K12a418

Dowker-Thistlethwaite code

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

Jones polynomial	$-q^{4}+5q^{3}-12q^{2}+21q-30+37q^{-1}-39q^{-2}+37q^{-3}-29q^{-4}+20q^{-5}-11q^{-6}+4q^{-7}-q^{-8}$
Alexander polynomial	$-t^{4}+8t^{3}-27t^{2}+54t-67+54t^{-1}-27t^{-2}+8t^{-3}-t^{-4}$
Conway polynomial	$-z^{8}+z^{4}+2z^{2}+1$
Determinant	247
Signature	-2
HOMFLY-PT polynomial	$-a^{2}z^{8}+2a^{4}z^{6}-4a^{2}z^{6}+2z^{6}-a^{6}z^{4}+6a^{4}z^{4}-8a^{2}z^{4}-z^{4}a^{-2}+5z^{4}-2a^{6}z^{2}+8a^{4}z^{2}-7a^{2}z^{2}-z^{2}a^{-2}+4z^{2}-2a^{6}+4a^{4}-2a^{2}+1$
Kauffman polynomial	$3a^{3}z^{11}+3az^{11}+11a^{4}z^{10}+20a^{2}z^{10}+9z^{10}+17a^{5}z^{9}+29a^{3}z^{9}+22az^{9}+10z^{9}a^{-1}+16a^{6}z^{8}+a^{4}z^{8}-31a^{2}z^{8}+5z^{8}a^{-2}-11z^{8}+10a^{7}z^{7}-25a^{5}z^{7}-89a^{3}z^{7}-82az^{7}-27z^{7}a^{-1}+z^{7}a^{-3}+4a^{8}z^{6}-26a^{6}z^{6}-41a^{4}z^{6}-20a^{2}z^{6}-13z^{6}a^{-2}-22z^{6}+a^{9}z^{5}-13a^{7}z^{5}+12a^{5}z^{5}+84a^{3}z^{5}+81az^{5}+21z^{5}a^{-1}-2z^{5}a^{-3}-3a^{8}z^{4}+22a^{6}z^{4}+47a^{4}z^{4}+45a^{2}z^{4}+10z^{4}a^{-2}+33z^{4}-a^{9}z^{3}+9a^{7}z^{3}+a^{5}z^{3}-33a^{3}z^{3}-31az^{3}-6z^{3}a^{-1}+z^{3}a^{-3}-10a^{6}z^{2}-21a^{4}z^{2}-19a^{2}z^{2}-3z^{2}a^{-2}-11z^{2}-3a^{7}z-2a^{5}z+4a^{3}z+4az+za^{-1}+2a^{6}+4a^{4}+2a^{2}+1$