12a
0548
(K12a
0548
)
A knot diagram
1
Linearized knot diagam
3 7 8 11 10 2 6 12 1 5 4 9
Solving Sequence
2,6
7 3 8 4
1,10
5 11 9 12
c
6
c
2
c
7
c
3
c
1
c
5
c
10
c
9
c
12
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.58134 × 10
20
u
62
+ 3.74205 × 10
20
u
61
+ ··· + 2.91973 × 10
21
b − 2.96150 × 10
21
,
− 1.26309 × 10
22
u
62
+ 1.69902 × 10
22
u
61
+ ··· + 8.75918 × 10
21
a − 5.81824 × 10
22
, u
63
− 2u
62
+ ··· + 5u − 3i
I
u
2
= h−u
2
a − au − u
2
+ b − u − 1, a
2
+ 2au + 3u
2
+ 2a + 2u + 1, u
3
+ u
2
− 1i
I
u
3
= hb, a − u + 1, u
3
− u
2
+ 1i
* 3 irreducible components of dim
C
= 0, with total 72 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−1.58×10
20
u
62
+3.74×10
20
u
61
+· · ·+2.92×10
21
b−2.96×10
21
, −1.26×
10
22
u
62
+1.70×10
22
u
61
+· · ·+8.76×10
21
a−5.82×10
22
, u
63
−2u
62
+· · ·+5u−3i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
4
=
u
7
− 2u
5
+ 2u
3
− 2u
−u
7
+ u
5
− 2u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
10
=
1.44202u
62
− 1.93971u
61
+ ··· + 0.661158u + 6.64244
0.0541605u
62
− 0.128165u
61
+ ··· − 0.441955u + 1.01431
a
5
=
−0.185702u
62
+ 0.0752726u
61
+ ··· − 2.14838u + 0.547461
0.719076u
62
− 0.662451u
61
+ ··· − 0.943387u + 1.09817
a
11
=
0.903442u
62
− 1.53591u
61
+ ··· + 1.76710u + 4.49679
−0.804672u
62
+ 1.13906u
61
+ ··· + 1.28977u − 3.03093
a
9
=
1.18523u
62
− 1.75085u
61
+ ··· + 1.47609u + 5.39500
−0.563042u
62
+ 0.514494u
61
+ ··· + 0.795969u − 0.856839
a
12
=
0.905223u
62
− 1.45026u
61
+ ··· + 0.887446u + 4.18778
−0.569552u
62
+ 0.745346u
61
+ ··· + 1.44587u − 2.47512
(ii) Obstruction class = −1
(iii) Cusp Shapes =
7126225419678175524155
1459863554716009717429
u
62
−
8012124561236711506684
1459863554716009717429
u
61
+ ··· −
14448360873832908916690
1459863554716009717429
u +
13917590278743478982007
1459863554716009717429
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
63
+ 22u
62
+ ··· + 79u + 9
c
2
, c
6
u
63
− 2u
62
+ ··· + 5u − 3
c
3
u
63
+ 2u
62
+ ··· − 2119u − 507
c
4
, c
5
, c
10
c
11
u
63
− u
62
+ ··· − 32u − 8
c
8
, c
9
, c
12
u
63
+ 4u
62
+ ··· + 12u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
63
+ 42y
62
+ ··· − 4037y −81
c
2
, c
6
y
63
− 22y
62
+ ··· + 79y −9
c
3
y
63
− 30y
62
+ ··· + 10968607y −257049
c
4
, c
5
, c
10
c
11
y
63
+ 77y
62
+ ··· − 384y −64
c
8
, c
9
, c
12
y
63
− 64y
62
+ ··· − 154y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.610001 + 0.784154I
a = −0.583306 − 0.639284I
b = 0.10442 + 1.60088I
−6.01435 + 3.73785I −6.21764 − 2.33056I
