12n
0647
(K12n
0647
)
A knot diagram
1
Linearized knot diagam
3 8 11 9 1 10 2 6 3 6 9 5
Solving Sequence
3,9 6,10
11 4 8 2 1 5 7 12
c
9
c
10
c
3
c
8
c
2
c
1
c
5
c
7
c
12
c
4
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.15739 × 10
38
u
21
+ 2.59794 × 10
38
u
20
+ ··· + 5.63971 × 10
39
b + 2.94029 × 10
39
,
1.52370 × 10
39
u
21
− 3.15147 × 10
38
u
20
+ ··· + 5.63971 × 10
39
a + 6.37897 × 10
40
, u
22
− u
21
+ ··· − 7u + 1i
I
u
2
= h2u
10
− 2u
9
+ 3u
8
− 5u
7
− u
6
− 3u
5
− 5u
4
+ 8u
3
− 6u
2
+ b + 8u − 1,
u
10
− u
9
− u
7
− u
6
+ u
5
− 2u
4
+ 3u
3
+ a − u + 2, u
11
− u
8
− 3u
7
− u
6
− 3u
5
+ 2u
4
+ 2u
3
+ 3u − 1i
* 2 irreducible components of dim
C
= 0, with total 33 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−1.16×10
38
u
21
+2.60×10
38
u
20
+· · ·+5.64×10
39
b+2.94×10
39
, 1.52×
10
39
u
21
−3.15×10
38
u
20
+· · ·+5.64×10
39
a+6.38×10
40
, u
22
−u
21
+· · ·−7u+1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
6
=
−0.270174u
21
+ 0.0558800u
20
+ ··· + 42.5373u − 11.3108
0.0205221u
21
− 0.0460651u
20
+ ··· + 6.82322u − 0.521354
a
10
=
1
u
2
a
11
=
−1.35047u
21
+ 1.35347u
20
+ ··· − 117.421u + 7.69784
−0.209846u
21
+ 0.147595u
20
+ ··· − 6.54594u + 0.116749
a
4
=
2.15834u
21
− 2.04296u
20
+ ··· + 162.698u − 7.98991
0.318765u
21
− 0.225148u
20
+ ··· + 8.95792u − 0.0968802
a
8
=
1.18213u
21
− 1.17546u
20
+ ··· + 97.8267u − 4.07571
0.214154u
21
− 0.137619u
20
+ ··· + 5.41053u − 0.123423
a
2
=
−1.66406u
21
+ 1.47272u
20
+ ··· − 96.5661u − 0.246377
−0.256597u
21
+ 0.176966u
20
+ ··· − 3.09765u + 0.0237528
a
1
=
−1.66406u
21
+ 1.47272u
20
+ ··· − 96.5661u − 0.246377
−0.227217u
21
+ 0.158707u
20
+ ··· − 3.42237u − 0.167580
a
5
=
1.83958u
21
− 1.81781u
20
+ ··· + 153.740u − 7.89303
0.318765u
21
− 0.225148u
20
+ ··· + 8.95792u − 0.0968802
a
7
=
−0.297455u
21
+ 0.112963u
20
+ ··· + 34.4842u − 10.5752
0.0338753u
21
− 0.0534463u
20
+ ··· + 7.05911u − 0.551156
a
12
=
1.14063u
21
− 1.20587u
20
+ ··· + 110.875u − 7.58109
0.209846u
21
− 0.147595u
20
+ ··· + 6.54594u − 0.116749
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.01325u
21
+ 1.04755u
20
+ ··· − 80.2731u − 9.63814
