K12a218

Dowker-Thistlethwaite code

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

Jones polynomial	$q^{9}-3q^{8}+7q^{7}-14q^{6}+20q^{5}-25q^{4}+28q^{3}-26q^{2}+22q-15+9q^{-1}-4q^{-2}+q^{-3}$
Alexander polynomial	$2t^{3}-15t^{2}+42t-57+42t^{-1}-15t^{-2}+2t^{-3}$
Conway polynomial	$2z^{6}-3z^{4}+1$
Determinant	175
Signature	2
HOMFLY-PT polynomial	$z^{6}a^{-2}+z^{6}a^{-4}+z^{4}a^{-4}-2z^{4}a^{-6}-2z^{4}+a^{2}z^{2}-z^{2}a^{-2}+3z^{2}a^{-4}-3z^{2}a^{-6}+z^{2}a^{-8}-z^{2}-a^{-2}+3a^{-4}-3a^{-6}+a^{-8}+1$
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 z^{11} a^{-3} +z^{11} a^{-5} +4 z^{10} a^{-2} +8 z^{10} a^{-4} +4 z^{10} a^{-6} +7 z^9 a^{-1} +14 z^9 a^{-3} +13 z^9 a^{-5} +6 z^9 a^{-7} +5 z^8 a^{-2} -7 z^8 a^{-4} +5 z^8 a^{-8} +7 z^8+4 a z^7-10 z^7 a^{-1} -37 z^7 a^{-3} -38 z^7 a^{-5} -12 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6-25 z^6 a^{-2} -11 z^6 a^{-4} -14 z^6 a^{-6} -11 z^6 a^{-8} +z^6 a^{-10} -15 z^6-9 a z^5+z^5 a^{-1} +40 z^5 a^{-3} +47 z^5 a^{-5} +9 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+23 z^4 a^{-2} +23 z^4 a^{-4} +21 z^4 a^{-6} +7 z^4 a^{-8} -3 z^4 a^{-10} +9 z^4+5 a z^3-2 z^3 a^{-1} -23 z^3 a^{-3} -24 z^3 a^{-5} -2 z^3 a^{-7} +6 z^3 a^{-9} +a^2 z^2-10 z^2 a^{-2} -13 z^2 a^{-4} -12 z^2 a^{-6} -3 z^2 a^{-8} +2 z^2 a^{-10} -3 z^2+2 z a^{-1} +6 z a^{-3} +4 z a^{-5} -2 z a^{-7} -2 z a^{-9} + a^{-2} +3 a^{-4} +3 a^{-6} + a^{-8} +1}