12a
0640
(K12a
0640
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 8 2 6 5 12 1 9 4
Solving Sequence
2,7 3,10
4 1 11 6 8 5 12 9
c
2
c
3
c
1
c
10
c
6
c
7
c
5
c
12
c
9
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.25642 × 10
19
u
64
− 2.04945 × 10
19
u
63
+ ··· + 2.31572 × 10
19
b − 3.37503 × 10
19
,
3.33691 × 10
20
u
64
+ 8.52592 × 10
20
u
63
+ ··· + 1.62101 × 10
20
a + 6.63020 × 10
20
, u
65
+ 2u
64
+ ··· − 3u − 1i
I
u
2
= hb − 1, u
2
+ a + u, u
3
+ u
2
− 1i
* 2 irreducible components of dim
C
= 0, with total 68 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−1.26×10
19
u
64
−2.05×10
19
u
63
+· · ·+2.32×10
19
b−3.38×10
19
, 3.34×
10
20
u
64
+8.53×10
20
u
63
+· · ·+1.62×10
20
a+6.63×10
20
, u
65
+2u
64
+· · ·−3u−1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
−2.05854u
64
− 5.25965u
63
+ ··· − 6.06473u − 4.09018
0.542560u
64
+ 0.885015u
63
+ ··· + 6.46360u + 1.45744
a
4
=
−4.79404u
64
− 9.62296u
63
+ ··· − 15.4240u − 0.688537
0.228872u
64
+ 3.24003u
63
+ ··· + 15.0884u + 3.99997
a
1
=
−u
2
+ 1
−u
4
a
11
=
−2.02908u
64
− 5.22916u
63
+ ··· − 8.16807u − 4.20542
0.571011u
64
+ 0.942649u
63
+ ··· + 6.49245u + 1.42898
a
6
=
u
u
a
8
=
−u
3
−u
3
+ u
a
5
=
u
5
+ u
u
5
− u
3
+ u
a
12
=
2.19411u
64
+ 5.79390u
63
+ ··· + 9.22067u + 4.42305
−0.605690u
64
− 1.01153u
63
+ ··· − 5.60577u − 1.39431
a
9
=
−u
7
− 2u
3
−u
7
+ u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
528336484950614213199
162100580461622483569
u
64
−
1127997666238273519001
162100580461622483569
u
63
+ ··· −
1505544510775395115944
162100580461622483569
u −
463719068585525000616
162100580461622483569
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
c
8
u
65
+ 12u
64
+ ··· + 7u + 1
c
2
, c
6
u
65
− 2u
64
+ ··· − 3u + 1
c
3
u
65
+ 3u
64
+ ··· − 742u + 44
c
4
u
65
+ u
64
+ ··· + 432488u + 133561
c
9
, c
11
u
65
+ 4u
64
+ ··· + 24u + 1
c
10
u
65
− 11u
64
+ ··· + 20u − 8
c
12
u
65
+ 4u
64
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
8
y
65
+ 84y
64
+ ··· − 5y −1
c
2
, c
6
y
65
− 12y
64
+ ··· + 7y −1
c
3
y
65
+ 83y
64
+ ··· − 100900y −1936
c
4
y
65
+ 19y
64
+ ··· + 435178968530y −17838540721
c
9
, c
11
y
65
− 54y
64
+ ··· + 1032y −1
c
10
y
65
+ 21y
64
+ ··· + 464y −64
c
12
y
65
− 8y
64
+ ··· + 7y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.820055 + 0.571414I
a = −0.75883 − 1.23938I
b = −0.689094 − 0.473723I
1.92122 + 2.92849I −1.28212 − 3.41898I
u = −0.820055 − 0.571414I
a = −0.75883 + 1.23938I
b = −0.689094 + 0.473723I
1.92122 − 2.92849I −1.28212 + 3.41898I
u = −0.969463 + 0.241716I
a = −1.47695 − 0.01532I
b = −0.541831 − 0.359416I
1.53983 + 7.60011I −3.30399 − 8.68829I
u = −0.969463 − 0.241716I
a = −1.47695 + 0.01532I
b = −0.541831 + 0.359416I
1.53983 − 7.60011I −3.30399 + 8.68829I
u = 0.744354 + 0.673066I
a = −1.77437 + 1.77616I
b = −2.00526 − 0.95542I
6.17006 − 0.54961I 7.09242 + 0.I