u = 0.610001 − 0.784154I
a = −0.583306 + 0.639284I
b = 0.10442 − 1.60088I
−6.01435 − 3.73785I −6.21764 + 2.33056I
u = −0.691211 + 0.731938I
a = −0.984563 + 0.325099I
b = 0.423366 − 0.660007I
1.70446 − 1.85626I −3.28574 + 4.17386I
u = −0.691211 − 0.731938I
a = −0.984563 − 0.325099I
b = 0.423366 + 0.660007I
1.70446 + 1.85626I −3.28574 − 4.17386I
u = 0.984690 + 0.048731I
a = 0.390182 + 1.262910I
b = −0.214172 + 0.744109I
−3.63603 − 1.98289I −12.79221 + 5.30533I
u = 0.984690 − 0.048731I
a = 0.390182 − 1.262910I
b = −0.214172 − 0.744109I
−3.63603 + 1.98289I −12.79221 − 5.30533I
u = −0.617889 + 0.811854I
a = 1.21265 − 0.77110I
b = −0.569733 + 0.792616I
−4.01161 − 5.24201I −7.19231 + 3.97955I
u = −0.617889 − 0.811854I
a = 1.21265 + 0.77110I
b = −0.569733 − 0.792616I
−4.01161 + 5.24201I −7.19231 − 3.97955I
u = −0.800531 + 0.652431I
a = 0.356242 + 0.321397I
b = −0.225169 + 0.600163I
0.12008 + 2.15047I −8.15527 − 1.56284I
u = −0.800531 − 0.652431I
a = 0.356242 − 0.321397I
b = −0.225169 − 0.600163I
0.12008 − 2.15047I −8.15527 + 1.56284I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.809657 + 0.514097I
a = 2.00737 + 1.05562I
b = −0.143570 − 1.274290I
−6.22882 + 2.00042I −11.28661 − 3.42546I
u = −0.809657 − 0.514097I
a = 2.00737 − 1.05562I
b = −0.143570 + 1.274290I
−6.22882 − 2.00042I −11.28661 + 3.42546I
u = 0.785085 + 0.714910I
a = −1.190430 + 0.036937I
b = 0.504608 − 0.222274I
2.98803 − 1.39468I 0
u = 0.785085 − 0.714910I
a = −1.190430 − 0.036937I
b = 0.504608 + 0.222274I
2.98803 + 1.39468I 0
u = 0.600448 + 0.711632I
a = 1.70429 + 0.06119I
b = −0.710743 + 0.153011I
−2.09343 + 0.92231I −4.75363 + 0.62378I
u = 0.600448 − 0.711632I
a = 1.70429 − 0.06119I
b = −0.710743 − 0.153011I
−2.09343 − 0.92231I −4.75363 − 0.62378I
u = 0.625396 + 0.875190I
a = 0.658938 + 1.166250I
b = −0.16972 − 1.64610I
−12.3245 + 8.0761I 0
u = 0.625396 − 0.875190I
a = 0.658938 − 1.166250I
b = −0.16972 + 1.64610I
−12.3245 − 8.0761I 0
u = −1.07798
a = −0.363979
b = 0.794949
−7.41534 −11.6850
u = −1.095210 + 0.048926I
a = 0.55949 − 2.15472I
b = −0.04899 − 1.63658I
−11.94220 + 2.91582I −13.41371 + 0.I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.095210 − 0.048926I
a = 0.55949 + 2.15472I
b = −0.04899 + 1.63658I
−11.94220 − 2.91582I −13.41371 + 0.I
u = 1.104710 + 0.076472I
a = −0.598094 − 0.752936I
b = 0.537709 − 0.922877I
−10.23730 − 4.46631I 0
u = 1.104710 − 0.076472I
a = −0.598094 + 0.752936I
b = 0.537709 + 0.922877I
−10.23730 + 4.46631I 0
u = −0.924553 + 0.652788I
