u
4
(u
6
+ u
5
+ ··· + u − 1)(u
72
+ 2u
71
+ ··· + 64u + 16)
c
6
u
6
(u
2
− u − 1)
2
(u
72
+ 3u
71
+ ··· − 320u − 64)
c
7
, c
8
(u
2
+ u − 1)
2
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
72
+ 4u
71
+ ··· + 4u + 1)
c
9
u
4
(u
6
− u
5
+ ··· − u − 1)(u
72
+ 2u
71
+ ··· + 64u + 16)
c
10
(u
2
+ u − 1)
2
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)
· (u
72
− 20u
71
+ ··· − 3276u − 79)
c
11
, c
12
(u
2
− u − 1)
2
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)
· (u
72
+ 4u
71
+ ··· + 4u + 1)
25
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
((y −1)
6
)(y
2
− 3y + 1)
2
(y
72
− 71y
71
+ ··· − 369y + 1)
c
3
, c
6
y
6
(y
2
− 3y + 1)
2
(y
72
− 45y
71
+ ··· − 241664y + 4096)
c
5
, c
9
y
4
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
· (y
72
+ 30y
71
+ ··· − 3712y + 256)
c
7
, c
8
, c
11
c
12
(y
2
− 3y + 1)
2
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
72
− 84y
71
+ ··· − 20y + 1)
c
10
(y
2
− 3y + 1)
2
(y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1)
· (y
72
− 12y
71
+ ··· − 11660268y + 6241)
26