u = 0.744354 − 0.673066I
a = −1.77437 − 1.77616I
b = −2.00526 + 0.95542I
6.17006 + 0.54961I 7.09242 + 0.I
u = 0.596268 + 0.796205I
a = −0.84320 + 1.39289I
b = −1.84547 + 0.11090I
7.82451 + 7.18297I 3.58934 − 3.88549I
u = 0.596268 − 0.796205I
a = −0.84320 − 1.39289I
b = −1.84547 − 0.11090I
7.82451 − 7.18297I 3.58934 + 3.88549I
u = −0.558053 + 0.817613I
a = −0.294812 + 1.037710I
b = 0.840197 + 0.843216I
7.30694 + 1.58876I 6.94400 − 2.45858I
u = −0.558053 − 0.817613I
a = −0.294812 − 1.037710I
b = 0.840197 − 0.843216I
7.30694 − 1.58876I 6.94400 + 2.45858I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.998178 + 0.175665I
a = 0.203083 + 0.942676I
b = 0.383549 + 0.157322I
1.14078 + 1.78516I −1.11805 − 3.43956I
u = 0.998178 − 0.175665I
a = 0.203083 − 0.942676I
b = 0.383549 − 0.157322I
1.14078 − 1.78516I −1.11805 + 3.43956I
u = −0.767755 + 0.612962I
a = 3.39308 + 2.93420I
b = 3.54263 + 0.73826I
3.80285 + 2.31034I −25.0391 + 4.5996I
u = −0.767755 − 0.612962I
a = 3.39308 − 2.93420I
b = 3.54263 − 0.73826I
3.80285 − 2.31034I −25.0391 − 4.5996I
u = 0.812707 + 0.650110I
a = 0.19129 + 2.01588I
b = −2.00190 + 1.46282I
5.94798 − 4.38359I 6.03810 + 7.34576I
u = 0.812707 − 0.650110I
a = 0.19129 − 2.01588I
b = −2.00190 − 1.46282I
5.94798 + 4.38359I 6.03810 − 7.34576I
u = 0.870827 + 0.601767I
a = 1.54614 − 1.58787I
b = 1.54992 + 0.15321I
1.78299 − 6.95651I 0. + 9.98928I
u = 0.870827 − 0.601767I
a = 1.54614 + 1.58787I
b = 1.54992 − 0.15321I
1.78299 + 6.95651I 0. − 9.98928I
u = 0.648812 + 0.671920I
a = 0.167707 − 0.999965I
b = 1.50126 − 0.72002I
2.49850 + 2.18973I 1.25971 − 3.64342I
u = 0.648812 − 0.671920I
a = 0.167707 + 0.999965I
b = 1.50126 + 0.72002I
2.49850 − 2.18973I 1.25971 + 3.64342I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.684737 + 0.604855I
a = −1.010310 − 0.522879I
b = −1.022020 − 0.286519I
2.35987 + 1.53086I 1.14672 − 4.64603I
u = −0.684737 − 0.604855I
a = −1.010310 + 0.522879I
b = −1.022020 + 0.286519I
2.35987 − 1.53086I 1.14672 + 4.64603I
u = 0.956434 + 0.623323I
a = −1.40109 + 1.80097I
b = −2.02007 + 0.57048I
6.62284 − 12.39710I 0
u = 0.956434 − 0.623323I
a = −1.40109 − 1.80097I
b = −2.02007 − 0.57048I
6.62284 + 12.39710I 0
u = −0.831440 + 0.172732I
a = 2.04727 − 0.37107I
b = 0.655355 − 0.212384I
−2.33387 + 3.36125I −9.80190 − 7.73059I
u = −0.831440 − 0.172732I
a = 2.04727 + 0.37107I
b = 0.655355 + 0.212384I
−2.33387 − 3.36125I −9.80190 + 7.73059I
u = 0.798114 + 0.280411I
a = 0.172582 − 1.311990I
b = 0.339896 − 0.283030I
−1.85279 − 0.67069I −10.04650 + 3.48460I
u = 0.798114 − 0.280411I
a = 0.172582 + 1.311990I
b = 0.339896 + 0.283030I
−1.85279 + 0.67069I −10.04650 − 3.48460I
u = −0.994683 + 0.610182I
a = 1.168940 + 0.182146I
b = 1.080470 − 0.508571I
5.85453 + 3.65774I 0
u = −0.994683 − 0.610182I
a = 1.168940 − 0.182146I
b = 1.080470 + 0.508571I