a = −1.041360 + 0.503496I
b = 0.120631 + 0.731259I
−0.27540 + 2.92512I 0
u = −0.924553 − 0.652788I
a = −1.041360 − 0.503496I
b = 0.120631 − 0.731259I
−0.27540 − 2.92512I 0
u = −0.857291
a = 0.117983
b = −0.362513
−1.52387 −4.27340
u = −0.869676 + 0.750012I
a = −1.07018 − 1.26107I
b = 0.01356 + 1.42114I
−1.90031 + 2.83940I 0
u = −0.869676 − 0.750012I
a = −1.07018 + 1.26107I
b = 0.01356 − 1.42114I
−1.90031 − 2.83940I 0
u = 0.275496 + 0.805252I
a = 0.721010 − 1.151510I
b = −0.10473 + 1.66585I
−14.3129 − 4.3810I −9.57041 + 2.65515I
u = 0.275496 − 0.805252I
a = 0.721010 + 1.151510I
b = −0.10473 − 1.66585I
−14.3129 + 4.3810I −9.57041 − 2.65515I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926875 + 0.695254I
a = 0.771343 + 0.660731I
b = −0.511668 − 0.144834I
2.55508 − 4.00808I 0
u = 0.926875 − 0.695254I
a = 0.771343 − 0.660731I
b = −0.511668 + 0.144834I
2.55508 + 4.00808I 0
u = −1.157940 + 0.127426I
a = −1.00083 + 1.33298I
b = 0.14561 + 1.68788I
−19.2613 + 7.1339I 0
u = −1.157940 − 0.127426I
a = −1.00083 − 1.33298I
b = 0.14561 − 1.68788I
−19.2613 − 7.1339I 0
u = −1.012450 + 0.583469I
a = 0.326595 + 0.686319I
b = 0.395006 − 1.064730I
−7.17296 + 2.09708I 0
u = −1.012450 − 0.583469I
a = 0.326595 − 0.686319I
b = 0.395006 + 1.064730I
−7.17296 − 2.09708I 0
u = 0.881182 + 0.793135I
a = 0.465108 − 1.062750I
b = −0.041752 + 0.558255I
0.64338 − 2.97205I 0
u = 0.881182 − 0.793135I
a = 0.465108 + 1.062750I
b = −0.041752 − 0.558255I
0.64338 + 2.97205I 0
u = 1.017390 + 0.618478I
a = −1.87775 − 0.74485I
b = 0.03214 − 1.62578I
−8.45630 − 3.51087I 0
u = 1.017390 − 0.618478I
a = −1.87775 + 0.74485I
b = 0.03214 + 1.62578I
−8.45630 + 3.51087I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.985609 + 0.683922I
a = 1.70144 − 0.50584I
b = −0.424758 − 0.732772I
0.82025 + 7.27682I 0
u = −0.985609 − 0.683922I
a = 1.70144 + 0.50584I
b = −0.424758 + 0.732772I
0.82025 − 7.27682I 0
u = 1.092490 + 0.516377I
a = 1.131500 + 0.316734I
b = 0.08034 + 1.69877I
−16.8215 − 0.3894I 0
u = 1.092490 − 0.516377I
a = 1.131500 − 0.316734I
b = 0.08034 − 1.69877I
−16.8215 + 0.3894I 0
u = 1.018900 + 0.657892I
a = −1.055480 − 0.878323I
b = 0.792174 + 0.156872I
−3.31368 − 6.20587I 0
u = 1.018900 − 0.657892I
a = −1.055480 + 0.878323I
b = 0.792174 − 0.156872I
−3.31368 + 6.20587I 0
u = 0.683095 + 0.384601I
a = −0.398095 − 0.889020I
b = −0.04461 − 1.50376I
−6.96067 − 1.23913I −9.15719 + 5.40608I
u = 0.683095 − 0.384601I
a = −0.398095 + 0.889020I
b = −0.04461 + 1.50376I
−6.96067 + 1.23913I −9.15719 − 5.40608I