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
22
+ 9u
21
+ ··· + 637u + 49
c
2
, c
7
u
22
+ u
21
+ ··· − 35u − 7
c
3
, c
5
, c
12
u
22
+ 2u
21
+ ··· − u + 1
c
4
u
22
+ 2u
21
+ ··· − 5u + 1
c
6
, c
10
u
22
+ 2u
21
+ ··· − 66u − 19
c
8
u
22
− 3u
21
+ ··· + 85u + 23
c
9
u
22
− u
21
+ ··· − 7u + 1
c
11
u
22
− 6u
21
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 19y
21
+ ··· − 134113y + 2401
c
2
, c
7
y
22
− 9y
21
+ ··· − 637y + 49
c
3
, c
5
, c
12
y
22
− 20y
21
+ ··· − 85y + 1
c
4
y
22
− 40y
21
+ ··· − 25y + 1
c
6
, c
10
y
22
+ 24y
21
+ ··· − 4660y + 361
c
8
y
22
+ 29y
21
+ ··· − 9065y + 529
c
9
y
22
+ 39y
21
+ ··· + 117y + 1
c
11
y
22
− 52y
21
+ ··· − 36y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.922193 + 0.451969I
a = −0.140167 + 0.079897I
b = −1.135600 + 0.625368I
−3.68279 − 0.94185I −15.4912 + 3.1680I
u = 0.922193 − 0.451969I
a = −0.140167 − 0.079897I
b = −1.135600 − 0.625368I
−3.68279 + 0.94185I −15.4912 − 3.1680I
u = −0.918387 + 0.590013I
a = 0.823390 + 0.318747I
b = 0.795349 + 0.331962I
−0.88400 − 1.53763I −11.84759 + 1.75542I
u = −0.918387 − 0.590013I
a = 0.823390 − 0.318747I
b = 0.795349 − 0.331962I
−0.88400 + 1.53763I −11.84759 − 1.75542I
u = −0.015535 + 1.113510I
a = 0.50175 + 1.35452I
b = −0.093079 − 0.699578I
−1.24345 − 2.09162I −12.32634 + 3.76479I
u = −0.015535 − 1.113510I
a = 0.50175 − 1.35452I
b = −0.093079 + 0.699578I
−1.24345 + 2.09162I −12.32634 − 3.76479I
u = 1.14626
a = −0.626888
b = 0.600846
−7.73402 −2.06680
u = 0.40719 + 1.44071I
a = 0.364074 − 0.930543I
b = −0.38730 + 1.37848I
1.70191 + 1.70598I −14.8255 − 1.4132I
u = 0.40719 − 1.44071I
a = 0.364074 + 0.930543I
b = −0.38730 − 1.37848I
1.70191 − 1.70598I −14.8255 + 1.4132I
u = 0.317847 + 0.269046I
a = 2.62385 − 0.79046I
b = −0.085195 + 0.903480I
1.56638 + 2.34323I −10.66731 − 5.68174I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.317847 − 0.269046I
a = 2.62385 + 0.79046I
b = −0.085195 − 0.903480I
1.56638 − 2.34323I −10.66731 + 5.68174I
u = 0.403521
a = 2.31915
b = 1.67477
−13.6204 −17.7340
u = −0.352636
a = 0.655926
b = −0.220728
−0.550682 −18.1690
u = −1.87169
a = −0.326736
b = −0.803005
