K12a1057

Dowker-Thistlethwaite code

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

Jones polynomial	$-q^{7}+5q^{6}-13q^{5}+22q^{4}-31q^{3}+38q^{2}-39q+37-29q^{-1}+19q^{-2}-10q^{-3}+4q^{-4}-q^{-5}$
Alexander polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3 t^3+22 t^2-59 t+81-59 t^{-1} +22 t^{-2} -3 t^{-3} }
Conway polynomial	$-3z^{6}+4z^{4}+2z^{2}+1$
Determinant	249
Signature	0
HOMFLY-PT polynomial	$-2z^{6}a^{-2}-z^{6}+2a^{2}z^{4}-3z^{4}a^{-2}+3z^{4}a^{-4}+2z^{4}-a^{4}z^{2}-2z^{2}a^{-2}+2z^{2}a^{-4}-z^{2}a^{-6}+4z^{2}-a^{2}+a^{-2}-a^{-4}+2$
Kauffman polynomial	$4z^{11}a^{-1}+4z^{11}a^{-3}+23z^{10}a^{-2}+11z^{10}a^{-4}+12z^{10}+16az^{9}+23z^{9}a^{-1}+18z^{9}a^{-3}+11z^{9}a^{-5}+14a^{2}z^{8}-48z^{8}a^{-2}-21z^{8}a^{-4}+5z^{8}a^{-6}-8z^{8}+9a^{3}z^{7}-24az^{7}-78z^{7}a^{-1}-76z^{7}a^{-3}-30z^{7}a^{-5}+z^{7}a^{-7}+4a^{4}z^{6}-20a^{2}z^{6}+14z^{6}a^{-2}-2z^{6}a^{-4}-12z^{6}a^{-6}-20z^{6}+a^{5}z^{5}-11a^{3}z^{5}+14az^{5}+75z^{5}a^{-1}+75z^{5}a^{-3}+24z^{5}a^{-5}-2z^{5}a^{-7}-4a^{4}z^{4}+14a^{2}z^{4}+14z^{4}a^{-2}+12z^{4}a^{-4}+8z^{4}a^{-6}+28z^{4}-a^{5}z^{3}+6a^{3}z^{3}-2az^{3}-29z^{3}a^{-1}-30z^{3}a^{-3}-9z^{3}a^{-5}+z^{3}a^{-7}+a^{4}z^{2}-5a^{2}z^{2}-6z^{2}a^{-2}-2z^{2}a^{-4}-2z^{2}a^{-6}-12z^{2}-a^{3}z+4za^{-1}+6za^{-3}+3za^{-5}+a^{2}-a^{-2}-a^{-4}+2$