K13a4687

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a4687

Polynomial invariants

Jones polynomial	Data:K13a4687/Jones Polynomial
Alexander polynomial	$2t^{4}-14t^{3}+42t^{2}-76t+93-76t^{-1}+42t^{-2}-14t^{-3}+2t^{-4}$
Conway polynomial	Data:K13a4687/Conway Polynomial
Determinant	361
Signature	0
HOMFLY-PT polynomial	$z^{8}a^{-2}+z^{8}-a^{2}z^{6}+2z^{6}a^{-2}-2z^{6}a^{-4}+3z^{6}-2a^{2}z^{4}-4z^{4}a^{-4}+z^{4}a^{-6}+3z^{4}-2z^{2}a^{-2}-z^{2}a^{-4}+z^{2}a^{-6}+a^{2}-a^{-2}+a^{-4}$
Kauffman polynomial	$5z^{12}a^{-2}+5z^{12}a^{-4}+15z^{11}a^{-1}+27z^{11}a^{-3}+12z^{11}a^{-5}+22z^{10}a^{-2}+10z^{10}a^{-4}+11z^{10}a^{-6}+23z^{10}+25az^{9}-11z^{9}a^{-1}-78z^{9}a^{-3}-37z^{9}a^{-5}+5z^{9}a^{-7}+20a^{2}z^{8}-87z^{8}a^{-2}-75z^{8}a^{-4}-40z^{8}a^{-6}+z^{8}a^{-8}-33z^{8}+12a^{3}z^{7}-38az^{7}-31z^{7}a^{-1}+68z^{7}a^{-3}+32z^{7}a^{-5}-17z^{7}a^{-7}+5a^{4}z^{6}-25a^{2}z^{6}+75z^{6}a^{-2}+96z^{6}a^{-4}+46z^{6}a^{-6}-3z^{6}a^{-8}-2z^{6}+a^{5}z^{5}-11a^{3}z^{5}+14az^{5}+26z^{5}a^{-1}-26z^{5}a^{-3}-10z^{5}a^{-5}+16z^{5}a^{-7}-3a^{4}z^{4}+8a^{2}z^{4}-16z^{4}a^{-2}-43z^{4}a^{-4}-20z^{4}a^{-6}+2z^{4}a^{-8}+16z^{4}+2a^{3}z^{3}+3az^{3}+5z^{3}a^{-3}+3z^{3}a^{-5}-3z^{3}a^{-7}+a^{2}z^{2}-4z^{2}a^{-2}+3z^{2}a^{-4}+4z^{2}a^{-6}-2z^{2}-az-za^{-1}-za^{-3}-za^{-5}-a^{2}+a^{-2}+a^{-4}$

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