K13n1001

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13n1001

Polynomial invariants

Jones polynomial	Data:K13n1001/Jones Polynomial
Alexander polynomial	$t^{4}-4t^{3}+8t^{2}-11t+13-11t^{-1}+8t^{-2}-4t^{-3}+t^{-4}$
Conway polynomial	Data:K13n1001/Conway Polynomial
Determinant	61
Signature	4
HOMFLY-PT polynomial	$z^{8}a^{-2}+6z^{6}a^{-2}-z^{6}a^{-4}-z^{6}+12z^{4}a^{-2}-4z^{4}a^{-4}-4z^{4}+9z^{2}a^{-2}-4z^{2}a^{-4}-4z^{2}+2a^{-2}-a^{-4}$
Kauffman polynomial	$2z^{11}a^{-1}+2z^{11}a^{-3}+9z^{10}a^{-2}+6z^{10}a^{-4}+3z^{10}+az^{9}-7z^{9}a^{-1}-z^{9}a^{-3}+7z^{9}a^{-5}-53z^{8}a^{-2}-30z^{8}a^{-4}+4z^{8}a^{-6}-19z^{8}-6az^{7}-8z^{7}a^{-1}-40z^{7}a^{-3}-37z^{7}a^{-5}+z^{7}a^{-7}+97z^{6}a^{-2}+38z^{6}a^{-4}-19z^{6}a^{-6}+40z^{6}+12az^{5}+44z^{5}a^{-1}+90z^{5}a^{-3}+54z^{5}a^{-5}-4z^{5}a^{-7}-68z^{4}a^{-2}-15z^{4}a^{-4}+19z^{4}a^{-6}-34z^{4}-10az^{3}-41z^{3}a^{-1}-62z^{3}a^{-3}-31z^{3}a^{-5}+18z^{2}a^{-2}+4z^{2}a^{-4}-5z^{2}a^{-6}-z^{2}a^{-8}+10z^{2}+3az+10za^{-1}+13za^{-3}+7za^{-5}+za^{-7}-2a^{-2}-a^{-4}$

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