12a
0833
(K12a
0833
)
A knot diagram
1
Linearized knot diagam
4 5 8 9 3 11 12 2 1 6 7 10
Solving Sequence
6,11
7 12
3,8
4 5 2 10 1 9
c
6
c
11
c
7
c
3
c
5
c
2
c
10
c
12
c
9
c
1
, c
4
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h6.92226 × 10
23
u
76
+ 2.25852 × 10
24
u
75
+ ··· + 3.76421 × 10
24
b + 1.44507 × 10
24
,
− 8.36115 × 10
24
u
76
− 3.47813 × 10
25
u
75
+ ··· + 3.76421 × 10
24
a + 4.23354 × 10
25
, u
77
+ 2u
76
+ ··· + u + 1i
I
u
2
= hb − 1, a − u − 3, u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 79 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
= h6.92×10
23
u
76
+2.26×10
24
u
75
+· · ·+3.76×10
24
b+1.45×10
24
, −8.36×
10
24
u
76
−3.48×10
25
u
75
+· · ·+3.76×10
24
a+4.23×10
25
, u
77
+2u
76
+· · ·+u+1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
u
2
a
12
=
−u
−u
3
+ u
a
3
=
2.22122u
76
+ 9.24000u
75
+ ··· − 29.9150u − 11.2468
−0.183897u
76
− 0.599998u
75
+ ··· + 1.78805u − 0.383897
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
2.46730u
76
+ 6.84009u
75
+ ··· − 19.3082u − 7.80666
0.0679123u
76
− 1.39991u
75
+ ··· + 6.03396u + 1.46791
a
5
=
−1.93121u
76
− 8.43999u
75
+ ··· + 27.5519u + 11.3966
0.264412u
76
+ 0.600009u
75
+ ··· − 1.84779u + 0.464412
a
2
=
1.23607u
76
+ 1.79998u
75
+ ··· − 5.48564u − 0.683416
0.838969u
76
− 0.0000226859u
75
+ ··· + 0.119485u + 0.838970
a
10
=
u
u
a
1
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
a
9
=
u
9
− 4u
7
+ 3u
5
+ 2u
3
+ u
u
9
− 5u
7
+ 7u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
18898874875970222080511766
3764208987280068409379969
u
76
+
23036948754797654651395635
3764208987280068409379969
u
75
+
··· +
89792714215852879307532136
3764208987280068409379969
u +
28083545111696464689731405
3764208987280068409379969
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
− 13u
76
+ ··· + 28u − 4
c
2
, c
5
u
77
+ 3u
76
+ ··· − 28u − 1
c
3
u
77
+ 2u
76
+ ··· + 36927u − 10649
c
4
u
77
+ 46u
75
+ ··· − 3159u − 521
c
6
, c
7
, c
10
c
11
u
77
− 2u
76
+ ··· + u − 1
c
8
u
77
− 4u
76
+ ··· − u + 1
c
9
, c
12
u
77
− 12u
76
+ ··· − 7323u + 937
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
+ 15y
76
+ ··· + 8y −16
c
2
, c
5
y
77
− 59y
76
+ ··· + 840y −1
c
3
y
77
+ 36y
76
+ ··· + 7037007165y −113401201
c
4
y
77
+ 92y
76
+ ··· + 6188485y −271441
c
6
, c
7
, c
10
c
11
y
77
− 84y
76
+ ··· + 9y −1
c
8
y
77
− 16y
76
+ ··· + 9y −1
c
9
, c
12
y
77
+ 60y
76
+ ··· − 6663999y −877969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.853925 + 0.296160I
a = 0.973281 − 0.595252I
b = 1.172540 + 0.189613I
1.07224 + 1.58898I 0
u = 0.853925 − 0.296160I
a = 0.973281 + 0.595252I
b = 1.172540 − 0.189613I
1.07224 − 1.58898I 0
u = −0.593838 + 0.645320I
a = −0.63075 + 1.51672I
b = 1.270780 + 0.133216I
7.55124 + 4.72924I 0. − 6.30385I
u = −0.593838 − 0.645320I
a = −0.63075 − 1.51672I
b = 1.270780 − 0.133216I
7.55124 − 4.72924I 0. + 6.30385I
u = 0.581242 + 0.631919I
a = −1.12909 − 2.01443I
b = 1.44071 − 0.50854I
8.3310 − 13.1724I 0. + 9.15625I
u = 0.581242 − 0.631919I
a = −1.12909 + 2.01443I
b = 1.44071 + 0.50854I
8.3310 + 13.1724I 0. − 9.15625I
u = −0.766915 + 0.349815I
