12a
0860
(K12a
0860
)
A knot diagram
1
Linearized knot diagam
4 5 10 9 3 11 12 1 2 6 8 7
Solving Sequence
8,11
12 7
1,4
2 9 6 10 3 5
c
11
c
7
c
12
c
1
c
8
c
6
c
10
c
3
c
5
c
2
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.29007 × 10
24
u
76
+ 1.01626 × 10
25
u
75
+ ··· + 1.55594 × 10
24
b + 8.02867 × 10
24
,
8.96223 × 10
24
u
76
− 1.26342 × 10
25
u
75
+ ··· + 1.55594 × 10
24
a − 1.05097 × 10
25
, u
77
− 2u
76
+ ··· − 7u + 1i
I
u
2
= hu
2
+ b + 1, −u
2
+ a − 2, u
3
− u
2
+ 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 80 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−5.29×10
24
u
76
+1.02×10
25
u
75
+· · ·+1.56×10
24
b+8.03×10
24
, 8.96×
10
24
u
76
−1.26×10
25
u
75
+· · ·+1.56×10
24
a−1.05×10
25
, u
77
−2u
76
+· · ·−7u+1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
−u
u
3
+ u
a
1
=
u
2
+ 1
−u
4
− 2u
2
a
4
=
−5.76000u
76
+ 8.11999u
75
+ ··· − 49.9977u + 6.75457
3.39991u
76
− 6.53146u
75
+ ··· + 29.1654u − 5.16000
a
2
=
0.200000u
76
+ 0.0000233782u
75
+ ··· − 1.10414u − 0.722387
−0.400023u
76
− 0.0418941u
75
+ ··· − 0.677613u + 0.200000
a
9
=
u
5
+ 2u
3
+ u
−u
7
− 3u
5
− 2u
3
+ u
a
6
=
−u
3
− 2u
u
3
+ u
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
u
6
+ 2u
4
+ u
2
a
3
=
−4.16000u
76
+ 4.92014u
75
+ ··· − 30.5063u + 3.54293
3.60000u
76
− 6.98916u
75
+ ··· + 37.6171u − 6.96000
a
5
=
−3.96000u
76
+ 4.71990u
75
+ ··· − 32.2944u + 3.21217
3.40001u
76
− 6.65993u
75
+ ··· + 37.1478u − 6.76000
(ii) Obstruction class = −1
(iii) Cusp Shapes =
39428653274113013343690898
1555942872114780833899609
u
76
−
62426554058064260098232498
1555942872114780833899609
u
75
+
··· +
513166216142495611295460359
1555942872114780833899609
u −
100110429527755677393611749
1555942872114780833899609
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
− 13u
76
+ ··· + 20u + 8
c
2
, c
5
u
77
+ 4u
76
+ ··· − 14u + 1
c
3
u
77
+ u
76
+ ··· + 887410u + 302321
c
4
u
77
+ 3u
76
+ ··· − 1548u + 181
c
6
, c
8
, c
10
u
77
+ 2u
76
+ ··· − 147u + 17
c
7
, c
11
, c
12
u
77
− 2u
76
+ ··· − 7u + 1
c
9
u
77
− 2u
76
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
+ 21y
76
+ ··· − 432y −64
c
2
, c
5
y
77
− 62y
76
+ ··· + 26y −1
c
3
y
77
− 33y
76
+ ··· − 1941705110116y −91397987041
c
4
y
77
− 101y
76
+ ··· + 3284652y −32761
c
6
, c
8
, c
10
y
77
− 84y
76
+ ··· − 4639y −289
c
7
, c
11
, c
12
y
77
+ 60y
76
+ ··· + y −1
c
9
y
77
+ 12y
76
+ ··· + y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.913802 + 0.063108I
a = 0.33472 − 1.92033I
b = −0.27119 + 1.94599I
