K13a3051

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a3051

Polynomial invariants

Jones polynomial	Data:K13a3051/Jones Polynomial
Alexander polynomial	$-2t^{4}+16t^{3}-55t^{2}+108t-133+108t^{-1}-55t^{-2}+16t^{-3}-2t^{-4}$
Conway polynomial	Data:K13a3051/Conway Polynomial
Determinant	495
Signature	2
HOMFLY-PT polynomial	$-z^{8}a^{-2}-z^{8}a^{-4}-3z^{6}a^{-2}+2z^{6}a^{-6}+z^{6}-7z^{4}a^{-2}+6z^{4}a^{-4}+z^{4}a^{-6}-z^{4}a^{-8}+2z^{4}-7z^{2}a^{-2}+9z^{2}a^{-4}-4z^{2}a^{-6}+2z^{2}-a^{-2}+3a^{-4}-3a^{-6}+a^{-8}+1$
Kauffman polynomial	$5z^{12}a^{-4}+5z^{12}a^{-6}+17z^{11}a^{-3}+34z^{11}a^{-5}+17z^{11}a^{-7}+25z^{10}a^{-2}+50z^{10}a^{-4}+48z^{10}a^{-6}+23z^{10}a^{-8}+22z^{9}a^{-1}+12z^{9}a^{-3}-26z^{9}a^{-5}+16z^{9}a^{-9}-29z^{8}a^{-2}-121z^{8}a^{-4}-128z^{8}a^{-6}-43z^{8}a^{-8}+6z^{8}a^{-10}+13z^{8}+5az^{7}-34z^{7}a^{-1}-84z^{7}a^{-3}-81z^{7}a^{-5}-70z^{7}a^{-7}-33z^{7}a^{-9}+z^{7}a^{-11}+a^{2}z^{6}-5z^{6}a^{-2}+69z^{6}a^{-4}+82z^{6}a^{-6}+18z^{6}a^{-8}-10z^{6}a^{-10}-19z^{6}-6az^{5}+24z^{5}a^{-1}+90z^{5}a^{-3}+106z^{5}a^{-5}+70z^{5}a^{-7}+23z^{5}a^{-9}-z^{5}a^{-11}-a^{2}z^{4}+30z^{4}a^{-2}+11z^{4}a^{-4}-7z^{4}a^{-6}+3z^{4}a^{-8}+5z^{4}a^{-10}+13z^{4}+2az^{3}-8z^{3}a^{-1}-38z^{3}a^{-3}-49z^{3}a^{-5}-26z^{3}a^{-7}-5z^{3}a^{-9}-16z^{2}a^{-2}-19z^{2}a^{-4}-11z^{2}a^{-6}-3z^{2}a^{-8}-5z^{2}+2za^{-1}+8za^{-3}+10za^{-5}+4za^{-7}+a^{-2}+3a^{-4}+3a^{-6}+a^{-8}+1$

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