u = 0.464167 + 0.618799I
a = −0.455453 + 0.164648I
b = −0.00190 − 1.57015I
−7.04509 − 1.37731I −7.22554 + 3.34935I
u = 0.464167 − 0.618799I
a = −0.455453 − 0.164648I
b = −0.00190 + 1.57015I
−7.04509 + 1.37731I −7.22554 − 3.34935I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.899452 + 0.851726I
a = 0.97396 + 1.50330I
b = −0.01020 − 1.60392I
−6.99761 + 3.15141I 0
u = −0.899452 − 0.851726I
a = 0.97396 − 1.50330I
b = −0.01020 + 1.60392I
−6.99761 − 3.15141I 0
u = 1.035350 + 0.682439I
a = 2.42596 + 0.27809I
b = −0.11553 + 1.62619I
−7.28355 − 9.28433I 0
u = 1.035350 − 0.682439I
a = 2.42596 − 0.27809I
b = −0.11553 − 1.62619I
−7.28355 + 9.28433I 0
u = −0.350286 + 0.666278I
a = 1.17109 + 0.95740I
b = −0.371640 − 0.892558I
−5.46380 + 2.51444I −8.36255 − 3.99940I
u = −0.350286 − 0.666278I
a = 1.17109 − 0.95740I
b = −0.371640 + 0.892558I
−5.46380 − 2.51444I −8.36255 + 3.99940I
u = −1.041560 + 0.694554I
a = −1.90739 + 0.36362I
b = 0.617502 + 0.812473I
−5.28758 + 10.90360I 0
u = −1.041560 − 0.694554I
a = −1.90739 − 0.36362I
b = 0.617502 − 0.812473I
−5.28758 − 10.90360I 0
u = 1.063920 + 0.720846I
a = −2.43149 + 0.20835I
b = 0.18673 − 1.65389I
−13.6698 − 14.0027I 0
u = 1.063920 − 0.720846I
a = −2.43149 − 0.20835I
b = 0.18673 + 1.65389I
−13.6698 + 14.0027I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.514170
a = 2.57325
b = −0.355506
−2.33892 2.37070
u = −0.202617 + 0.344744I
a = −0.979704 − 0.005239I
b = 0.216636 + 0.455539I
−0.134368 + 0.901804I −2.96446 − 7.62176I
u = −0.202617 − 0.344744I
a = −0.979704 + 0.005239I
b = 0.216636 − 0.455539I
−0.134368 − 0.901804I −2.96446 + 7.62176I
11
II.
I
u
2
= h−u
2
a − au − u
2
+ b − u − 1, a
2
+ 2au + 3u
2
+ 2a + 2u + 1, u
3
+ u
2
− 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
u
2
+ u − 1
a
8
=
−u
2
+ 1
u
2
a
4
=
−1
0
a
1
=
−u
2
+ 1
u
2
a
10
=
a
u
2
a + au + u
2
+ u + 1
a
5
=
−u
2
a − au − u
2
− a − 4u − 1
−2
a
11
=
u
2
a + au + u
2
− a + u + 1
−u
2
a − au − u
2
− u − 1
a
9
=
−u
2
+ a + 1
u
2
a + au + 2u
2
+ u + 1
a
12
=
−a
−u
2
a − au − u
2
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u − 12
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
3
− u
2
+ 2u − 1)
2
c
2
(u
3
− u
2
+ 1)
2
c
3
, c
7
(u
3
+ u
2
+ 2u + 1)
2
c
4
, c
5
, c
10
c
11
(u
2
+ 2)
3
c
6
(u
3
+ u
2
− 1)
2
c
8
, c
9
(u + 1)
6
c
12
(u − 1)
6
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
(y
3
+ 3y
2
+ 2y −1)
2
c
2
, c
6
(y
3
− y
2
+ 2y −1)
2
c
4
, c
5
, c
10
c
11
(y + 2)
6
c
8
, c
9
, c
12
(y −1)
6