13.03970 − 3.23619I 15.5734 + 0.I
u = −0.913802 − 0.063108I
a = 0.33472 + 1.92033I
b = −0.27119 − 1.94599I
13.03970 + 3.23619I 15.5734 + 0.I
u = 0.906595 + 0.055280I
a = 0.34629 − 3.14143I
b = −0.32424 + 3.20304I
13.6932 + 11.6268I 13.0485 − 6.1237I
u = 0.906595 − 0.055280I
a = 0.34629 + 3.14143I
b = −0.32424 − 3.20304I
13.6932 − 11.6268I 13.0485 + 6.1237I
u = −0.326996 + 0.842532I
a = −0.541376 + 0.646495I
b = 0.402390 − 0.782201I
3.66083 + 4.79876I 0
u = −0.326996 − 0.842532I
a = −0.541376 − 0.646495I
b = 0.402390 + 0.782201I
3.66083 − 4.79876I 0
u = 0.894206 + 0.008927I
a = 1.91536 + 2.58709I
b = −1.44994 − 2.51862I
12.52080 + 2.21530I 17.1121 − 3.0542I
u = 0.894206 − 0.008927I
a = 1.91536 − 2.58709I
b = −1.44994 + 2.51862I
12.52080 − 2.21530I 17.1121 + 3.0542I
u = 0.887210 + 0.029674I
a = −0.78127 + 3.57061I
b = 0.65963 − 3.44289I
8.27458 + 5.48443I 11.67244 − 5.84044I
u = 0.887210 − 0.029674I
a = −0.78127 − 3.57061I
b = 0.65963 + 3.44289I
8.27458 − 5.48443I 11.67244 + 5.84044I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.054607 + 1.112520I
a = 0.513405 − 1.069200I
b = −0.660143 + 0.296254I
−1.43943 + 1.45452I 0
u = −0.054607 − 1.112520I
a = 0.513405 + 1.069200I
b = −0.660143 − 0.296254I
−1.43943 − 1.45452I 0
u = −0.882807
a = 2.61824
b = −3.54585
9.90045 −3.11330
u = −0.874751 + 0.019237I
a = −0.76012 + 2.37591I
b = 0.95744 − 2.48019I
7.97257 − 1.22260I 10.90582 − 1.45578I
u = −0.874751 − 0.019237I
a = −0.76012 − 2.37591I
b = 0.95744 + 2.48019I
7.97257 + 1.22260I 10.90582 + 1.45578I
u = 0.361283 + 0.751844I
a = −0.295918 + 0.495393I
b = 0.171946 − 0.640949I
3.46003 + 4.32392I 11.42298 − 6.33256I
u = 0.361283 − 0.751844I
a = −0.295918 − 0.495393I
b = 0.171946 + 0.640949I
3.46003 − 4.32392I 11.42298 + 6.33256I
u = −0.183088 + 1.165940I
a = −0.266992 − 0.369562I
b = −1.37755 + 1.07744I
1.26375 − 1.05598I 0
u = −0.183088 − 1.165940I
a = −0.266992 + 0.369562I
b = −1.37755 − 1.07744I
1.26375 + 1.05598I 0
u = 0.092580 + 1.209120I
a = 0.10678 − 1.57343I
b = −1.35466 + 0.92333I
−1.84582 + 1.52815I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.092580 − 1.209120I
a = 0.10678 + 1.57343I
b = −1.35466 − 0.92333I
−1.84582 − 1.52815I 0
u = 0.161416 + 1.229950I
a = 0.15681 + 2.49802I
b = 3.50115 − 1.48373I
−1.14368 + 2.23292I 0
u = 0.161416 − 1.229950I
a = 0.15681 − 2.49802I
b = 3.50115 + 1.48373I
−1.14368 − 2.23292I 0
u = −0.210827 + 1.234980I
a = −0.754554 + 0.782417I
b = −0.430198 + 0.502926I
0.54834 − 4.47323I 0
u = −0.210827 − 1.234980I
a = −0.754554 − 0.782417I