a = 0.45233 + 1.81840I
b = 1.257950 + 0.389125I
1.58579 + 7.91925I −4.00000 − 9.21393I
u = −0.766915 − 0.349815I
a = 0.45233 − 1.81840I
b = 1.257950 − 0.389125I
1.58579 − 7.91925I −4.00000 + 9.21393I
u = 0.546540 + 0.601133I
a = 1.244280 + 0.506121I
b = −0.172494 + 1.220390I
3.24579 − 7.19707I −1.99256 + 9.26795I
u = 0.546540 − 0.601133I
a = 1.244280 − 0.506121I
b = −0.172494 − 1.220390I
3.24579 + 7.19707I −1.99256 − 9.26795I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.511919 + 0.613048I
a = 1.43493 + 1.72189I
b = −1.55248 + 0.63641I
7.52474 − 4.19900I 4.30781 + 6.64099I
u = 0.511919 − 0.613048I
a = 1.43493 − 1.72189I
b = −1.55248 − 0.63641I
7.52474 + 4.19900I 4.30781 − 6.64099I
u = −0.401184 + 0.687267I
a = −0.832182 + 0.272529I
b = 1.287680 − 0.080245I
8.12227 − 0.25245I 4.74578 − 0.31294I
u = −0.401184 − 0.687267I
a = −0.832182 − 0.272529I
b = 1.287680 + 0.080245I
8.12227 + 0.25245I 4.74578 + 0.31294I
u = 0.411672 + 0.667315I
a = −0.830610 − 0.220703I
b = 1.44202 + 0.47832I
8.83402 + 8.79252I 0.88977 − 3.35804I
u = 0.411672 − 0.667315I
a = −0.830610 + 0.220703I
b = 1.44202 − 0.47832I
8.83402 − 8.79252I 0.88977 + 3.35804I
u = −0.529363 + 0.577415I
a = −0.135208 − 0.789858I
b = −0.209697 − 0.347656I
3.14595 + 2.98011I −2.41069 − 2.46896I
u = −0.529363 − 0.577415I
a = −0.135208 + 0.789858I
b = −0.209697 + 0.347656I
3.14595 − 2.98011I −2.41069 + 2.46896I
u = 0.480416 + 0.616913I
a = 0.579023 + 0.909776I
b = −1.58087 − 0.58209I
7.61770 + 0.01954I 4.76574 + 0.17184I
u = 0.480416 − 0.616913I
a = 0.579023 − 0.909776I
b = −1.58087 + 0.58209I
7.61770 − 0.01954I 4.76574 − 0.17184I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.494713 + 0.592724I
a = 3.16136 − 1.21835I
b = −1.125500 − 0.016130I
5.08899 + 2.02411I −19.3118 − 1.4800I
u = −0.494713 − 0.592724I
a = 3.16136 + 1.21835I
b = −1.125500 + 0.016130I
5.08899 − 2.02411I −19.3118 + 1.4800I
u = 0.438086 + 0.613550I
a = −0.671045 + 0.081730I
b = −0.234394 − 1.182410I
3.56479 + 3.06303I −0.82722 − 2.95608I
u = 0.438086 − 0.613550I
a = −0.671045 − 0.081730I
b = −0.234394 + 1.182410I
3.56479 − 3.06303I −0.82722 + 2.95608I
u = −0.454585 + 0.581796I
a = −0.700983 + 0.414818I
b = −0.299545 + 0.306129I
3.36686 + 0.99145I −1.25975 − 4.73968I
u = −0.454585 − 0.581796I
a = −0.700983 − 0.414818I
b = −0.299545 − 0.306129I
3.36686 − 0.99145I −1.25975 + 4.73968I
u = −0.662313 + 0.211934I
a = 0.35497 − 1.59761I
b = 0.052783 − 0.855449I
−2.18565 + 3.46642I −10.30084 − 8.03918I
u = −0.662313 − 0.211934I
a = 0.35497 + 1.59761I
b = 0.052783 + 0.855449I
−2.18565 − 3.46642I −10.30084 + 8.03918I
u = 0.582849 + 0.322676I
a = −1.21537 − 0.97656I
b = 0.305951 − 0.408414I
−1.56034 − 0.79420I −10.59198 + 4.32165I
u = 0.582849 − 0.322676I
a = −1.21537 + 0.97656I
b = 0.305951 + 0.408414I
−1.56034 + 0.79420I −10.59198 − 4.32165I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.036520 + 0.599242I
a = −0.827030 + 0.013934I
b = 1.257970 − 0.282910I
3.88684 − 4.68919I 2.22512 + 5.21190I
u = −0.036520 − 0.599242I
a = −0.827030 − 0.013934I
b = 1.257970 + 0.282910I
3.88684 + 4.68919I 2.22512 − 5.21190I
u = 0.563481
