K14a17824
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Contents
1
Knot presentations
2
Polynomial invariants
3
Modifying This Page
Knot presentations
Dowker-Thistlethwaite code
6 20 14 22 26 18 4 24 12 10 2 28 16 8
Notes on presentations of K14a17824
Polynomial invariants
Jones polynomial
Data:K14a17824/Jones Polynomial
Alexander polynomial
2
t
4
−
17
t
3
+
57
t
2
−
104
t
+
125
−
104
t
−
1
+
57
t
−
2
−
17
t
−
3
+
2
t
−
4
{\displaystyle 2t^{4}-17t^{3}+57t^{2}-104t+125-104t^{-1}+57t^{-2}-17t^{-3}+2t^{-4}}
Conway polynomial
Data:K14a17824/Conway Polynomial
Determinant
Data:K14a17824/Determinant
Signature
Data:K14a17824/Signature
HOMFLY-PT polynomial
z
8
a
−
4
+
z
8
a
−
6
−
2
z
6
a
−
2
+
z
6
a
−
4
+
2
z
6
a
−
6
−
2
z
6
a
−
8
−
4
z
4
a
−
2
−
z
4
a
−
4
+
3
z
4
a
−
6
−
5
z
4
a
−
8
+
z
4
a
−
10
+
z
4
−
3
z
2
a
−
2
+
2
z
2
a
−
4
+
4
z
2
a
−
6
−
4
z
2
a
−
8
+
2
z
2
a
−
10
+
2
z
2
−
2
a
−
2
+
3
a
−
4
−
a
−
8
+
1
{\displaystyle z^{8}a^{-4}+z^{8}a^{-6}-2z^{6}a^{-2}+z^{6}a^{-4}+2z^{6}a^{-6}-2z^{6}a^{-8}-4z^{4}a^{-2}-z^{4}a^{-4}+3z^{4}a^{-6}-5z^{4}a^{-8}+z^{4}a^{-10}+z^{4}-3z^{2}a^{-2}+2z^{2}a^{-4}+4z^{2}a^{-6}-4z^{2}a^{-8}+2z^{2}a^{-10}+2z^{2}-2a^{-2}+3a^{-4}-a^{-8}+1}
Kauffman polynomial
3
z
13
$
F
a
i
l
e
d
−
1
+
3
z
13
$
F
a
i
l
e
d
−
1
+
8
z
12
$
F
a
i
l
e
d
−
1
+
20
z
12
$
F
a
i
l
e
d
−
1
+
12
z
12
$
F
a
i
l
e
d
−
1
+
10
z
11
$
F
a
i
l
e
d
−
1
+
18
z
11
$
F
a
i
l
e
d
−
1
+
29
z
11
$
F
a
i
l
e
d
−
1
+
21
z
11
$
F
a
i
l
e
d
−
1
+
8
z
10
$
F
a
i
l
e
d
−
1
−
5
z
10
$
F
a
i
l
e
d
−
1
−
42
z
10
$
F
a
i
l
e
d
−
1
−
7
z
10
$
F
a
i
l
e
d
−
1
+
22
z
10
$
F
a
i
l
e
d
−
1
+
4
z
9
$
F
a
i
l
e
d
−
1
−
19
z
9
$
F
a
i
l
e
d
−
1
−
63
z
9
$
F
a
i
l
e
d
−
1
−
111
z
9
$
F
a
i
l
e
d
−
1
−
55
z
9
$
F
a
i
l
e
d
−
1
+
16
z
9
$
F
a
i
l
e
d
−
1
−
22
z
8
$
F
a
i
l
e
d
−
1
−
22
z
8
$
F
a
i
l
e
d
−
1
+
23
z
8
$
F
a
i
l
e
d
−
1
−
50
z
8
$
F
a
i
l
e
d
−
1
−
63
z
8
$
F
a
i
l
e
d
−
1
+
9
z
8
$
F
a
i
l
e
d
−
1
+
z
8
−
14
z
7
$
F
a
i
l
e
d
−
1
−
6
z
7
$
F
a
i
l
e
d
−
1
+
60
z
7
$
F
a
i
l
e
d
−
1
+
155
z
7
$
F
a
i
l
e
d
−
1
+
60
z
7
$
F
a
i
l
e
d
−
1
−
39
z
7
$
F
a
i
l
e
d
−
1
+
4
z
7
$
F
a
i
l
e
d
−
1
+
14
z
6
$
F
a
i
l
e
d
−
1
+
2
z
6
$
F
a
i
l
e
d
−
1
−
10
z
6
$
F
a
i
l
e
d
−
1
+
107
z
6
$
F
a
i
l
e
d
−
1
+
82
z
6
$
F
a
i
l
e
d
−
1
−
18
z
6
$
F
a
i
l
e
d
−
1
+
z
6
$
F
a
i
l
e
d
−
1
−
4
z
6
+
18
z
5
$
F
a
i
l
e
d
−
1
+
22
z
5
$
F
a
i
l
e
d
−
1
−
43
z
5
$
F
a
i
l
e
d
−