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.877439 + 0.744862I
a = 0.930832 + 0.496024I
b = − 1.414210I
−3.55561 + 2.82812I −8.49024 − 2.97945I
u = −0.877439 + 0.744862I
a = −1.17595 − 1.98575I
b = 1.414210I
−3.55561 + 2.82812I −8.49024 − 2.97945I
u = −0.877439 − 0.744862I
a = 0.930832 − 0.496024I
b = 1.414210I
−3.55561 − 2.82812I −8.49024 + 2.97945I
u = −0.877439 − 0.744862I
a = −1.17595 + 1.98575I
b = − 1.414210I
−3.55561 − 2.82812I −8.49024 + 2.97945I
u = 0.754878
a = −1.75488 + 1.06756I
b = 1.414210I
−7.69319 −15.0200
u = 0.754878
a = −1.75488 − 1.06756I
b = − 1.414210I
−7.69319 −15.0200
15
III. I
u
3
= hb, a − u + 1, u
3
− u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
u
2
a
3
=
−u
−u
2
+ u + 1
a
8
=
−u
2
+ 1
u
2
a
4
=
1
0
a
1
=
u
2
− 1
−u
2
a
10
=
u − 1
0
a
5
=
1
0
a
11
=
u − 1
0
a
9
=
−u
2
+ u
u
2
a
12
=
u − 1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 10u − 8
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
3
− u
2
+ 2u − 1
c
2
u
3
+ u
2
− 1
c
4
, c
5
, c
10
c
11
u
3
c
6
u
3
− u
2
+ 1
c
7
u
3
+ u
2
+ 2u + 1
c
8
, c
9
(u − 1)
3
c
12
(u + 1)
3
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
7
y
3
+ 3y
2
+ 2y −1
c
2
, c
6
y
3
− y
2
+ 2y −1
c
4
, c
5
, c
10
c
11
y
3
c
8
, c
9
, c
12
(y −1)
3
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.877439 + 0.744862I
a = −0.122561 + 0.744862I
b = 0
1.37919 − 2.82812I −0.08593 + 2.22005I
u = 0.877439 − 0.744862I
a = −0.122561 − 0.744862I
b = 0
1.37919 + 2.82812I −0.08593 − 2.22005I
u = −0.754878
a = −1.75488
b = 0
−2.75839 −17.8280
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
3
− u
2
+ 2u − 1)
3
)(u
63
+ 22u
62
+ ··· + 79u + 9)
c
2
((u
3
− u
2
+ 1)
2
)(u
3
+ u
2
− 1)(u
63
− 2u
62
+ ··· + 5u − 3)
c
3
(u
3
− u
2
+ 2u − 1)(u
3
+ u
2
+ 2u + 1)
2
(u
63
+ 2u
62
+ ··· − 2119u − 507)
c
4
, c
5
, c
10
c
11
u
3
(u
2
+ 2)
3
(u
63
− u
62
+ ··· − 32u − 8)
c
6
(u
3
− u
2
+ 1)(u
3
+ u
2
− 1)
2
(u
63
− 2u
62
+ ··· + 5u − 3)
c
7
((u
3
+ u
2
+ 2u + 1)
3
)(u
63
+ 22u
62
+ ··· + 79u + 9)
c
8
, c
9
((u − 1)
3
)(u + 1)
6
(u
63
+ 4u
62
+ ··· + 12u − 1)
c
12
((u − 1)
6
)(u + 1)
3
(u
63
+ 4u
62
+ ··· + 12u − 1)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y
3
+ 3y
2
+ 2y −1)
3
)(y
63
+ 42y
62
+ ··· − 4037y −81)
c
2
, c
6
((y
3
− y
2
+ 2y −1)
3
)(y
63
− 22y
62
+ ··· + 79y −9)
c
3
((y
3
+ 3y
2
+ 2y −1)
3
)(y
63
− 30y
62
+ ··· + 1.09686 × 10
7
y −257049)
c
4
, c
5
, c
10
c
11
y
3
(y + 2)
6
(y
63
+ 77y
62
+ ··· − 384y −64)
c
8
, c
9
, c
12
((y −1)
9
)(y
63
− 64y
62
+ ··· − 154y −1)
21
