12a
0152
(K12a
0152
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 12 11 4 1 8 7 6
Solving Sequence
7,11 4,8
9 12 3 6 1 10 5 2
c
7
c
8
c
11
c
3
c
6
c
12
c
10
c
5
c
2
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h2u
59
+ 3u
58
+ ··· + b − 1, u
60
+ 39u
58
+ ··· + a + 1, u
61
+ 2u
60
+ ··· − u − 1i
I
u
2
= h−u
3
+ u
2
+ b − 2u + 1, u
4
+ 3u
2
+ a + 1, u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1i
* 2 irreducible components of dim
C
= 0, with total 66 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
= h2u
59
+3u
58
+· · ·+b−1, u
60
+39u
58
+· · ·+a+1, u
61
+2u
60
+· · ·−u−1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−u
60
− 39u
58
+ ··· − u
2
− 1
−2u
59
− 3u
58
+ ··· + 2u + 1
a
8
=
1
u
2
a
9
=
u
9
+ 6u
7
+ 11u
5
+ 6u
3
+ u
−u
9
− 5u
7
− 7u
5
− 2u
3
+ u
a
12
=
−u
u
a
3
=
−u
60
− 2u
59
+ ··· − 3u
3
− u
2
−u
58
− 2u
57
+ ··· + u + 1
a
6
=
u
2
+ 1
−u
2
a
1
=
−u
3
− 2u
u
3
+ u
a
10
=
u
u
3
+ u
a
5
=
−u
6
− 3u
4
+ 1
−u
8
− 4u
6
− 4u
4
− 2u
2
a
2
=
−u
60
− u
59
+ ··· + 2u
3
− 2u
2
−u
59
− 2u
58
+ ··· + 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = u
60
+ 2u
59
+ ··· − 13u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
61
+ 28u
60
+ ··· + 25u + 1
c
2
, c
4
u
61
− 6u
60
+ ··· + u + 1
c
3
, c
8
u
61
− u
60
+ ··· + 32u + 32
c
5
u
61
− 2u
60
+ ··· + 3487u + 389
c
6
, c
7
, c
10
c
11
, c
12
u
61
− 2u
60
+ ··· − u + 1
c
9
u
61
+ 8u
60
+ ··· + 6443u + 1751
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
61
+ 16y
60
+ ··· + 1049y −1
c
2
, c
4
y
61
− 28y
60
+ ··· + 25y −1
c
3
, c
8
y
61
+ 33y
60
+ ··· − 9728y −1024
c
5
y
61
+ 16y
60
+ ··· + 1506015y −151321
c
6
, c
7
, c
10
c
11
, c
12
y
61
+ 80y
60
+ ··· + 7y −1
c
9
y
61
+ 28y
60
+ ··· − 9774541y −3066001
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.254354 + 0.981103I
a = −1.25198 − 2.54671I
b = 0.07492 + 2.00861I
1.22942 + 3.29969I 0
u = −0.254354 − 0.981103I
a = −1.25198 + 2.54671I
b = 0.07492 − 2.00861I
1.22942 − 3.29969I 0
u = 0.211321 + 1.001770I
a = −0.322034 − 0.875785I
b = −0.289419 + 0.657547I
3.12919 − 1.33617I 0
u = 0.211321 − 1.001770I
a = −0.322034 + 0.875785I
b = −0.289419 − 0.657547I
3.12919 + 1.33617I 0
u = 0.281128 + 0.997371I
a = 0.582713 + 0.789402I
b = 0.070322 − 0.761861I
2.34136 − 5.73880I 0
u = 0.281128 − 0.997371I
a = 0.582713 − 0.789402I
b = 0.070322 + 0.761861I
2.34136 + 5.73880I 0
u = −0.328410 + 1.012920I
a = −1.51065 − 2.03863I
b = 0.68097 + 1.62757I
5.15125 + 11.89640I 0
u = −0.328410 − 1.012920I
a = −1.51065 + 2.03863I
b = 0.68097 − 1.62757I
5.15125 − 11.89640I 0
u = −0.302074 + 1.025430I
a = 1.38727 + 2.07338I
b = −0.49004 − 1.57864I
7.28412 + 6.15559I 0
u = −0.302074 − 1.025430I
a = 1.38727 − 2.07338I
b = −0.49004 + 1.57864I
