K12n565

Dowker-Thistlethwaite code

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

Jones polynomial	$q^{2}-2q+3-5q^{-1}+7q^{-2}-6q^{-3}+7q^{-4}-6q^{-5}+4q^{-6}-3q^{-7}+q^{-8}$
Alexander polynomial	$-2t^{3}+7t^{2}-9t+9-9t^{-1}+7t^{-2}-2t^{-3}$
Conway polynomial	$-2z^{6}-5z^{4}+z^{2}+1$
Determinant	45
Signature	-4
HOMFLY-PT polynomial	$z^{4}a^{6}+2z^{2}a^{6}-a^{6}-z^{6}a^{4}-3z^{4}a^{4}+2a^{4}-z^{6}a^{2}-4z^{4}a^{2}-4z^{2}a^{2}-a^{2}+z^{4}+3z^{2}+1$
Kauffman polynomial	$z^{2}a^{10}+3z^{3}a^{9}-za^{9}+z^{6}a^{8}+z^{2}a^{8}+2z^{7}a^{7}-4z^{5}a^{7}+4z^{3}a^{7}-3za^{7}+2z^{8}a^{6}-3z^{6}a^{6}-4z^{4}a^{6}+3z^{2}a^{6}+a^{6}+2z^{9}a^{5}-6z^{7}a^{5}+5z^{5}a^{5}-5z^{3}a^{5}+z^{10}a^{4}-2z^{8}a^{4}-z^{6}a^{4}-3z^{4}a^{4}+3z^{2}a^{4}+2a^{4}+4z^{9}a^{3}-20z^{7}a^{3}+32z^{5}a^{3}-21z^{3}a^{3}+4za^{3}+z^{10}a^{2}-3z^{8}a^{2}-3z^{6}a^{2}+12z^{4}a^{2}-6z^{2}a^{2}+a^{2}+2z^{9}a-12z^{7}a+23z^{5}a-15z^{3}a+2za+z^{8}-6z^{6}+11z^{4}-6z^{2}+1$