a = −0.745038
b = 0.0349557
−0.922835 −10.6560
u = 1.42367 + 0.20238I
a = 0.304978 − 0.285826I
b = 1.311050 + 0.004533I
2.29463 − 2.93841I 0
u = 1.42367 − 0.20238I
a = 0.304978 + 0.285826I
b = 1.311050 − 0.004533I
2.29463 + 2.93841I 0
u = −1.44300 + 0.19292I
a = 0.428691 − 0.138349I
b = 1.44221 − 0.43358I
2.88358 − 5.72307I 0
u = −1.44300 − 0.19292I
a = 0.428691 + 0.138349I
b = 1.44221 + 0.43358I
2.88358 + 5.72307I 0
u = −0.481253 + 0.252904I
a = −0.87479 − 2.48795I
b = −1.085940 − 0.463047I
1.84563 + 2.21443I −1.06316 − 9.09042I
u = −0.481253 − 0.252904I
a = −0.87479 + 2.48795I
b = −1.085940 + 0.463047I
1.84563 − 2.21443I −1.06316 + 9.09042I
u = −1.48480 + 0.16334I
a = −0.928276 + 0.982359I
b = −0.330290 + 1.148720I
−2.68476 − 0.33795I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.48480 − 0.16334I
a = −0.928276 − 0.982359I
b = −0.330290 − 1.148720I
−2.68476 + 0.33795I 0
u = 1.49604
a = −1.27137
b = −1.51544
−3.24017 0
u = 0.492260 + 0.077362I
a = −2.26092 + 6.41672I
b = −0.953862 + 0.013143I
0.798661 − 0.174787I 27.8903 − 10.4954I
u = 0.492260 − 0.077362I
a = −2.26092 − 6.41672I
b = −0.953862 − 0.013143I
0.798661 + 0.174787I 27.8903 + 10.4954I
u = 1.50405 + 0.15591I
a = −1.037770 − 0.828109I
b = −0.415857 − 0.300870I
−3.06301 − 3.56838I 0
u = 1.50405 − 0.15591I
a = −1.037770 + 0.828109I
b = −0.415857 + 0.300870I
−3.06301 + 3.56838I 0
u = −1.50575 + 0.17891I
a = −0.822676 − 0.369551I
b = −1.61992 + 0.52632I
1.10913 + 2.81557I 0
u = −1.50575 − 0.17891I
a = −0.822676 + 0.369551I
b = −1.61992 − 0.52632I
1.10913 − 2.81557I 0
u = 1.51956 + 0.04330I
a = −1.33810 + 1.94670I
b = −1.010310 + 0.705360I
−4.84400 − 3.13283I 0
u = 1.51956 − 0.04330I
a = −1.33810 − 1.94670I
b = −1.010310 − 0.705360I
−4.84400 + 3.13283I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.51829 + 0.17105I
a = 1.87369 + 1.53109I
b = −1.129620 + 0.048557I
−1.54754 − 4.74455I 0
u = 1.51829 − 0.17105I
a = 1.87369 − 1.53109I
b = −1.129620 − 0.048557I
−1.54754 + 4.74455I 0
u = −1.52209 + 0.18329I
a = −0.04272 − 2.17243I
b = −1.52902 − 0.69215I
0.82414 + 7.06092I 0
u = −1.52209 − 0.18329I
a = −0.04272 + 2.17243I
b = −1.52902 + 0.69215I
0.82414 − 7.06092I 0
u = −1.53326 + 0.01568I
a = −0.95067 − 3.21890I
b = −0.921461 − 0.114945I
−6.07296 + 0.47946I 0
u = −1.53326 − 0.01568I
a = −0.95067 + 3.21890I
b = −0.921461 + 0.114945I
−6.07296 − 0.47946I 0
u = 1.53565 + 0.17005I
a = −0.246452 + 0.988043I
b = −0.141987 + 0.396231I
−3.70464 − 5.66720I 0
u = 1.53565 − 0.17005I
a = −0.246452 − 0.988043I
b = −0.141987 − 0.396231I
−3.70464 + 5.66720I 0
u = −1.53946 + 0.18227I
a = 0.94700 − 1.54313I
b = −0.121748 − 1.253750I
−3.66455 + 10.03570I 0
u = −1.53946 − 0.18227I
a = 0.94700 + 1.54313I
b = −0.121748 + 1.253750I
−3.66455 − 10.03570I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.55599 + 0.08870I
a = −0.40942 + 1.36638I
b = 0.502249 + 0.525672I
−8.78367 + 2.27960I 0
u = −1.55599 − 0.08870I
a = −0.40942 − 1.36638I
b = 0.502249 − 0.525672I
−8.78367 − 2.27960I 0
u = −1.55314 + 0.19785I
a = 0.12361 + 2.22057I
b = 1.43690 + 0.53476I
1.2566 + 16.2112I 0
u = −1.55314 − 0.19785I