7.28412 − 6.15559I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.316983 + 0.866277I
a = 0.824553 + 0.132321I
b = −0.397869 − 0.455885I
1.00389 − 1.16184I 0
u = 0.316983 − 0.866277I
a = 0.824553 − 0.132321I
b = −0.397869 + 0.455885I
1.00389 + 1.16184I 0
u = −0.207432 + 1.073920I
a = 0.85102 + 1.88063I
b = 0.092713 − 1.158660I
8.38349 + 1.96602I 0
u = −0.207432 − 1.073920I
a = 0.85102 − 1.88063I
b = 0.092713 + 1.158660I
8.38349 − 1.96602I 0
u = −0.156803 + 1.097010I
a = −0.65117 − 1.69342I
b = −0.278390 + 0.945645I
7.08755 − 3.73090I 0
u = −0.156803 − 1.097010I
a = −0.65117 + 1.69342I
b = −0.278390 − 0.945645I
7.08755 + 3.73090I 0
u = 0.148119 + 0.845043I
a = 0.414383 − 0.713810I
b = −0.575491 + 0.156747I
1.88176 − 1.60682I −5.29446 + 5.04055I
u = 0.148119 − 0.845043I
a = 0.414383 + 0.713810I
b = −0.575491 − 0.156747I
1.88176 + 1.60682I −5.29446 − 5.04055I
u = 0.325121 + 0.738493I
a = −1.089280 + 0.346297I
b = 0.705617 + 0.283188I
0.29625 − 4.76842I −9.08610 + 8.21702I
u = 0.325121 − 0.738493I
a = −1.089280 − 0.346297I
b = 0.705617 − 0.283188I
0.29625 + 4.76842I −9.08610 − 8.21702I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.092397 + 0.693687I
a = −1.029970 + 0.913793I
b = 1.174630 + 0.233112I
−0.987120 + 0.988516I −11.84015 − 0.12287I
u = −0.092397 − 0.693687I
a = −1.029970 − 0.913793I
b = 1.174630 − 0.233112I
−0.987120 − 0.988516I −11.84015 + 0.12287I
u = −0.429667 + 0.466787I
a = 0.300862 − 0.006110I
b = 0.537163 + 1.081280I
2.11665 − 5.58640I −9.13002 + 1.98520I
u = −0.429667 − 0.466787I
a = 0.300862 + 0.006110I
b = 0.537163 − 1.081280I
2.11665 + 5.58640I −9.13002 − 1.98520I
u = −0.556702 + 0.224542I
a = 2.03671 + 0.31639I
b = −0.005895 + 0.791176I
1.32668 + 8.88717I −11.5386 − 8.5026I
u = −0.556702 − 0.224542I
a = 2.03671 − 0.31639I
b = −0.005895 − 0.791176I
1.32668 − 8.88717I −11.5386 + 8.5026I
u = −0.437350 + 0.391378I
a = −0.666219 − 0.260171I
b = −0.393377 − 0.987812I
3.80352 − 0.17614I −6.56300 − 3.19514I
u = −0.437350 − 0.391378I
a = −0.666219 + 0.260171I
b = −0.393377 + 0.987812I
3.80352 + 0.17614I −6.56300 + 3.19514I
u = −0.523029 + 0.253421I
a = −1.74252 − 0.41441I
b = −0.088899 − 0.841462I
3.32476 + 3.34552I −8.30796 − 4.53572I
u = −0.523029 − 0.253421I
a = −1.74252 + 0.41441I
b = −0.088899 + 0.841462I
3.32476 − 3.34552I −8.30796 + 4.53572I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.544484 + 0.051126I
a = 0.271290 − 1.260450I
b = −0.152520 + 0.534984I
−1.77296 + 1.77637I −13.44810 − 3.42636I
u = 0.544484 − 0.051126I
a = 0.271290 + 1.260450I
b = −0.152520 − 0.534984I
−1.77296 − 1.77637I −13.44810 + 3.42636I
u = 0.479319 + 0.211089I
a = 0.97175 − 1.13377I
b = −0.539313 + 0.342045I
−1.38873 − 3.13575I −13.6527 + 6.6645I
u = 0.479319 − 0.211089I
a = 0.97175 + 1.13377I
b = −0.539313 − 0.342045I
