K13n520

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13n520

Polynomial invariants

Jones polynomial	Data:K13n520/Jones Polynomial
Alexander polynomial	$-t^{4}+7t^{3}-22t^{2}+41t-49+41t^{-1}-22t^{-2}+7t^{-3}-t^{-4}$
Conway polynomial	Data:K13n520/Conway Polynomial
Determinant	191
Signature	2
HOMFLY-PT polynomial	$-z^{8}a^{-4}+2z^{6}a^{-2}-4z^{6}a^{-4}+z^{6}a^{-6}+5z^{4}a^{-2}-6z^{4}a^{-4}+2z^{4}a^{-6}-z^{4}+3z^{2}a^{-2}-3z^{2}a^{-4}+z^{2}a^{-6}-z^{2}+1$
Kauffman polynomial	$2z^{11}a^{-3}+2z^{11}a^{-5}+4z^{10}a^{-2}+12z^{10}a^{-4}+8z^{10}a^{-6}+2z^{9}a^{-1}+6z^{9}a^{-3}+17z^{9}a^{-5}+13z^{9}a^{-7}-10z^{8}a^{-2}-24z^{8}a^{-4}-3z^{8}a^{-6}+11z^{8}a^{-8}-2z^{7}a^{-1}-23z^{7}a^{-3}-51z^{7}a^{-5}-25z^{7}a^{-7}+5z^{7}a^{-9}+25z^{6}a^{-2}+20z^{6}a^{-4}-23z^{6}a^{-6}-22z^{6}a^{-8}+z^{6}a^{-10}+5z^{6}+az^{5}+10z^{5}a^{-1}+42z^{5}a^{-3}+51z^{5}a^{-5}+10z^{5}a^{-7}-8z^{5}a^{-9}-21z^{4}a^{-2}-4z^{4}a^{-4}+20z^{4}a^{-6}+10z^{4}a^{-8}-z^{4}a^{-10}-8z^{4}-2az^{3}-14z^{3}a^{-1}-29z^{3}a^{-3}-22z^{3}a^{-5}-3z^{3}a^{-7}+2z^{3}a^{-9}+4z^{2}a^{-2}-4z^{2}a^{-6}-2z^{2}a^{-8}+2z^{2}+az+4za^{-1}+6za^{-3}+4za^{-5}+za^{-7}+1$

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