a = 0.12361 − 2.22057I
b = 1.43690 − 0.53476I
1.2566 − 16.2112I 0
u = −1.56614
a = −0.226660
b = 0.197297
−8.25195 0
u = 1.56818 + 0.04901I
a = 0.31464 + 1.98559I
b = 0.176625 + 0.965287I
−9.71978 − 4.36105I 0
u = 1.56818 − 0.04901I
a = 0.31464 − 1.98559I
b = 0.176625 − 0.965287I
−9.71978 + 4.36105I 0
u = 1.55754 + 0.20538I
a = 0.32466 − 1.44758I
b = 1.252100 − 0.181265I
0.42304 − 7.85842I 0
u = 1.55754 − 0.20538I
a = 0.32466 + 1.44758I
b = 1.252100 + 0.181265I
0.42304 + 7.85842I 0
u = 1.59711 + 0.08248I
a = 1.18450 − 1.70696I
b = 1.220860 − 0.468134I
−6.42327 − 9.43760I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59711 − 0.08248I
a = 1.18450 + 1.70696I
b = 1.220860 + 0.468134I
−6.42327 + 9.43760I 0
u = 0.036693 + 0.376347I
a = −0.936023 − 0.126763I
b = −0.072076 + 0.554674I
−0.11372 − 1.47103I −2.11863 + 4.15045I
u = 0.036693 − 0.376347I
a = −0.936023 + 0.126763I
b = −0.072076 − 0.554674I
−0.11372 + 1.47103I −2.11863 − 4.15045I
u = −1.62917 + 0.04871I
a = 1.266120 + 0.059325I
b = 1.042950 − 0.146994I
−7.44987 − 0.45114I 0
u = −1.62917 − 0.04871I
a = 1.266120 − 0.059325I
b = 1.042950 + 0.146994I
−7.44987 + 0.45114I 0
u = −0.218991 + 0.259933I
a = −0.526450 − 0.951049I
b = −1.224660 + 0.170875I
2.56830 − 0.25125I 2.88791 − 3.66761I
u = −0.218991 − 0.259933I
a = −0.526450 + 0.951049I
b = −1.224660 − 0.170875I
2.56830 + 0.25125I 2.88791 + 3.66761I
12
II. I
u
2
= hb − 1, a − u − 3, u
2
+ u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
7
=
1
−u + 1
a
12
=
−u
−u + 1
a
3
=
u + 3
1
a
8
=
u
u
a
4
=
u + 2
0
a
5
=
u + 4
1
a
2
=
−1
0
a
10
=
u
u
a
1
=
−1
0
a
9
=
2u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = 1
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
c
2
(u + 1)
2
c
3
, c
4
, c
10
c
11
, c
12
u
2
− u − 1
c
5
(u − 1)
2
c
6
, c
7
, c
8
c
9
u
2
+ u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
2
c
2
, c
5
(y −1)
2
c
3
, c
4
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
2
− 3y + 1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 3.61803
b = 1.00000
0.657974 1.00000
u = −1.61803
a = 1.38197
b = 1.00000
−7.23771 1.00000
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
2
(u
77
− 13u
76
+ ··· + 28u − 4)
c
2
((u + 1)
2
)(u
77
+ 3u
76
+ ··· − 28u − 1)
c
3
(u
2
− u − 1)(u
77
+ 2u
76
+ ··· + 36927u − 10649)
c
4
(u
2
− u − 1)(u
77
+ 46u
75
+ ··· − 3159u − 521)
c
5
((u − 1)
2
)(u
77
+ 3u
76
+ ··· − 28u − 1)
c
6
, c
7
(u
2
+ u − 1)(u
77
− 2u
76
+ ··· + u − 1)
c
8
(u
2
+ u − 1)(u
77
− 4u
76
+ ··· − u + 1)
c
9
(u
2
+ u − 1)(u
77
− 12u
76
+ ··· − 7323u + 937)
c
10
, c
11
(u
2
− u − 1)(u
77
− 2u
76
+ ··· + u − 1)
c
12
(u
2
− u − 1)(u
77
− 12u
76
+ ··· − 7323u + 937)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
2
(y
77
+ 15y
76
+ ··· + 8y −16)
c
2
, c
5
((y −1)
2
)(y
77
− 59y
76
+ ··· + 840y −1)
c
3
(y
2
− 3y + 1)(y
77
+ 36y
76
+ ··· + 7.03701 × 10
9
y −1.13401 × 10
8
)
c
4
(y
2
− 3y + 1)(y
77
+ 92y
76
+ ··· + 6188485y −271441)
c
6
, c
7
, c
10
c
11
(y
2
− 3y + 1)(y
77
− 84y
76
+ ··· + 9y −1)
c
8
(y
2
− 3y + 1)(y
77
− 16y
76
+ ··· + 9y −1)
c
9
, c
12
(y
2
− 3y + 1)(y
77
+ 60y
76
+ ··· − 6663999y −877969)
18
