K13a2457

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a2457

Polynomial invariants

Jones polynomial	Data:K13a2457/Jones Polynomial
Alexander polynomial	$-t^{5}+6t^{4}-18t^{3}+36t^{2}-51t+57-51t^{-1}+36t^{-2}-18t^{-3}+6t^{-4}-t^{-5}$
Conway polynomial	Data:K13a2457/Conway Polynomial
Determinant	281
Signature	4
HOMFLY-PT polynomial	$-z^{10}a^{-4}+z^{8}a^{-2}-7z^{8}a^{-4}+2z^{8}a^{-6}+5z^{6}a^{-2}-20z^{6}a^{-4}+11z^{6}a^{-6}-z^{6}a^{-8}+9z^{4}a^{-2}-29z^{4}a^{-4}+22z^{4}a^{-6}-4z^{4}a^{-8}+8z^{2}a^{-2}-20z^{2}a^{-4}+19z^{2}a^{-6}-5z^{2}a^{-8}+3a^{-2}-5a^{-4}+5a^{-6}-2a^{-8}$
Kauffman polynomial	$2z^{12}a^{-4}+2z^{12}a^{-6}+6z^{11}a^{-3}+14z^{11}a^{-5}+8z^{11}a^{-7}+7z^{10}a^{-2}+14z^{10}a^{-4}+22z^{10}a^{-6}+15z^{10}a^{-8}+4z^{9}a^{-1}-12z^{9}a^{-3}-30z^{9}a^{-5}+3z^{9}a^{-7}+17z^{9}a^{-9}-26z^{8}a^{-2}-70z^{8}a^{-4}-84z^{8}a^{-6}-27z^{8}a^{-8}+14z^{8}a^{-10}+z^{8}-16z^{7}a^{-1}-12z^{7}a^{-3}-7z^{7}a^{-5}-51z^{7}a^{-7}-31z^{7}a^{-9}+9z^{7}a^{-11}+30z^{6}a^{-2}+97z^{6}a^{-4}+109z^{6}a^{-6}+22z^{6}a^{-8}-20z^{6}a^{-10}+4z^{6}a^{-12}-4z^{6}+20z^{5}a^{-1}+31z^{5}a^{-3}+46z^{5}a^{-5}+75z^{5}a^{-7}+28z^{5}a^{-9}-11z^{5}a^{-11}+z^{5}a^{-13}-16z^{4}a^{-2}-68z^{4}a^{-4}-78z^{4}a^{-6}-16z^{4}a^{-8}+11z^{4}a^{-10}-4z^{4}a^{-12}+5z^{4}-9z^{3}a^{-1}-16z^{3}a^{-3}-34z^{3}a^{-5}-49z^{3}a^{-7}-16z^{3}a^{-9}+5z^{3}a^{-11}-z^{3}a^{-13}+8z^{2}a^{-2}+30z^{2}a^{-4}+30z^{2}a^{-6}+8z^{2}a^{-8}-z^{2}a^{-10}+z^{2}a^{-12}-2z^{2}+za^{-1}+4za^{-3}+8za^{-5}+10za^{-7}+5za^{-9}-3a^{-2}-5a^{-4}-5a^{-6}-2a^{-8}$

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