K13n757

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13n757

Polynomial invariants

Jones polynomial	Data:K13n757/Jones Polynomial
Alexander polynomial	$t^{4}-6t^{3}+19t^{2}-36t+45-36t^{-1}+19t^{-2}-6t^{-3}+t^{-4}$
Conway polynomial	Data:K13n757/Conway Polynomial
Determinant	169
Signature	0
HOMFLY-PT polynomial	$z^{8}-2a^{2}z^{6}-z^{6}a^{-2}+5z^{6}+a^{4}z^{4}-7a^{2}z^{4}-2z^{4}a^{-2}+11z^{4}+2a^{4}z^{2}-9a^{2}z^{2}-z^{2}a^{-2}-z^{2}a^{-4}+11z^{2}+a^{4}-4a^{2}-a^{-4}+5$
Kauffman polynomial	$az^{11}+z^{11}a^{-1}+4a^{2}z^{10}+3z^{10}a^{-2}+7z^{10}+7a^{3}z^{9}+13az^{9}+9z^{9}a^{-1}+3z^{9}a^{-3}+7a^{4}z^{8}+6a^{2}z^{8}+z^{8}a^{-4}-2z^{8}+4a^{5}z^{7}-8a^{3}z^{7}-29az^{7}-19z^{7}a^{-1}-2z^{7}a^{-3}+a^{6}z^{6}-14a^{4}z^{6}-28a^{2}z^{6}-4z^{6}a^{-2}+4z^{6}a^{-4}-21z^{6}-9a^{5}z^{5}-6a^{3}z^{5}+19az^{5}+14z^{5}a^{-1}+z^{5}a^{-3}+3z^{5}a^{-5}-2a^{6}z^{4}+7a^{4}z^{4}+27a^{2}z^{4}+5z^{4}a^{-2}-10z^{4}a^{-4}+33z^{4}+6a^{5}z^{3}+7a^{3}z^{3}-az^{3}-4z^{3}a^{-3}-6z^{3}a^{-5}+a^{6}z^{2}-2a^{4}z^{2}-15a^{2}z^{2}-2z^{2}a^{-2}+4z^{2}a^{-4}-18z^{2}-a^{5}z-3a^{3}z-3az-za^{-1}+2za^{-3}+2za^{-5}+a^{4}+4a^{2}-a^{-4}+5$

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