1
−
102
z
5
$
F
a
i
l
e
d
−
1
−
10
z
5
$
F
a
i
l
e
d
−
1
+
37
z
5
$
F
a
i
l
e
d
−
1
−
8
z
5
$
F
a
i
l
e
d
−
1
+
7
z
4
$
F
a
i
l
e
d
−
1
+
22
z
4
$
F
a
i
l
e
d
−
1
+
3
z
4
$
F
a
i
l
e
d
−
1
−
68
z
4
$
F
a
i
l
e
d
−
1
−
40
z
4
$
F
a
i
l
e
d
−
1
+
8
z
4
$
F
a
i
l
e
d
−
1
−
2
z
4
$
F
a
i
l
e
d
−
1
+
6
z
4
−
10
z
3
$
F
a
i
l
e
d
−
1
−
12
z
3
$
F
a
i
l
e
d
−
1
+
17
z
3
$
F
a
i
l
e
d
−
1
+
25
z
3
$
F
a
i
l
e
d
−
1
−
7
z
3
$
F
a
i
l
e
d
−
1
−
11
z
3
$
F
a
i
l
e
d
−
1
+
2
z
3
$
F
a
i
l
e
d
−
1
−
9
z
2
$
F
a
i
l
e
d
−
1
−
13
z
2
$
F
a
i
l
e
d
−
1
−
z
2
$
F
a
i
l
e
d
−
1
+
14
z
2
$
F
a
i
l
e
d
−
1
+
7
z
2
$
F
a
i
l
e
d
−
1
−
4
z
2
+
2
z
$
F
a
i
l
e
d
−
1
+
3
z
$
F
a
i
l
e
d
−
1
−
z
$
F
a
i
l
e
d
−
1
+
2
z
$
F
a
i
l
e
d
−
1
+
2
$
F
a
i
l
e
d
−
1
+
3
$
F
a
i
l
e
d
−
1
−
$
F
a
i
l
e
d
−
1
+
1
{\displaystyle 3z^{13}\$Failed^{-1}+3z^{13}\$Failed^{-1}+8z^{12}\$Failed^{-1}+20z^{12}\$Failed^{-1}+12z^{12}\$Failed^{-1}+10z^{11}\$Failed^{-1}+18z^{11}\$Failed^{-1}+29z^{11}\$Failed^{-1}+21z^{11}\$Failed^{-1}+8z^{10}\$Failed^{-1}-5z^{10}\$Failed^{-1}-42z^{10}\$Failed^{-1}-7z^{10}\$Failed^{-1}+22z^{10}\$Failed^{-1}+4z^{9}\$Failed^{-1}-19z^{9}\$Failed^{-1}-63z^{9}\$Failed^{-1}-111z^{9}\$Failed^{-1}-55z^{9}\$Failed^{-1}+16z^{9}\$Failed^{-1}-22z^{8}\$Failed^{-1}-22z^{8}\$Failed^{-1}+23z^{8}\$Failed^{-1}-50z^{8}\$Failed^{-1}-63z^{8}\$Failed^{-1}+9z^{8}\$Failed^{-1}+z^{8}-14z^{7}\$Failed^{-1}-6z^{7}\$Failed^{-1}+60z^{7}\$Failed^{-1}+155z^{7}\$Failed^{-1}+60z^{7}\$Failed^{-1}-39z^{7}\$Failed^{-1}+4z^{7}\$Failed^{-1}+14z^{6}\$Failed^{-1}+2z^{6}\$Failed^{-1}-10z^{6}\$Failed^{-1}+107z^{6}\$Failed^{-1}+82z^{6}\$Failed^{-1}-18z^{6}\$Failed^{-1}+z^{6}\$Failed^{-1}-4z^{6}+18z^{5}\$Failed^{-1}+22z^{5}\$Failed^{-1}-43z^{5}\$Failed^{-1}-102z^{5}\$Failed^{-1}-10z^{5}\$Failed^{-1}+37z^{5}\$Failed^{-1}-8z^{5}\$Failed^{-1}+7z^{4}\$Failed^{-1}+22z^{4}\$Failed^{-1}+3z^{4}\$Failed^{-1}-68z^{4}\$Failed^{-1}-40z^{4}\$Failed^{-1}+8z^{4}\$Failed^{-1}-2z^{4}\$Failed^{-1}+6z^{4}-10z^{3}\$Failed^{-1}-12z^{3}\$Failed^{-1}+17z^{3}\$Failed^{-1}+25z^{3}\$Failed^{-1}-7z^{3}\$Failed^{-1}-11z^{3}\$Failed^{-1}+2z^{3}\$Failed^{-1}-9z^{2}\$Failed^{-1}-13z^{2}\$Failed^{-1}-z^{2}\$Failed^{-1}+14z^{2}\$Failed^{-1}+7z^{2}\$Failed^{-1}-4z^{2}+2z\$Failed^{-1}+3z\$Failed^{-1}-z\$Failed^{-1}+2z\$Failed^{-1}+2\$Failed^{-1}+3\$Failed^{-1}-\$Failed^{-1}+1}
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