K12a1099

Dowker-Thistlethwaite code

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

Jones polynomial	$-q+4-9q^{-1}+17q^{-2}-25q^{-3}+32q^{-4}-34q^{-5}+33q^{-6}-27q^{-7}+19q^{-8}-11q^{-9}+4q^{-10}-q^{-11}$
Alexander polynomial	$2t^{4}-10t^{3}+27t^{2}-44t+51-44t^{-1}+27t^{-2}-10t^{-3}+2t^{-4}$
Conway polynomial	$2z^{8}+6z^{6}+7z^{4}+6z^{2}+1$
Determinant	217
Signature	-4
HOMFLY-PT polynomial	$-z^{6}a^{8}-3z^{4}a^{8}-4z^{2}a^{8}-3a^{8}+z^{8}a^{6}+4z^{6}a^{6}+7z^{4}a^{6}+8z^{2}a^{6}+4a^{6}+z^{8}a^{4}+4z^{6}a^{4}+6z^{4}a^{4}+4z^{2}a^{4}-z^{6}a^{2}-3z^{4}a^{2}-2z^{2}a^{2}$
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 z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-3 z^4 a^{12}+10 z^7 a^{11}-14 z^5 a^{11}+10 z^3 a^{11}-4 z a^{11}+15 z^8 a^{10}-24 z^6 a^{10}+16 z^4 a^{10}-4 z^2 a^{10}+15 z^9 a^9-22 z^7 a^9+9 z^5 a^9+z^3 a^9+10 z^{10} a^8-8 z^8 a^8-4 z^6 a^8-4 z^4 a^8+10 z^2 a^8-3 a^8+3 z^{11} a^7+17 z^9 a^7-55 z^7 a^7+58 z^5 a^7-33 z^3 a^7+8 z a^7+17 z^{10} a^6-42 z^8 a^6+41 z^6 a^6-30 z^4 a^6+15 z^2 a^6-4 a^6+3 z^{11} a^5+9 z^9 a^5-45 z^7 a^5+56 z^5 a^5-32 z^3 a^5+6 z a^5+7 z^{10} a^4-15 z^8 a^4+4 z^6 a^4+5 z^4 a^4-2 z^2 a^4+7 z^9 a^3-21 z^7 a^3+19 z^5 a^3-7 z^3 a^3+2 z a^3+4 z^8 a^2-13 z^6 a^2+12 z^4 a^2-3 z^2 a^2+z^7 a-3 z^5 a+2 z^3 a}