−1.38873 + 3.13575I −13.6527 − 6.6645I
u = −0.425241 + 0.171006I
a = 1.80164 + 1.52641I
b = 0.240942 + 0.694488I
−2.33602 + 0.95454I −12.3987 − 7.0289I
u = −0.425241 − 0.171006I
a = 1.80164 − 1.52641I
b = 0.240942 − 0.694488I
−2.33602 − 0.95454I −12.3987 + 7.0289I
u = 0.307712 + 0.317136I
a = −1.21859 + 0.96164I
b = 0.621069 − 0.032600I
−0.798120 + 0.509659I −11.36907 + 1.74616I
u = 0.307712 − 0.317136I
a = −1.21859 − 0.96164I
b = 0.621069 + 0.032600I
−0.798120 − 0.509659I −11.36907 − 1.74616I
u = 0.04390 + 1.64371I
a = 0.471528 − 0.589481I
b = −1.69900 + 0.69117I
8.54157 − 5.92897I 0
u = 0.04390 − 1.64371I
a = 0.471528 + 0.589481I
b = −1.69900 − 0.69117I
8.54157 + 5.92897I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00808 + 1.66823I
a = 0.636613 − 0.961433I
b = −2.50286 + 1.98917I
7.54962 + 1.22321I 0
u = −0.00808 − 1.66823I
a = 0.636613 + 0.961433I
b = −2.50286 − 1.98917I
7.54962 − 1.22321I 0
u = 0.07133 + 1.68137I
a = −0.481555 + 0.218553I
b = 1.133360 + 0.000284I
9.95685 − 2.59158I 0
u = 0.07133 − 1.68137I
a = −0.481555 − 0.218553I
b = 1.133360 − 0.000284I
9.95685 + 2.59158I 0
u = 0.02693 + 1.68333I
a = −0.182151 + 0.761285I
b = 1.04861 − 1.56495I
10.86580 − 2.21377I 0
u = 0.02693 − 1.68333I
a = −0.182151 − 0.761285I
b = 1.04861 + 1.56495I
10.86580 + 2.21377I 0
u = 0.316056
a = −1.09435
b = 0.309110
−0.608532 −16.3260
u = −0.06576 + 1.71571I
a = 0.82473 + 2.57511I
b = −2.07010 − 6.76803I
10.82330 + 4.58248I 0
u = −0.06576 − 1.71571I
a = 0.82473 − 2.57511I
b = −2.07010 + 6.76803I
10.82330 − 4.58248I 0
u = 0.07278 + 1.71903I
a = −0.769346 − 0.337131I
b = 1.25059 + 1.17834I
11.99390 − 7.16364I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.07278 − 1.71903I
a = −0.769346 + 0.337131I
b = 1.25059 − 1.17834I
11.99390 + 7.16364I 0
u = 0.05627 + 1.72019I
a = 0.607773 + 0.556302I
b = −0.85094 − 1.51707I
12.83490 − 2.42911I 0
u = 0.05627 − 1.72019I
a = 0.607773 − 0.556302I
b = −0.85094 + 1.51707I
12.83490 + 2.42911I 0
u = −0.08659 + 1.72253I
a = 0.88576 + 2.17643I
b = −2.64835 − 5.43557I
14.8480 + 13.5808I 0
u = −0.08659 − 1.72253I
a = 0.88576 − 2.17643I
b = −2.64835 + 5.43557I
14.8480 − 13.5808I 0
u = −0.07895 + 1.72628I
a = −0.83698 − 2.26090I
b = 2.34895 + 5.64277I
17.0651 + 7.7083I 0
u = −0.07895 − 1.72628I
a = −0.83698 + 2.26090I
b = 2.34895 − 5.64277I
17.0651 − 7.7083I 0
u = −0.05183 + 1.73689I
a = −0.57601 − 2.21329I
b = 1.15538 + 5.39428I
18.4431 + 3.0304I 0
u = −0.05183 − 1.73689I
a = −0.57601 + 2.21329I
b = 1.15538 − 5.39428I
18.4431 − 3.0304I 0
u = −0.03876 + 1.73935I
a = 0.50704 + 2.06226I
b = −0.80734 − 4.96112I
17.2479 − 2.9269I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.03876 − 1.73935I
a = 0.50704 − 2.06226I
b = −0.80734 + 4.96112I
17.2479 + 2.9269I 0
11
II.
