K14a15311

Knot presentations

Dowker-Thistlethwaite code

6 12 16 28 22 18 4 24 2 10 26 14 8 20

Polynomial invariants

Jones polynomial	Data:K14a15311/Jones Polynomial
Alexander polynomial	$3t^{4}-21t^{3}+63t^{2}-117t+145-117t^{-1}+63t^{-2}-21t^{-3}+3t^{-4}$
Conway polynomial	Data:K14a15311/Conway Polynomial
Determinant	Data:K14a15311/Determinant
Signature	Data:K14a15311/Signature
HOMFLY-PT polynomial	$2z^{8}a^{-2}+z^{8}-2a^{2}z^{6}+7z^{6}a^{-2}-3z^{6}a^{-4}+z^{6}+a^{4}z^{4}-5a^{2}z^{4}+10z^{4}a^{-2}-8z^{4}a^{-4}+z^{4}a^{-6}-2z^{4}+2a^{4}z^{2}-4a^{2}z^{2}+6z^{2}a^{-2}-8z^{2}a^{-4}+2z^{2}a^{-6}-4z^{2}+a^{4}+2a^{-2}-3a^{-4}+2a^{-6}-1$
Kauffman polynomial	$4z^{13}a^{-1}+4z^{13}a^{-3}+26z^{12}a^{-2}+13z^{12}a^{-4}+13z^{12}+20az^{11}+32z^{11}a^{-1}+30z^{11}a^{-3}+18z^{11}a^{-5}+20a^{2}z^{10}-46z^{10}a^{-2}-12z^{10}a^{-4}+13z^{10}a^{-6}-z^{10}+15a^{3}z^{9}-34az^{9}-108z^{9}a^{-1}-114z^{9}a^{-3}-50z^{9}a^{-5}+5z^{9}a^{-7}+9a^{4}z^{8}-38a^{2}z^{8}-19z^{8}a^{-2}-51z^{8}a^{-4}-40z^{8}a^{-6}+z^{8}a^{-8}-56z^{8}+4a^{5}z^{7}-26a^{3}z^{7}+17az^{7}+107z^{7}a^{-1}+115z^{7}a^{-3}+41z^{7}a^{-5}-14z^{7}a^{-7}+a^{6}z^{6}-15a^{4}z^{6}+33a^{2}z^{6}+69z^{6}a^{-2}+82z^{6}a^{-4}+43z^{6}a^{-6}-3z^{6}a^{-8}+82z^{6}-7a^{5}z^{5}+20a^{3}z^{5}+11az^{5}-35z^{5}a^{-1}-52z^{5}a^{-3}-21z^{5}a^{-5}+12z^{5}a^{-7}-2a^{6}z^{4}+9a^{4}z^{4}-10a^{2}z^{4}-44z^{4}a^{-2}-58z^{4}a^{-4}-28z^{4}a^{-6}+3z^{4}a^{-8}-38z^{4}+3a^{5}z^{3}-9a^{3}z^{3}-7az^{3}+2z^{3}a^{-1}+12z^{3}a^{-3}+12z^{3}a^{-5}-3z^{3}a^{-7}+a^{6}z^{2}-4a^{4}z^{2}-a^{2}z^{2}+12z^{2}a^{-2}+22z^{2}a^{-4}+14z^{2}a^{-6}-z^{2}a^{-8}+9z^{2}+a^{3}z+az+za^{-1}-3za^{-3}-4za^{-5}+a^{4}-2a^{-2}-3a^{-4}-2a^{-6}-1$