K13n4002

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13n4002

Polynomial invariants

Jones polynomial	Data:K13n4002/Jones Polynomial
Alexander polynomial	$t^{4}-4t^{3}+8t^{2}-10t+11-10t^{-1}+8t^{-2}-4t^{-3}+t^{-4}$
Conway polynomial	Data:K13n4002/Conway Polynomial
Determinant	57
Signature	0
HOMFLY-PT polynomial	$z^{8}a^{-2}+5z^{6}a^{-2}-z^{6}a^{-4}-a^{2}z^{4}+7z^{4}a^{-2}-3z^{4}a^{-4}+z^{4}-2a^{2}z^{2}+3z^{2}a^{-2}-2z^{2}a^{-4}+3z^{2}-a^{2}+a^{-2}-a^{-4}+2$
Kauffman polynomial	$z^{11}a^{-1}+z^{11}a^{-3}+5z^{10}a^{-2}+4z^{10}a^{-4}+z^{10}+az^{9}-3z^{9}a^{-1}+2z^{9}a^{-3}+6z^{9}a^{-5}+2a^{2}z^{8}-26z^{8}a^{-2}-14z^{8}a^{-4}+4z^{8}a^{-6}-6z^{8}+a^{3}z^{7}-7az^{7}-8z^{7}a^{-1}-24z^{7}a^{-3}-23z^{7}a^{-5}+z^{7}a^{-7}-12a^{2}z^{6}+37z^{6}a^{-2}+9z^{6}a^{-4}-14z^{6}a^{-6}+2z^{6}-5a^{3}z^{5}+5az^{5}+20z^{5}a^{-1}+33z^{5}a^{-3}+20z^{5}a^{-5}-3z^{5}a^{-7}+15a^{2}z^{4}-17z^{4}a^{-2}-5z^{4}a^{-4}+10z^{4}a^{-6}+13z^{4}+5a^{3}z^{3}+7az^{3}-4z^{3}a^{-1}-15z^{3}a^{-3}-7z^{3}a^{-5}+2z^{3}a^{-7}-6a^{2}z^{2}+2z^{2}a^{-2}+3z^{2}a^{-4}-z^{2}a^{-6}-8z^{2}-2a^{3}z-4az-2za^{-1}+2za^{-3}+2za^{-5}+a^{2}-a^{-2}-a^{-4}+2$

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