−14.8041 −12.3900
u = 0.0195375 + 0.1177480I
a = −10.81320 + 5.82406I
b = −0.225273 + 0.760617I
−3.29787 + 5.70936I −15.2173 − 7.8009I
u = 0.0195375 − 0.1177480I
a = −10.81320 − 5.82406I
b = −0.225273 − 0.760617I
−3.29787 − 5.70936I −15.2173 + 7.8009I
u = 0.78622 + 2.42733I
a = 0.107388 − 0.674968I
b = 0.95174 + 2.08123I
5.54115 − 10.77480I 0
u = 0.78622 − 2.42733I
a = 0.107388 + 0.674968I
b = 0.95174 − 2.08123I
5.54115 + 10.77480I 0
u = −0.24073 + 2.68361I
a = −0.036423 − 0.623368I
b = 0.27638 + 2.41167I
8.25134 + 2.56104I 0
u = −0.24073 − 2.68361I
a = −0.036423 + 0.623368I
b = 0.27638 − 2.41167I
8.25134 − 2.56104I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.44105 + 2.79932I
a = 0.058592 + 0.603776I
b = 0.77704 − 2.39189I
11.22440 + 4.41241I 0
u = −0.44105 − 2.79932I
a = 0.058592 − 0.603776I
b = 0.77704 + 2.39189I
11.22440 − 4.41241I 0
7
II. I
u
2
= h2u
10
− 2u
9
+ · · · + b − 1, u
10
− u
9
− u
7
− u
6
+ u
5
− 2u
4
+ 3u
3
+ a −
u + 2, u
11
− u
8
− 3u
7
− u
6
− 3u
5
+ 2u
4
+ 2u
3
+ 3u − 1i
(i) Arc colorings
a
3
=
0
u
a
9
=
1
0
a
6
=
−u
10
+ u
9
+ u
7
+ u
6
− u
5
+ 2u
4
− 3u
3
+ u − 2
−2u
10
+ 2u
9
− 3u
8
+ 5u
7
+ u
6
+ 3u
5
+ 5u
4
− 8u
3
+ 6u
2
− 8u + 1
a
10
=
1
u
2
a
11
=
2u
10
− u
9
+ u
8
− 3u
7
− 3u
6
− 2u
5
− 5u
4
+ 5u
3
− u
2
+ 2u + 2
u
2
+ 1
a
4
=
u
10
− 2u
9
+ 3u
8
− 4u
7
+ 2u
6
− 2u
5
− 2u
4
+ 6u
3
− 8u
2
+ 8u − 4
2u
10
− 3u
9
+ 3u
8
− 6u
7
+ u
6
− u
5
− 3u
4
+ 11u
3
− 7u
2
+ 9u − 3
a
8
=
−2u
10
+ 2u
9
− 2u
8
+ 4u
7
+ u
6
+ u
5
+ 5u
4
− 7u
3
+ 5u
2
− 4u
−2u
10
+ 2u
9
− 3u
8
+ 5u
7
+ u
6
+ 3u
5
+ 5u
4
− 8u
3
+ 5u
2
− 8u + 1
a
2
=
u
10
− 2u
9
+ 2u
8
− 3u
7
+ u
6
− 2u
4
+ 7u
3
− 5u
2
+ 5u − 1
−2u
10
+ 3u
9
− 3u
8
+ 5u
7
− u
6
+ u
5
+ 4u
4
− 10u
3
+ 8u
2
− 6u + 2
a
1
=
u
10
− 2u
9
+ 2u
8
− 3u
7
+ u
6
− 2u
4
+ 7u
3
− 5u
2
+ 5u − 1
−4u
10
+ 5u
9
− 5u
8
+ 10u
7
+ 2u
5
+ 7u
4
− 19u
3
+ 12u
2
− 13u + 4
a
5
=
−u
10
+ u
9
+ 2u
7
+ u
6
− u
5
+ u
4
− 5u
3
− u
2
− u − 1
2u
10
− 3u
9
+ 3u
8
− 6u
7
+ u
6
− u
5
− 3u
4
+ 11u
3
− 7u
2
+ 9u − 3
a
7
=
u
10
− u
9
+ 2u
8
− 3u
7
− 2u
5
− 3u
4
+ 4u
3
− 5u
2
+ 5u − 2
−1
a
12
=
2u
10
− u
9
+ u
8
− 3u
7
− 3u
6
− 2u
5
− 5u
4
+ 5u
3
− 2u
2
+ 2u + 1
u
2