5.85453 − 3.65774I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.886696 + 0.799693I
a = 0.049918 + 0.520198I
b = 0.688654 + 0.067457I
4.04012 + 2.99291I 0
u = −0.886696 − 0.799693I
a = 0.049918 − 0.520198I
b = 0.688654 − 0.067457I
4.04012 − 2.99291I 0
u = 0.715886
a = −0.806878
b = 0.0728787
−1.06061 −9.36050
u = −0.036225 + 0.711406I
a = −0.646922 − 1.148690I
b = −0.293062 − 0.445219I
4.70553 − 4.54910I 4.84912 + 4.44515I
u = −0.036225 − 0.711406I
a = −0.646922 + 1.148690I
b = −0.293062 + 0.445219I
4.70553 + 4.54910I 4.84912 − 4.44515I
u = −0.660304 + 0.263461I
a = −0.92327 − 2.16146I
b = −0.65397 − 1.36006I
1.59886 + 2.23743I −0.09200 − 8.25781I
u = −0.660304 − 0.263461I
a = −0.92327 + 2.16146I
b = −0.65397 + 1.36006I
1.59886 − 2.23743I −0.09200 + 8.25781I
u = 0.923672 + 0.910982I
a = −1.33275 + 0.68563I
b = −2.27621 − 1.05859I
11.31760 − 2.00493I 0
u = 0.923672 − 0.910982I
a = −1.33275 − 0.68563I
b = −2.27621 + 1.05859I
11.31760 + 2.00493I 0
u = −0.920176 + 0.922248I
a = 0.437881 + 1.136740I
b = 2.72886 + 0.25698I
11.70890 − 2.29417I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.920176 − 0.922248I
a = 0.437881 − 1.136740I
b = 2.72886 − 0.25698I
11.70890 + 2.29417I 0
u = 0.948041 + 0.898495I
a = −0.00686 + 1.89178I
b = −2.10420 + 1.27127I
11.23820 − 4.66383I 0
u = 0.948041 − 0.898495I
a = −0.00686 − 1.89178I
b = −2.10420 − 1.27127I
11.23820 + 4.66383I 0
u = 0.938818 + 0.910131I
a = 1.94266 − 3.67219I
b = 6.37132 − 0.20498I
13.25270 − 3.35212I 0
u = 0.938818 − 0.910131I
a = 1.94266 + 3.67219I
b = 6.37132 + 0.20498I
13.25270 + 3.35212I 0
u = −0.906041 + 0.944348I
a = −0.96248 − 1.58621I
b = −3.52611 + 0.26832I
17.2883 − 8.5608I 0
u = −0.906041 − 0.944348I
a = −0.96248 + 1.58621I
b = −3.52611 − 0.26832I
17.2883 + 8.5608I 0
u = 0.902391 + 0.951587I
a = 0.047768 − 1.069910I
b = 1.97152 − 0.78996I
16.6895 + 0.2053I 0
u = 0.902391 − 0.951587I
a = 0.047768 + 1.069910I
b = 1.97152 + 0.78996I
16.6895 − 0.2053I 0
u = −0.936676 + 0.920511I
a = −1.11522 − 1.81897I
b = −3.01179 + 1.07212I
15.9561 + 1.1091I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.936676 − 0.920511I
a = −1.11522 + 1.81897I
b = −3.01179 − 1.07212I
15.9561 − 1.1091I 0
u = −0.958520 + 0.902088I
a = 0.73789 + 1.98899I
b = 2.69761 − 0.07690I
11.5836 + 9.0106I 0
u = −0.958520 − 0.902088I
a = 0.73789 − 1.98899I
b = 2.69761 + 0.07690I
11.5836 − 9.0106I 0
u = −0.948403 + 0.914191I
a = 0.16245 − 1.67524I
b = −3.04131 − 1.20975I
15.9177 + 5.6422I 0
u = −0.948403 − 0.914191I
a = 0.16245 + 1.67524I
b = −3.04131 + 1.20975I
15.9177 − 5.6422I 0
u = −0.981573 + 0.901998I
a = −0.76506 − 2.45787I
b = −3.56067 − 0.50087I
17.0389 + 15.3461I 0
u = −0.981573 − 0.901998I
a = −0.76506 + 2.45787I
b = −3.56067 + 0.50087I
17.0389 − 15.3461I 0
u = 0.988719 + 0.902991I
a = 0.98242 − 1.12974I
b = 2.00991 + 0.63394I
16.4045 − 7.0166I 0
