K14a13171
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Contents
1
Knot presentations
2
Polynomial invariants
3
Modifying This Page
Knot presentations
Dowker-Thistlethwaite code
6 8 16 2 20 22 26 4 24 12 10 28 14 18
Notes on presentations of K14a13171
Polynomial invariants
Jones polynomial
Data:K14a13171/Jones Polynomial
Alexander polynomial
7
t
4
−
27
t
3
+
58
t
2
−
88
t
+
101
−
88
t
−
1
+
58
t
−
2
−
27
t
−
3
+
7
t
−
4
{\displaystyle 7t^{4}-27t^{3}+58t^{2}-88t+101-88t^{-1}+58t^{-2}-27t^{-3}+7t^{-4}}
Conway polynomial
Data:K14a13171/Conway Polynomial
Determinant
Data:K14a13171/Determinant
Signature
Data:K14a13171/Signature
HOMFLY-PT polynomial
z
8
a
−
8
+
3
z
8
a
−
10
+
3
z
8
a
−
12
+
5
z
6
a
−
8
+
15
z
6
a
−
10
+
13
z
6
a
−
12
−
4
z
6
a
−
14
+
8
z
4
a
−
8
+
26
z
4
a
−
10
+
16
z
4
a
−
12
−
15
z
4
a
−
14
+
z
4
a
−
16
+
4
z
2
a
−
8
+
19
z
2
a
−
10
+
3
z
2
a
−
12
−
16
z
2
a
−
14
+
3
z
2
a
−
16
+
6
a
−
10
−
3
a
−
12
−
4
a
−
14
+
2
a
−
16
{\displaystyle z^{8}a^{-8}+3z^{8}a^{-10}+3z^{8}a^{-12}+5z^{6}a^{-8}+15z^{6}a^{-10}+13z^{6}a^{-12}-4z^{6}a^{-14}+8z^{4}a^{-8}+26z^{4}a^{-10}+16z^{4}a^{-12}-15z^{4}a^{-14}+z^{4}a^{-16}+4z^{2}a^{-8}+19z^{2}a^{-10}+3z^{2}a^{-12}-16z^{2}a^{-14}+3z^{2}a^{-16}+6a^{-10}-3a^{-12}-4a^{-14}+2a^{-16}}
Kauffman polynomial
2
z
13
$
F
a
i
l
e
d
−
1
+
2
z
13
$
F
a
i
l
e
d
−
1
+
6
z
12
$
F
a
i
l
e
d
−
1
+
15
z
12
$
F
a
i
l
e
d
−
1
+
9
z
12
$
F
a
i
l
e
d
−
1
+
7
z
11
$
F
a
i
l
e
d
−
1
+
16
z
11
$
F
a
i
l
e
d
−
1
+
28
z
11
$
F
a
i
l
e
d
−
1
+
19
z
11
$
F
a
i
l
e
d
−
1
+
6
z
10
$
F
a
i
l
e
d
−
1
−
10
z
10
$
F
a
i
l
e
d
−
1
−
27
z
10
$
F
a
i
l
e
d
−
1
+
14
z
10
$
F
a
i
l
e
d
−
1
+
25
z
10
$
F
a
i
l
e
d
−
1
+
3
z
9
$
F
a
i
l
e
d
−
1
−
20
z
9
$
F
a
i
l
e
d
−
1
−
70
z
9
$
F
a
i
l
e
d
−
1
−
90
z
9
$
F
a
i
l
e
d
−
1
−
21
z
9
$
F
a
i
l
e
d
−
1
+
22
z
9
$
F
a
i
l
e
d
−
1
+
z
8
$
F
a
i
l
e
d
−
1
−
24
z
8
$
F
a
i
l
e
d
−
1
−
5
z
8
$
F
a
i
l
e
d
−
1
−
79
z
8
$
F
a
i
l
e
d
−
1
−
46
z
8
$
F
a
i
l
e
d
−
1
+
13
z
8
$
F
a
i
l
e
d
−
1
−
12
z
7
$
F
a
i
l
e
d
−
1
+
16
z
7
$
F
a
i
l
e
d
−
1
+
117
z
7
$
F
a
i
l
e
d
−
1
+
117
z
7
$
F
a
i
l
e
d
−
1
−
18
z
7
$
F
a
i
l
e
d
−
1
−
41
z
7
$
F
a
i
l
e
d
−
1
+
5
z
7
$
F
a
i
l
e
d
−
1
−
5
z
6
$
F
a
i
l
e
d
−
1
+
38
z
6
$
F
a
i
l
e
d
−
1
+
25
z
6
$
F
a
i
l
e
d
−
1
+
35
z
6
$
F
a
i
l
e
d
−
1
+
103
z
6
$
F
a
i
l
e
d
−
1
+
29
z
6
$
F
a
i
l
e
d
−
1
−
20
z
6
$
F
a
i
l
e
d
−
1
+
z
6
$
F
a
i
l
e
d
−
1
+
14
z
5
$
F
a
i
l
e
d
−
1
−
z
5
$
F
a
i
l
e
d
−
1
−
102
z
5
$
F
a
i
l
e
d
−
1
−
84
z
5
$
F
a
i
l
e
d
−
1
+
38
z
5
$
F
a
i
l
e
d
−
1