+ 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 18u
10
− 18u
9
+ 22u
8
− 45u
7
− 8u
6
− 17u
5
− 37u
4
+ 76u
3
− 49u
2
+ 62u − 28
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
11
− 12u
10
+ ··· + 19u − 1
c
2
u
11
− 6u
9
+ u
8
+ 14u
7
− 4u
6
− 17u
5
+ 6u
4
+ 11u
3
− 5u
2
− 3u + 1
c
3
, c
5
u
11
− u
10
− 7u
9
+ 6u
8
+ 18u
7
− 12u
6
− 20u
5
+ 8u
4
+ 7u
3
+ u
2
+ u − 1
c
4
u
11
+ u
10
+ ··· + 7u − 1
c
6
u
11
+ u
10
− u
9
+ 2u
8
− 2u
6
+ 3u
5
− 3u
4
+ u
2
− 2u + 1
c
7
u
11
− 6u
9
− u
8
+ 14u
7
+ 4u
6
− 17u
5
− 6u
4
+ 11u
3
+ 5u
2
− 3u − 1
c
8
u
11
+ 2u
10
+ u
9
− 3u
7
− 3u
6
− 2u
5
+ 2u
3
+ u
2
+ u − 1
c
9
u
11
− u
8
− 3u
7
− u
6
− 3u
5
+ 2u
4
+ 2u
3
+ 3u − 1
c
10
u
11
− u
10
− u
9
− 2u
8
+ 2u
6
+ 3u
5
+ 3u
4
− u
2
− 2u − 1
c
11
u
11
+ 11u
10
+ ··· + 6u + 1
c
12
u
11
+ u
10
− 7u
9
− 6u
8
+ 18u
7
+ 12u
6
− 20u
5
− 8u
4
+ 7u
3
− u
2
+ u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
11
− 16y
10
+ ··· + 155y − 1
c
2
, c
7
y
11
− 12y
10
+ ··· + 19y − 1
c
3
, c
5
, c
12
y
11
− 15y
10
+ ··· + 3y − 1
c
4
y
11
− 31y
10
+ ··· + 15y − 1
c
6
, c
10
y
11
− 3y
10
− 3y
9
+ 6y
8
+ 8y
7
+ 2y
6
− 5y
5
− 9y
4
− 2y
3
+ 5y
2
+ 2y − 1
c
8
y
11
− 2y
10
− 5y
9
+ 2y
8
+ 9y
7
+ 5y
6
− 2y
5
− 8y
4
− 6y
3
+ 3y
2
+ 3y − 1
c
9
y
11
− 6y
9
− 7y
8
+ 11y
7
+ 27y
6
+ y
5
− 36y
4
− 16y
3
+ 16y
2
+ 9y − 1
c
11
y
11
− 23y
10
+ ··· − 10y − 1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.946698
a = −1.31867
b = 0.570624
−10.8918 −14.2030
u = 0.107517 + 0.921326I
a = −0.41829 + 1.75925I
b = −0.627508 − 0.776878I
−1.39916 + 0.85773I −12.76968 + 1.45970I
u = 0.107517 − 0.921326I
a = −0.41829 − 1.75925I
b = −0.627508 + 0.776878I
−1.39916 − 0.85773I −12.76968 − 1.45970I
u = −1.13392
a = −0.477082
b = 0.739267
−8.01807 −30.7780
u = −1.14734
a = −0.896870
b = −1.75156
−12.5057 −9.97480
u = 0.206612 + 1.130010I
a = 0.53803 − 1.36462I
b = −0.270708 + 1.018240I
2.65235 + 1.78346I −4.71612 − 3.09744I
u = 0.206612 − 1.130010I
a = 0.53803 + 1.36462I
b = −0.270708 − 1.018240I
2.65235 − 1.78346I −4.71612 + 3.09744I
u = −0.562339 + 1.094490I
a = 1.066280 + 0.765572I
b = 0.113141 − 1.003800I
−2.63212 − 4.42190I −12.78415 + 2.93693I
