K12a337

Dowker-Thistlethwaite code

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

Jones polynomial	$q^{9}-5q^{8}+12q^{7}-22q^{6}+32q^{5}-39q^{4}+42q^{3}-38q^{2}+31q-21+11q^{-1}-4q^{-2}+q^{-3}$
Alexander polynomial	$3t^{3}-22t^{2}+62t-85+62t^{-1}-22t^{-2}+3t^{-3}$
Conway 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 z^6-4 z^4+z^2+1}
Determinant	259
Signature	2
HOMFLY-PT polynomial	$z^{6}a^{-2}+2z^{6}a^{-4}-3z^{4}a^{-2}+4z^{4}a^{-4}-3z^{4}a^{-6}-2z^{4}+a^{2}z^{2}-7z^{2}a^{-2}+8z^{2}a^{-4}-3z^{2}a^{-6}+z^{2}a^{-8}+z^{2}-4a^{-2}+5a^{-4}-2a^{-6}+2$
Kauffman polynomial	$3z^{11}a^{-3}+3z^{11}a^{-5}+10z^{10}a^{-2}+20z^{10}a^{-4}+10z^{10}a^{-6}+13z^{9}a^{-1}+26z^{9}a^{-3}+27z^{9}a^{-5}+14z^{9}a^{-7}-5z^{8}a^{-2}-24z^{8}a^{-4}+z^{8}a^{-6}+11z^{8}a^{-8}+9z^{8}+4az^{7}-26z^{7}a^{-1}-77z^{7}a^{-3}-74z^{7}a^{-5}-22z^{7}a^{-7}+5z^{7}a^{-9}+a^{2}z^{6}-22z^{6}a^{-2}-20z^{6}a^{-4}-37z^{6}a^{-6}-20z^{6}a^{-8}+z^{6}a^{-10}-17z^{6}-7az^{5}+25z^{5}a^{-1}+81z^{5}a^{-3}+63z^{5}a^{-5}+6z^{5}a^{-7}-8z^{5}a^{-9}-2a^{2}z^{4}+34z^{4}a^{-2}+44z^{4}a^{-4}+37z^{4}a^{-6}+11z^{4}a^{-8}-z^{4}a^{-10}+13z^{4}+3az^{3}-16z^{3}a^{-1}-38z^{3}a^{-3}-20z^{3}a^{-5}+2z^{3}a^{-7}+3z^{3}a^{-9}+a^{2}z^{2}-21z^{2}a^{-2}-23z^{2}a^{-4}-13z^{2}a^{-6}-3z^{2}a^{-8}-7z^{2}+3za^{-1}+6za^{-3}+2za^{-5}-za^{-7}+4a^{-2}+5a^{-4}+2a^{-6}+2$