I
u
2
= h−u
3
+ u
2
+ b − 2u + 1, u
4
+ 3u
2
+ a + 1, u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−u
4
− 3u
2
− 1
u
3
− u
2
+ 2u − 1
a
8
=
1
u
2
a
9
=
1
u
2
a
12
=
−u
u
a
3
=
−u
4
− 3u
2
− 1
u
3
− u
2
+ 2u − 1
a
6
=
u
2
+ 1
−u
2
a
1
=
−u
3
− 2u
u
3
+ u
a
10
=
u
u
3
+ u
a
5
=
u
3
+ 2u
−u
3
− u
a
2
=
−u
4
− u
3
− 3u
2
− 2u − 1
2u
3
− u
2
+ 3u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −3u
4
+ 3u
3
− 12u
2
+ 10u − 19
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
8
u
5
c
4
(u + 1)
5
c
5
, c
9
u
5
− u
4
+ u
2
+ u − 1
c
6
, c
7
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
10
, c
11
, c
12
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
5
c
3
, c
8
y
5
c
5
, c
9
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1
c
6
, c
7
, c
10
c
11
, c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.233677 + 0.885557I
a = 0.827780 − 0.637683I
b = −0.340036 + 0.807849I
0.17487 − 2.21397I −10.60206 + 4.05273I
u = 0.233677 − 0.885557I
a = 0.827780 + 0.637683I
b = −0.340036 − 0.807849I
0.17487 + 2.21397I −10.60206 − 4.05273I
u = 0.416284
a = −1.54991
b = −0.268586
−2.52712 −16.7900
u = 0.05818 + 1.69128I
a = −0.552827 + 0.534136I
b = 1.47433 − 1.63485I
9.31336 − 3.33174I −10.00277 + 3.46299I
u = 0.05818 − 1.69128I
a = −0.552827 − 0.534136I
b = 1.47433 + 1.63485I
9.31336 + 3.33174I −10.00277 − 3.46299I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
61
+ 28u
60
+ ··· + 25u + 1)
c
2
((u − 1)
5
)(u
61
− 6u
60
+ ··· + u + 1)
c
3
, c
8
u
5
(u
61
− u
60
+ ··· + 32u + 32)
c
4
((u + 1)
5
)(u
61
− 6u
60
+ ··· + u + 1)
c
5
(u
5
− u
4
+ u
2
+ u − 1)(u
61
− 2u
60
+ ··· + 3487u + 389)
c
6
, c
7
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
61
− 2u
60
+ ··· − u + 1)
c
9
(u
5
− u
4
+ u
2
+ u − 1)(u
61
+ 8u
60
+ ··· + 6443u + 1751)
c
10
, c
11
, c
12
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
61
− 2u
60
+ ··· − u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
5
)(y
61
+ 16y
60
+ ··· + 1049y −1)
c
2
, c
4
((y −1)
5
)(y
61
− 28y
60
+ ··· + 25y −1)
c
3
, c
8
y
5
(y
61
+ 33y
60
+ ··· − 9728y −1024)
c
5
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
· (y
61
+ 16y
60
+ ··· + 1506015y −151321)
c
6
, c
7
, c
10
c
11
, c
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y −1)(y
61
+ 80y
60
+ ··· + 7y −1)
c
9
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y −1)
· (y
61
+ 28y
60
+ ··· − 9774541y −3066001)
17
