K12a582

Dowker-Thistlethwaite code

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

Jones polynomial	$-q^{2}+3q-6+11q^{-1}-15q^{-2}+19q^{-3}-20q^{-4}+19q^{-5}-15q^{-6}+11q^{-7}-7q^{-8}+3q^{-9}-q^{-10}$
Alexander polynomial	$4t^{3}-15t^{2}+29t-35+29t^{-1}-15t^{-2}+4t^{-3}$
Conway polynomial	$4z^{6}+9z^{4}+5z^{2}+1$
Determinant	131
Signature	-2
HOMFLY-PT polynomial	$-z^{4}a^{8}-2z^{2}a^{8}-a^{8}+z^{6}a^{6}+2z^{4}a^{6}-a^{6}+2z^{6}a^{4}+7z^{4}a^{4}+9z^{2}a^{4}+4a^{4}+z^{6}a^{2}+2z^{4}a^{2}-a^{2}-z^{4}-2z^{2}$
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^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-11 z^6 a^{10}+11 z^4 a^{10}-3 z^2 a^{10}+4 z^9 a^9-12 z^7 a^9+7 z^5 a^9+z a^9+3 z^{10} a^8-5 z^8 a^8-4 z^6 a^8+2 z^4 a^8+4 z^2 a^8-a^8+z^{11} a^7+5 z^9 a^7-21 z^7 a^7+22 z^5 a^7-14 z^3 a^7+4 z a^7+6 z^{10} a^6-14 z^8 a^6+10 z^6 a^6-2 z^4 a^6-3 z^2 a^6+a^6+z^{11} a^5+6 z^9 a^5-21 z^7 a^5+27 z^5 a^5-14 z^3 a^5+z a^5+3 z^{10} a^4-13 z^6 a^4+27 z^4 a^4-18 z^2 a^4+4 a^4+5 z^9 a^3-8 z^7 a^3+5 z^5 a^3+3 z^3 a^3-z a^3+6 z^8 a^2-13 z^6 a^2+14 z^4 a^2-6 z^2 a^2+a^2+5 z^7 a-10 z^5 a+6 z^3 a-z a+3 z^6-6 z^4+2 z^2+z^5 a^{-1} -2 z^3 a^{-1} }