b = −0.430198 − 0.502926I
0.54834 + 4.47323I 0
u = 0.658448 + 0.323972I
a = 0.751995 + 0.291567I
b = 0.029394 − 0.146081I
4.80945 − 0.45159I 15.7916 + 0.4639I
u = 0.658448 − 0.323972I
a = 0.751995 − 0.291567I
b = 0.029394 + 0.146081I
4.80945 + 0.45159I 15.7916 − 0.4639I
u = 0.150237 + 1.273730I
a = 0.526714 + 0.048722I
b = −0.812204 − 0.549214I
−3.21431 + 2.39962I 0
u = 0.150237 − 1.273730I
a = 0.526714 − 0.048722I
b = −0.812204 + 0.549214I
−3.21431 − 2.39962I 0
u = −0.658985 + 0.265213I
a = −0.49122 + 1.57510I
b = −0.125247 − 0.445150I
5.38906 − 8.57192I 11.9706 + 8.1913I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.658985 − 0.265213I
a = −0.49122 − 1.57510I
b = −0.125247 + 0.445150I
5.38906 + 8.57192I 11.9706 − 8.1913I
u = 0.698912
a = −1.05888
b = 0.453650
1.62149 4.73710
u = −0.028016 + 1.301540I
a = 0.256976 + 0.051421I
b = 1.053210 − 0.861329I
−5.86592 + 1.11778I 0
u = −0.028016 − 1.301540I
a = 0.256976 − 0.051421I
b = 1.053210 + 0.861329I
−5.86592 − 1.11778I 0
u = 0.289500 + 1.270280I
a = 0.234588 − 0.583710I
b = −0.548186 + 0.321533I
−2.33279 + 3.56920I 0
u = 0.289500 − 1.270280I
a = 0.234588 + 0.583710I
b = −0.548186 − 0.321533I
−2.33279 − 3.56920I 0
u = −0.198314 + 1.296690I
a = −0.502123 + 0.738377I
b = 0.980901 − 0.670423I
−3.85925 − 6.47132I 0
u = −0.198314 − 1.296690I
a = −0.502123 − 0.738377I
b = 0.980901 + 0.670423I
−3.85925 + 6.47132I 0
u = −0.462815 + 1.228630I
a = 1.063350 − 0.751492I
b = 0.73021 + 1.61220I
9.44703 − 1.66736I 0
u = −0.462815 − 1.228630I
a = 1.063350 + 0.751492I
b = 0.73021 − 1.61220I
9.44703 + 1.66736I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.453502 + 1.234510I
a = −2.00885 − 0.56842I
b = −0.42347 + 2.73870I
10.05520 − 6.77668I 0
u = 0.453502 − 1.234510I
a = −2.00885 + 0.56842I
b = −0.42347 − 2.73870I
10.05520 + 6.77668I 0
u = 0.426332 + 1.253220I
a = 2.34854 + 0.48663I
b = 0.11887 − 3.15154I
4.48799 − 0.78739I 0
u = 0.426332 − 1.253220I
a = 2.34854 − 0.48663I
b = 0.11887 + 3.15154I
4.48799 + 0.78739I 0
u = −0.413163 + 1.260620I
a = −1.26088 + 1.13233I
b = −1.70921 − 1.82672I
4.12598 − 3.38895I 0
u = −0.413163 − 1.260620I
a = −1.26088 − 1.13233I
b = −1.70921 + 1.82672I
4.12598 + 3.38895I 0
u = 0.427750 + 1.273090I
a = 0.95805 + 1.80831I
b = 1.99298 − 2.44923I
8.59850 + 2.51088I 0
u = 0.427750 − 1.273090I
a = 0.95805 − 1.80831I
b = 1.99298 + 2.44923I
8.59850 − 2.51088I 0
u = −0.416478 + 1.278250I
a = −0.43242 − 1.68397I
b = 3.25434 − 1.51855I
5.93001 − 4.65047I 0
u = −0.416478 − 1.278250I
a = −0.43242 + 1.68397I
