K13a3642

Knot presentations

Dowker-Thistlethwaite code

6 10 18 16 22 4 24 26 2 14 8 12 20

Notes on presentations of K13a3642

Polynomial invariants

Jones polynomial	Data:K13a3642/Jones Polynomial
Alexander polynomial	$t^{5}-7t^{4}+25t^{3}-56t^{2}+89t-103+89t^{-1}-56t^{-2}+25t^{-3}-7t^{-4}+t^{-5}$
Conway polynomial	Data:K13a3642/Conway Polynomial
Determinant	459
Signature	2
HOMFLY-PT polynomial	$z^{10}a^{-2}+6z^{8}a^{-2}-2z^{8}a^{-4}-z^{8}+16z^{6}a^{-2}-9z^{6}a^{-4}+z^{6}a^{-6}-4z^{6}+23z^{4}a^{-2}-15z^{4}a^{-4}+3z^{4}a^{-6}-7z^{4}+16z^{2}a^{-2}-9z^{2}a^{-4}+2z^{2}a^{-6}-6z^{2}+3a^{-2}-a^{-6}-1$
Kauffman polynomial	$5z^{12}a^{-2}+5z^{12}a^{-4}+16z^{11}a^{-1}+33z^{11}a^{-3}+17z^{11}a^{-5}+40z^{10}a^{-2}+44z^{10}a^{-4}+24z^{10}a^{-6}+20z^{10}+13az^{9}-12z^{9}a^{-1}-48z^{9}a^{-3}-3z^{9}a^{-5}+20z^{9}a^{-7}+5a^{2}z^{8}-132z^{8}a^{-2}-132z^{8}a^{-4}-38z^{8}a^{-6}+12z^{8}a^{-8}-45z^{8}+a^{3}z^{7}-29az^{7}-38z^{7}a^{-1}-18z^{7}a^{-3}-45z^{7}a^{-5}-30z^{7}a^{-7}+5z^{7}a^{-9}-10a^{2}z^{6}+144z^{6}a^{-2}+137z^{6}a^{-4}+24z^{6}a^{-6}-17z^{6}a^{-8}+z^{6}a^{-10}+39z^{6}-2a^{3}z^{5}+24az^{5}+51z^{5}a^{-1}+52z^{5}a^{-3}+48z^{5}a^{-5}+14z^{5}a^{-7}-7z^{5}a^{-9}+6a^{2}z^{4}-86z^{4}a^{-2}-69z^{4}a^{-4}-5z^{4}a^{-6}+8z^{4}a^{-8}-z^{4}a^{-10}-25z^{4}+a^{3}z^{3}-11az^{3}-26z^{3}a^{-1}-25z^{3}a^{-3}-11z^{3}a^{-5}+3z^{3}a^{-7}+3z^{3}a^{-9}-a^{2}z^{2}+27z^{2}a^{-2}+15z^{2}a^{-4}-2z^{2}a^{-6}-z^{2}a^{-8}+10z^{2}+2az+5za^{-1}+4za^{-3}-2za^{-5}-3za^{-7}-3a^{-2}+a^{-6}-1$

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