+
29
z
5
$
F
a
i
l
e
d
−
1
−
6
z
5
$
F
a
i
l
e
d
−
1
+
8
z
4
$
F
a
i
l
e
d
−
1
−
38
z
4
$
F
a
i
l
e
d
−
1
−
36
z
4
$
F
a
i
l
e
d
−
1
−
26
z
4
$
F
a
i
l
e
d
−
1
−
54
z
4
$
F
a
i
l
e
d
−
1
−
8
z
4
$
F
a
i
l
e
d
−
1
+
9
z
4
$
F
a
i
l
e
d
−
1
−
z
4
$
F
a
i
l
e
d
−
1
−
4
z
3
$
F
a
i
l
e
d
−
1
−
8
z
3
$
F
a
i
l
e
d
−
1
+
37
z
3
$
F
a
i
l
e
d
−
1
+
38
z
3
$
F
a
i
l
e
d
−
1
−
16
z
3
$
F
a
i
l
e
d
−
1
−
12
z
3
$
F
a
i
l
e
d
−
1
+
z
3
$
F
a
i
l
e
d
−
1
−
4
z
2
$
F
a
i
l
e
d
−
1
+
25
z
2
$
F
a
i
l
e
d
−
1
+
20
z
2
$
F
a
i
l
e
d
−
1
−
4
z
2
$
F
a
i
l
e
d
−
1
+
9
z
2
$
F
a
i
l
e
d
−
1
+
2
z
2
$
F
a
i
l
e
d
−
1
−
2
z
2
$
F
a
i
l
e
d
−
1
+
5
z
$
F
a
i
l
e
d
−
1
−
5
z
$
F
a
i
l
e
d
−
1
−
10
z
$
F
a
i
l
e
d
−
1
+
2
z
$
F
a
i
l
e
d
−
1
+
2
z
$
F
a
i
l
e
d
−
1
−
6
$
F
a
i
l
e
d
−
1
−
3
$
F
a
i
l
e
d
−
1
+
4
$
F
a
i
l
e
d
−
1
+
2
$
F
a
i
l
e
d
−
1
{\displaystyle 2z^{13}\$Failed^{-1}+2z^{13}\$Failed^{-1}+6z^{12}\$Failed^{-1}+15z^{12}\$Failed^{-1}+9z^{12}\$Failed^{-1}+7z^{11}\$Failed^{-1}+16z^{11}\$Failed^{-1}+28z^{11}\$Failed^{-1}+19z^{11}\$Failed^{-1}+6z^{10}\$Failed^{-1}-10z^{10}\$Failed^{-1}-27z^{10}\$Failed^{-1}+14z^{10}\$Failed^{-1}+25z^{10}\$Failed^{-1}+3z^{9}\$Failed^{-1}-20z^{9}\$Failed^{-1}-70z^{9}\$Failed^{-1}-90z^{9}\$Failed^{-1}-21z^{9}\$Failed^{-1}+22z^{9}\$Failed^{-1}+z^{8}\$Failed^{-1}-24z^{8}\$Failed^{-1}-5z^{8}\$Failed^{-1}-79z^{8}\$Failed^{-1}-46z^{8}\$Failed^{-1}+13z^{8}\$Failed^{-1}-12z^{7}\$Failed^{-1}+16z^{7}\$Failed^{-1}+117z^{7}\$Failed^{-1}+117z^{7}\$Failed^{-1}-18z^{7}\$Failed^{-1}-41z^{7}\$Failed^{-1}+5z^{7}\$Failed^{-1}-5z^{6}\$Failed^{-1}+38z^{6}\$Failed^{-1}+25z^{6}\$Failed^{-1}+35z^{6}\$Failed^{-1}+103z^{6}\$Failed^{-1}+29z^{6}\$Failed^{-1}-20z^{6}\$Failed^{-1}+z^{6}\$Failed^{-1}+14z^{5}\$Failed^{-1}-z^{5}\$Failed^{-1}-102z^{5}\$Failed^{-1}-84z^{5}\$Failed^{-1}+38z^{5}\$Failed^{-1}+29z^{5}\$Failed^{-1}-6z^{5}\$Failed^{-1}+8z^{4}\$Failed^{-1}-38z^{4}\$Failed^{-1}-36z^{4}\$Failed^{-1}-26z^{4}\$Failed^{-1}-54z^{4}\$Failed^{-1}-8z^{4}\$Failed^{-1}+9z^{4}\$Failed^{-1}-z^{4}\$Failed^{-1}-4z^{3}\$Failed^{-1}-8z^{3}\$Failed^{-1}+37z^{3}\$Failed^{-1}+38z^{3}\$Failed^{-1}-16z^{3}\$Failed^{-1}-12z^{3}\$Failed^{-1}+z^{3}\$Failed^{-1}-4z^{2}\$Failed^{-1}+25z^{2}\$Failed^{-1}+20z^{2}\$Failed^{-1}-4z^{2}\$Failed^{-1}+9z^{2}\$Failed^{-1}+2z^{2}\$Failed^{-1}-2z^{2}\$Failed^{-1}+5z\$Failed^{-1}-5z\$Failed^{-1}-10z\$Failed^{-1}+2z\$Failed^{-1}+2z\$Failed^{-1}-6\$Failed^{-1}-3\$Failed^{-1}+4\$Failed^{-1}+2\$Failed^{-1}}
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