K12a256

Dowker-Thistlethwaite code

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

Jones polynomial	$q^{9}-4q^{8}+10q^{7}-18q^{6}+26q^{5}-33q^{4}+35q^{3}-32q^{2}+27q-18+10q^{-1}-4q^{-2}+q^{-3}$
Alexander polynomial	$3t^{3}-20t^{2}+52t-69+52t^{-1}-20t^{-2}+3t^{-3}$
Conway polynomial	$3z^{6}-2z^{4}-z^{2}+1$
Determinant	219
Signature	2
HOMFLY-PT polynomial	$z^{6}a^{-2}+2z^{6}a^{-4}-2z^{4}a^{-2}+5z^{4}a^{-4}-3z^{4}a^{-6}-2z^{4}+a^{2}z^{2}-6z^{2}a^{-2}+8z^{2}a^{-4}-5z^{2}a^{-6}+z^{2}a^{-8}-3a^{-2}+4a^{-4}-3a^{-6}+a^{-8}+2$
Kauffman 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 2 z^{11} a^{-3} +2 z^{11} a^{-5} +7 z^{10} a^{-2} +14 z^{10} a^{-4} +7 z^{10} a^{-6} +10 z^9 a^{-1} +20 z^9 a^{-3} +20 z^9 a^{-5} +10 z^9 a^{-7} -16 z^8 a^{-4} +8 z^8 a^{-8} +8 z^8+4 a z^7-18 z^7 a^{-1} -59 z^7 a^{-3} -59 z^7 a^{-5} -18 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-26 z^6 a^{-2} -19 z^6 a^{-4} -27 z^6 a^{-6} -16 z^6 a^{-8} +z^6 a^{-10} -16 z^6-8 a z^5+12 z^5 a^{-1} +64 z^5 a^{-3} +62 z^5 a^{-5} +10 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+35 z^4 a^{-2} +45 z^4 a^{-4} +35 z^4 a^{-6} +10 z^4 a^{-8} -2 z^4 a^{-10} +11 z^4+4 a z^3-8 z^3 a^{-1} -31 z^3 a^{-3} -27 z^3 a^{-5} -4 z^3 a^{-7} +4 z^3 a^{-9} +a^2 z^2-21 z^2 a^{-2} -25 z^2 a^{-4} -17 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} -6 z^2+2 z a^{-1} +6 z a^{-3} +6 z a^{-5} +z a^{-7} -z a^{-9} +3 a^{-2} +4 a^{-4} +3 a^{-6} + a^{-8} +2}