K12a67

Dowker-Thistlethwaite code

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

Jones polynomial	$-q^{4}+4q^{3}-9q^{2}+18q-26+32q^{-1}-35q^{-2}+33q^{-3}-27q^{-4}+19q^{-5}-10q^{-6}+4q^{-7}-q^{-8}$
Alexander polynomial	$-t^{4}+8t^{3}-26t^{2}+47t-55+47t^{-1}-26t^{-2}+8t^{-3}-t^{-4}$
Conway polynomial	$-z^{8}+2z^{4}-z^{2}+1$
Determinant	219
Signature	-2
HOMFLY-PT polynomial	$-a^{2}z^{8}+2a^{4}z^{6}-4a^{2}z^{6}+2z^{6}-a^{6}z^{4}+6a^{4}z^{4}-8a^{2}z^{4}-z^{4}a^{-2}+6z^{4}-2a^{6}z^{2}+7a^{4}z^{2}-10a^{2}z^{2}-2z^{2}a^{-2}+6z^{2}-a^{6}+4a^{4}-5a^{2}+3$
Kauffman polynomial	$2a^{3}z^{11}+2az^{11}+8a^{4}z^{10}+14a^{2}z^{10}+6z^{10}+14a^{5}z^{9}+24a^{3}z^{9}+17az^{9}+7z^{9}a^{-1}+14a^{6}z^{8}+8a^{4}z^{8}-15a^{2}z^{8}+4z^{8}a^{-2}-5z^{8}+9a^{7}z^{7}-18a^{5}z^{7}-66a^{3}z^{7}-60az^{7}-20z^{7}a^{-1}+z^{7}a^{-3}+4a^{8}z^{6}-22a^{6}z^{6}-48a^{4}z^{6}-33a^{2}z^{6}-13z^{6}a^{-2}-24z^{6}+a^{9}z^{5}-11a^{7}z^{5}+6a^{5}z^{5}+58a^{3}z^{5}+61az^{5}+18z^{5}a^{-1}-3z^{5}a^{-3}-4a^{8}z^{4}+18a^{6}z^{4}+53a^{4}z^{4}+56a^{2}z^{4}+14z^{4}a^{-2}+39z^{4}-a^{9}z^{3}+6a^{7}z^{3}+a^{5}z^{3}-26a^{3}z^{3}-29az^{3}-7z^{3}a^{-1}+2z^{3}a^{-3}+a^{8}z^{2}-7a^{6}z^{2}-25a^{4}z^{2}-31a^{2}z^{2}-6z^{2}a^{-2}-20z^{2}-a^{7}z+6a^{3}z+7az+2za^{-1}+a^{6}+4a^{4}+5a^{2}+3$