u = −0.562339 − 1.094490I
a = 1.066280 − 0.765572I
b = 0.113141 + 1.003800I
−2.63212 + 4.42190I −12.78415 − 2.93693I
u = 1.52035
a = 0.0829538
b = 1.10046
−15.4881 −24.9010
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.310641
a = −1.76236
b = −1.08864
−2.97640 −11.6020
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
11
− 12u
10
+ ··· + 19u − 1)(u
22
+ 9u
21
+ ··· + 637u + 49)
c
2
(u
11
− 6u
9
+ u
8
+ 14u
7
− 4u
6
− 17u
5
+ 6u
4
+ 11u
3
− 5u
2
− 3u + 1)
· (u
22
+ u
21
+ ··· − 35u − 7)
c
3
, c
5
(u
11
− u
10
− 7u
9
+ 6u
8
+ 18u
7
− 12u
6
− 20u
5
+ 8u
4
+ 7u
3
+ u
2
+ u − 1)
· (u
22
+ 2u
21
+ ··· − u + 1)
c
4
(u
11
+ u
10
+ ··· + 7u − 1)(u
22
+ 2u
21
+ ··· − 5u + 1)
c
6
(u
11
+ u
10
− u
9
+ 2u
8
− 2u
6
+ 3u
5
− 3u
4
+ u
2
− 2u + 1)
· (u
22
+ 2u
21
+ ··· − 66u − 19)
c
7
(u
11
− 6u
9
− u
8
+ 14u
7
+ 4u
6
− 17u
5
− 6u
4
+ 11u
3
+ 5u
2
− 3u − 1)
· (u
22
+ u
21
+ ··· − 35u − 7)
c
8
(u
11
+ 2u
10
+ u
9
− 3u
7
− 3u
6
− 2u
5
+ 2u
3
+ u
2
+ u − 1)
· (u
22
− 3u
21
+ ··· + 85u + 23)
c
9
(u
11
− u
8
+ ··· + 3u − 1)(u
22
− u
21
+ ··· − 7u + 1)
c
10
(u
11
− u
10
− u
9
− 2u
8
+ 2u
6
+ 3u
5
+ 3u
4
− u
2
− 2u − 1)
· (u
22
+ 2u
21
+ ··· − 66u − 19)
c
11
(u
11
+ 11u
10
+ ··· + 6u + 1)(u
22
− 6u
21
+ ··· − 2u + 1)
c
12
(u
11
+ u
10
− 7u
9
− 6u
8
+ 18u
7
+ 12u
6
− 20u
5
− 8u
4
+ 7u
3
− u
2
+ u + 1)
· (u
22
+ 2u
21
+ ··· − u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
11
− 16y
10
+ ··· + 155y − 1)(y
22
+ 19y
21
+ ··· − 134113y + 2401)
c
2
, c
7
(y
11
− 12y
10
+ ··· + 19y − 1)(y
22
− 9y
21
+ ··· − 637y + 49)
c
3
, c
5
, c
12
(y
11
− 15y
10
+ ··· + 3y − 1)(y
22
− 20y
21
+ ··· − 85y + 1)
c
4
(y
11
− 31y
10
+ ··· + 15y − 1)(y
22
− 40y
21
+ ··· − 25y + 1)
c
6
, c
10
(y
11
− 3y
10
− 3y
9
+ 6y
8
+ 8y
7
+ 2y
6
− 5y
5
− 9y
4
− 2y
3
+ 5y
2
+ 2y − 1)
· (y
22
+ 24y
21
+ ··· − 4660y + 361)
c
8
(y
11
− 2y
10
− 5y
9
+ 2y
8
+ 9y
7
+ 5y
6
− 2y
5
− 8y
4
− 6y
3
+ 3y
2
+ 3y − 1)
· (y
22
+ 29y
21
+ ··· − 9065y + 529)
c
9
(y
11
− 6y
9
− 7y
8
+ 11y
7
+ 27y
6
+ y
5
− 36y
4
− 16y
3
+ 16y
2
+ 9y − 1)
· (y
22
+ 39y
21
+ ··· + 117y + 1)
c
11
(y
11
− 23y
10
+ ··· − 10y − 1)(y
22
− 52y
21
+ ··· − 36y + 1)
14