b = 3.25434 + 1.51855I
5.93001 + 4.65047I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.406803 + 1.291700I
a = 1.52766 − 0.20602I
b = −0.06857 + 2.76086I
3.89118 − 5.81428I 0
u = −0.406803 − 1.291700I
a = 1.52766 + 0.20602I
b = −0.06857 − 2.76086I
3.89118 + 5.81428I 0
u = 0.423725 + 1.287430I
a = −2.12946 + 0.38318I
b = 0.97652 + 2.37850I
8.49017 + 6.92911I 0
u = 0.423725 − 1.287430I
a = −2.12946 − 0.38318I
b = 0.97652 − 2.37850I
8.49017 − 6.92911I 0
u = 0.414262 + 1.301330I
a = −1.85647 − 1.47317I
b = −1.45440 + 3.42200I
4.12642 + 10.14420I 0
u = 0.414262 − 1.301330I
a = −1.85647 + 1.47317I
b = −1.45440 − 3.42200I
4.12642 − 10.14420I 0
u = −0.235156 + 1.346920I
a = 0.733057 − 0.616515I
b = −0.596383 + 0.773379I
0.32118 − 11.71550I 0
u = −0.235156 − 1.346920I
a = 0.733057 + 0.616515I
b = −0.596383 − 0.773379I
0.32118 + 11.71550I 0
u = 0.026010 + 1.380640I
a = 0.0205117 + 0.0989125I
b = −0.763915 + 0.702888I
−3.00730 + 4.91043I 0
u = 0.026010 − 1.380640I
a = 0.0205117 − 0.0989125I
b = −0.763915 − 0.702888I
−3.00730 − 4.91043I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.421371 + 1.322560I
a = 1.76986 + 1.12258I
b = 1.11872 − 3.28566I
9.3880 + 16.3776I 0
u = 0.421371 − 1.322560I
a = 1.76986 − 1.12258I
b = 1.11872 + 3.28566I
9.3880 − 16.3776I 0
u = −0.424789 + 1.329390I
a = −1.208660 + 0.425059I
b = −0.22264 − 1.99964I
8.68598 − 8.02392I 0
u = −0.424789 − 1.329390I
a = −1.208660 − 0.425059I
b = −0.22264 + 1.99964I
8.68598 + 8.02392I 0
u = 0.220478 + 1.386360I
a = −0.368808 + 0.007896I
b = 0.224428 − 0.133536I
−0.63581 + 2.62873I 0
u = 0.220478 − 1.386360I
a = −0.368808 − 0.007896I
b = 0.224428 + 0.133536I
−0.63581 − 2.62873I 0
u = −0.539636 + 0.187893I
a = 0.42741 − 1.76367I
b = −0.1137720 + 0.0518232I
0.70764 − 3.84105I 9.38498 + 8.87377I
u = −0.539636 − 0.187893I
a = 0.42741 + 1.76367I
b = −0.1137720 − 0.0518232I
0.70764 + 3.84105I 9.38498 − 8.87377I
u = −0.562693 + 0.059383I
a = 0.091377 − 1.045750I
b = 0.903662 − 0.072790I
4.44931 − 1.68114I 17.9349 + 4.6378I
u = −0.562693 − 0.059383I
a = 0.091377 + 1.045750I
b = 0.903662 + 0.072790I
4.44931 + 1.68114I 17.9349 − 4.6378I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.454776 + 0.112651I
a = −1.42735 − 0.78385I
b = 0.373505 + 0.219026I
0.990921 + 0.275354I 10.83194 − 1.70107I
u = 0.454776 − 0.112651I
a = −1.42735 + 0.78385I
b = 0.373505 − 0.219026I
0.990921 − 0.275354I 10.83194 + 1.70107I
u = 0.459569
a = 7.65144
b = −3.15496
2.54686 −58.3700
u = −0.057935 + 0.430382I
a = 0.260550 − 0.991074I
