K12a621

Dowker-Thistlethwaite code

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

Jones polynomial	$-q^{4}+4q^{3}-9q^{2}+15q-21+26q^{-1}-27q^{-2}+26q^{-3}-20q^{-4}+14q^{-5}-8q^{-6}+3q^{-7}-q^{-8}$
Alexander polynomial	$-t^{4}+8t^{3}-22t^{2}+36t-41+36t^{-1}-22t^{-2}+8t^{-3}-t^{-4}$
Conway polynomial	$-z^{8}+6z^{4}+4z^{2}+1$
Determinant	175
Signature	-2
HOMFLY-PT polynomial	$-a^{2}z^{8}+2a^{4}z^{6}-4a^{2}z^{6}+2z^{6}-a^{6}z^{4}+7a^{4}z^{4}-5a^{2}z^{4}-z^{4}a^{-2}+6z^{4}-3a^{6}z^{2}+7a^{4}z^{2}-a^{2}z^{2}-2z^{2}a^{-2}+3z^{2}-2a^{6}+2a^{4}+2a^{2}-1$
Kauffman polynomial	$2a^{3}z^{11}+2az^{11}+6a^{4}z^{10}+12a^{2}z^{10}+6z^{10}+8a^{5}z^{9}+11a^{3}z^{9}+10az^{9}+7z^{9}a^{-1}+8a^{6}z^{8}-6a^{4}z^{8}-31a^{2}z^{8}+4z^{8}a^{-2}-13z^{8}+6a^{7}z^{7}-11a^{5}z^{7}-42a^{3}z^{7}-49az^{7}-23z^{7}a^{-1}+z^{7}a^{-3}+3a^{8}z^{6}-12a^{6}z^{6}+27a^{2}z^{6}-13z^{6}a^{-2}-z^{6}+a^{9}z^{5}-9a^{7}z^{5}+7a^{5}z^{5}+55a^{3}z^{5}+63az^{5}+22z^{5}a^{-1}-3z^{5}a^{-3}-4a^{8}z^{4}+10a^{6}z^{4}+3a^{4}z^{4}-14a^{2}z^{4}+11z^{4}a^{-2}+8z^{4}-2a^{9}z^{3}+6a^{7}z^{3}-a^{5}z^{3}-33a^{3}z^{3}-36az^{3}-10z^{3}a^{-1}+2z^{3}a^{-3}+a^{8}z^{2}-6a^{6}z^{2}-3a^{4}z^{2}+7a^{2}z^{2}-3z^{2}a^{-2}+a^{9}z-2a^{7}z-a^{5}z+7a^{3}z+8az+3za^{-1}+2a^{6}+2a^{4}-2a^{2}-1$