u = 0.988719 − 0.902991I
a = 0.98242 + 1.12974I
b = 2.00991 − 0.63394I
16.4045 + 7.0166I 0
u = 0.656202 + 0.074693I
a = −0.19941 + 2.76051I
b = 0.712381 − 1.203220I
0.647228 − 0.175412I 27.9047 − 7.2168I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.656202 − 0.074693I
a = −0.19941 − 2.76051I
b = 0.712381 + 1.203220I
0.647228 + 0.175412I 27.9047 + 7.2168I
u = 0.025083 + 0.412212I
a = −0.276764 + 0.598990I
b = 0.383965 + 0.619009I
0.08844 − 1.51243I 0.26581 + 4.27826I
u = 0.025083 − 0.412212I
a = −0.276764 − 0.598990I
b = 0.383965 − 0.619009I
0.08844 + 1.51243I 0.26581 − 4.27826I
u = −0.305765 + 0.261881I
a = −4.05933 − 1.09380I
b = −0.900970 + 0.336871I
2.53402 − 0.11660I 3.78096 − 2.55604I
u = −0.305765 − 0.261881I
a = −4.05933 + 1.09380I
b = −0.900970 − 0.336871I
2.53402 + 0.11660I 3.78096 + 2.55604I
11
II. I
u
2
= hb − 1, u
2
+ a + u, u
3
+ u
2
− 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
−u
2
− u
1
a
4
=
−u
2
− u
u
2
+ u + 1
a
1
=
−u
2
+ 1
−u
2
− u + 1
a
11
=
−u
2
− u
1
a
6
=
u
u
a
8
=
u
2
− 1
u
2
+ u − 1
a
5
=
1
u
2
a
12
=
−u
2
− u + 1
1
a
9
=
−1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
2
+ 4
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
12
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
3
, c
4
u
3
− 2u
2
+ u − 1
c
6
u
3
− u
2
+ 1
c
7
, c
8
u
3
+ u
2
+ 2u + 1
c
9
(u + 1)
3
c
10
u
3
c
11
(u − 1)
3
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
8
, c
12
y
3
+ 3y
2
+ 2y −1
c
2
, c
6
y
3
− y
2
+ 2y −1
c
3
, c
4
y
3
− 2y
2
− 3y −1
c
9
, c
11
(y −1)
3
c
10
y
3
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.662359 + 0.562280I
b = 1.00000
4.66906 + 2.82812I 4.21508 − 1.30714I
u = −0.877439 − 0.744862I
a = 0.662359 − 0.562280I
b = 1.00000
4.66906 − 2.82812I 4.21508 + 1.30714I
u = 0.754878
a = −1.32472
b = 1.00000
0.531480 4.56980
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
(u
3
− u
2
+ 2u − 1)(u
65
+ 12u
64
+ ··· + 7u + 1)
c
2
(u
3
+ u
2
− 1)(u
65
− 2u
64
+ ··· − 3u + 1)
c
3
(u
3
− 2u
2
+ u − 1)(u
65
+ 3u
64
+ ··· − 742u + 44)
c
4
(u
3
− 2u
2
+ u − 1)(u
65
+ u
64
+ ··· + 432488u + 133561)
c
6
(u
3
− u
2
+ 1)(u
65
− 2u
64
+ ··· − 3u + 1)
c
7
, c
8
(u
3
+ u
2
+ 2u + 1)(u
65
+ 12u
64
+ ··· + 7u + 1)
c
9
((u + 1)
3
)(u
65
+ 4u
64
+ ··· + 24u + 1)
c
10
u
3
(u
65
− 11u
64
+ ··· + 20u − 8)
c
11
((u − 1)
3
)(u
65
+ 4u
64
+ ··· + 24u + 1)
c
12
(u
3
− u
2
+ 2u − 1)(u
65
+ 4u
64
+ ··· + u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
c
8
(y
3
+ 3y
2
+ 2y −1)(y
65
+ 84y
64
+ ··· − 5y −1)
c
2
, c
6
(y
3
− y
2
+ 2y −1)(y
65
− 12y
64
+ ··· + 7y −1)
c
3
(y
3
− 2y
2
− 3y −1)(y
65
+ 83y
64
+ ··· − 100900y −1936)
c
4
(y
3
− 2y
2
− 3y −1)
· (y
65
+ 19y
64
+ ··· + 435178968530y −17838540721)
c
9
, c
11
((y −1)
3
)(y
65
− 54y
64
+ ··· + 1032y −1)
c
10
y
3
(y
65
+ 21y
64
+ ··· + 464y −64)
c
12
(y
3
+ 3y
2
+ 2y −1)(y
65
− 8y
64
+ ··· + 7y −1)
17