b = −0.548092 + 0.409420I
−0.85332 + 1.45234I 1.68280 − 2.85990I
u = −0.057935 − 0.430382I
a = 0.260550 + 0.991074I
b = −0.548092 − 0.409420I
−0.85332 − 1.45234I 1.68280 + 2.85990I
u = 0.161338 + 0.194044I
a = −4.36295 + 0.20562I
b = 0.428285 + 0.893678I
1.94471 + 0.63814I 4.71193 + 1.24447I
u = 0.161338 − 0.194044I
a = −4.36295 − 0.20562I
b = 0.428285 − 0.893678I
1.94471 − 0.63814I 4.71193 − 1.24447I
12
II. I
u
2
= hu
2
+ b + 1, −u
2
+ a − 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
8
=
0
u
a
11
=
1
0
a
12
=
1
−u
2
a
7
=
−u
u
2
− u + 1
a
1
=
u
2
+ 1
−u
2
+ u − 1
a
4
=
u
2
+ 2
−u
2
− 1
a
2
=
u
2
+ 1
−u
2
+ u − 1
a
9
=
1
0
a
6
=
−u
2
− 1
u
2
− u + 1
a
10
=
0
u
a
3
=
u
2
+ 2
−2u
2
+ u − 2
a
5
=
1
−u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 7u
2
− 5u + 17
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
3
c
2
(u + 1)
3
c
3
, c
4
u
3
− u − 1
c
5
(u − 1)
3
c
6
, c
8
, c
9
u
3
− u
2
+ 1
c
7
u
3
+ u
2
+ 2u + 1
c
10
u
3
+ u
2
− 1
c
11
, c
12
u
3
− u
2
+ 2u − 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
3
c
2
, c
5
(y −1)
3
c
3
, c
4
y
3
− 2y
2
+ y −1
c
6
, c
8
, c
9
c
10
y
3
− y
2
+ 2y −1
c
7
, c
11
, c
12
y
3
+ 3y
2
+ 2y −1
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = 0.337641 + 0.562280I
b = 0.662359 − 0.562280I
−1.37919 + 2.82812I 4.28809 − 2.59975I
u = 0.215080 − 1.307140I
a = 0.337641 − 0.562280I
b = 0.662359 + 0.562280I
−1.37919 − 2.82812I 4.28809 + 2.59975I
u = 0.569840
a = 2.32472
b = −1.32472
2.75839 16.4240
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
3
(u
77
− 13u
76
+ ··· + 20u + 8)
c
2
((u + 1)
3
)(u
77
+ 4u
76
+ ··· − 14u + 1)
c
3
(u
3
− u − 1)(u
77
+ u
76
+ ··· + 887410u + 302321)
c
4
(u
3
− u − 1)(u
77
+ 3u
76
+ ··· − 1548u + 181)
c
5
((u − 1)
3
)(u
77
+ 4u
76
+ ··· − 14u + 1)
c
6
, c
8
(u
3
− u
2
+ 1)(u
77
+ 2u
76
+ ··· − 147u + 17)
c
7
(u
3
+ u
2
+ 2u + 1)(u
77
− 2u
76
+ ··· − 7u + 1)
c
9
(u
3
− u
2
+ 1)(u
77
− 2u
76
+ ··· − u + 1)
c
10
(u
3
+ u
2
− 1)(u
77
+ 2u
76
+ ··· − 147u + 17)
c
11
, c
12
(u
3
− u
2
+ 2u − 1)(u
77
− 2u
76
+ ··· − 7u + 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
3
(y
77
+ 21y
76
+ ··· − 432y −64)
c
2
, c
5
((y −1)
3
)(y
77
− 62y
76
+ ··· + 26y −1)
c
3
(y
3
− 2y
2
+ y −1)
· (y
77
− 33y
76
+ ··· − 1941705110116y −91397987041)
c
4
(y
3
− 2y
2
+ y −1)(y
77
− 101y
76
+ ··· + 3284652y −32761)
c
6
, c
8
, c
10
(y
3
− y
2
+ 2y −1)(y
77
− 84y
76
+ ··· − 4639y −289)
c
7
, c
11
, c
12
(y
3
+ 3y
2
+ 2y −1)(y
77
+ 60y
76
+ ··· + y −1)
c
9
(y
3
− y
2
+ 2y −1)(y
77
+ 12y
76
+ ··· + y −1)
18
