K13a4721

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a4721

Polynomial invariants

Jones polynomial	Data:K13a4721/Jones Polynomial
Alexander polynomial	$t^{5}-7t^{4}+24t^{3}-54t^{2}+88t-103+88t^{-1}-54t^{-2}+24t^{-3}-7t^{-4}+t^{-5}$
Conway polynomial	Data:K13a4721/Conway Polynomial
Determinant	451
Signature	2
HOMFLY-PT polynomial	$z^{10}a^{-2}+6z^{8}a^{-2}-2z^{8}a^{-4}-z^{8}+14z^{6}a^{-2}-8z^{6}a^{-4}+z^{6}a^{-6}-4z^{6}+12z^{4}a^{-2}-9z^{4}a^{-4}+2z^{4}a^{-6}-5z^{4}-z^{2}a^{-2}+2z^{2}a^{-4}-4a^{-2}+5a^{-4}-2a^{-6}+2$
Kauffman polynomial	$6z^{12}a^{-2}+6z^{12}a^{-4}+16z^{11}a^{-1}+35z^{11}a^{-3}+19z^{11}a^{-5}+26z^{10}a^{-2}+36z^{10}a^{-4}+28z^{10}a^{-6}+18z^{10}+12az^{9}-28z^{9}a^{-1}-75z^{9}a^{-3}-9z^{9}a^{-5}+26z^{9}a^{-7}+5a^{2}z^{8}-105z^{8}a^{-2}-110z^{8}a^{-4}-41z^{8}a^{-6}+16z^{8}a^{-8}-47z^{8}+a^{3}z^{7}-31az^{7}+4z^{7}a^{-1}+48z^{7}a^{-3}-34z^{7}a^{-5}-40z^{7}a^{-7}+6z^{7}a^{-9}-12a^{2}z^{6}+125z^{6}a^{-2}+97z^{6}a^{-4}+6z^{6}a^{-6}-21z^{6}a^{-8}+z^{6}a^{-10}+44z^{6}-2a^{3}z^{5}+24az^{5}+20z^{5}a^{-1}+22z^{5}a^{-5}+11z^{5}a^{-7}-5z^{5}a^{-9}+6a^{2}z^{4}-53z^{4}a^{-2}-24z^{4}a^{-4}+11z^{4}a^{-6}+5z^{4}a^{-8}-17z^{4}-6az^{3}-14z^{3}a^{-1}-7z^{3}a^{-3}+7z^{3}a^{-5}+6z^{3}a^{-7}-3z^{2}a^{-2}-9z^{2}a^{-4}-6z^{2}a^{-6}+za^{-1}-4za^{-5}-3za^{-7}+4a^{-2}+5a^{-4}+2a^{-6}+2$

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