K12a109

Dowker-Thistlethwaite code

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

Jones polynomial	$-q^{5}+3q^{4}-7q^{3}+13q^{2}-18q+22-23q^{-1}+22q^{-2}-17q^{-3}+12q^{-4}-7q^{-5}+3q^{-6}-q^{-7}$
Alexander polynomial	$-2t^{3}+14t^{2}-35t+47-35t^{-1}+14t^{-2}-2t^{-3}$
Conway polynomial	$-2z^{6}+2z^{4}+3z^{2}+1$
Determinant	149
Signature	0
HOMFLY-PT polynomial	$-z^{2}a^{6}-a^{6}+2z^{4}a^{4}+3z^{2}a^{4}+a^{4}-z^{6}a^{2}-z^{4}a^{2}+a^{2}-z^{6}-z^{4}-z^{2}-1+2z^{4}a^{-2}+3z^{2}a^{-2}+2a^{-2}-z^{2}a^{-4}-a^{-4}$
Kauffman polynomial	$a^{3}z^{11}+az^{11}+4a^{4}z^{10}+8a^{2}z^{10}+4z^{10}+5a^{5}z^{9}+11a^{3}z^{9}+12az^{9}+6z^{9}a^{-1}+3a^{6}z^{8}-8a^{4}z^{8}-18a^{2}z^{8}+6z^{8}a^{-2}-z^{8}+a^{7}z^{7}-18a^{5}z^{7}-51a^{3}z^{7}-44az^{7}-7z^{7}a^{-1}+5z^{7}a^{-3}-11a^{6}z^{6}-6a^{4}z^{6}+7a^{2}z^{6}-5z^{6}a^{-2}+3z^{6}a^{-4}-6z^{6}-4a^{7}z^{5}+20a^{5}z^{5}+75a^{3}z^{5}+64az^{5}+6z^{5}a^{-1}-6z^{5}a^{-3}+z^{5}a^{-5}+11a^{6}z^{4}+16a^{4}z^{4}+8a^{2}z^{4}-3z^{4}a^{-2}-5z^{4}a^{-4}+5z^{4}+4a^{7}z^{3}-12a^{5}z^{3}-49a^{3}z^{3}-43az^{3}-7z^{3}a^{-1}+z^{3}a^{-3}-2z^{3}a^{-5}-5a^{6}z^{2}-8a^{4}z^{2}-4a^{2}z^{2}+5z^{2}a^{-2}+3z^{2}a^{-4}+z^{2}-a^{7}z+4a^{5}z+12a^{3}z+10az+3za^{-1}+za^{-3}+za^{-5}+a^{6}+a^{4}-a^{2}-2a^{-2}-a^{-4}-1$