K12a609

Dowker-Thistlethwaite code

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

Jones polynomial	$-q^{2}+4q-10+19q^{-1}-27q^{-2}+34q^{-3}-35q^{-4}+33q^{-5}-27q^{-6}+18q^{-7}-10q^{-8}+4q^{-9}-q^{-10}$
Alexander polynomial	$5t^{3}-23t^{2}+51t-65+51t^{-1}-23t^{-2}+5t^{-3}$
Conway polynomial	$5z^{6}+7z^{4}+4z^{2}+1$
Determinant	223
Signature	-2
HOMFLY-PT polynomial	$-z^{4}a^{8}-z^{2}a^{8}+z^{6}a^{6}-3z^{2}a^{6}-3a^{6}+3z^{6}a^{4}+9z^{4}a^{4}+11z^{2}a^{4}+5a^{4}+z^{6}a^{2}-2z^{2}a^{2}-a^{2}-z^{4}-z^{2}$
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}-3 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-12 z^6 a^{10}+12 z^4 a^{10}-4 z^2 a^{10}+7 z^9 a^9-18 z^7 a^9+13 z^5 a^9-2 z^3 a^9+6 z^{10} a^8-4 z^8 a^8-21 z^6 a^8+24 z^4 a^8-6 z^2 a^8+2 z^{11} a^7+17 z^9 a^7-53 z^7 a^7+40 z^5 a^7-9 z^3 a^7-z a^7+14 z^{10} a^6-13 z^8 a^6-32 z^6 a^6+41 z^4 a^6-17 z^2 a^6+3 a^6+2 z^{11} a^5+24 z^9 a^5-60 z^7 a^5+39 z^5 a^5-5 z^3 a^5-3 z a^5+8 z^{10} a^4+9 z^8 a^4-49 z^6 a^4+52 z^4 a^4-24 z^2 a^4+5 a^4+14 z^9 a^3-17 z^7 a^3+3 z^5 a^3+6 z^3 a^3-2 z a^3+14 z^8 a^2-22 z^6 a^2+19 z^4 a^2-8 z^2 a^2+a^2+9 z^7 a-11 z^5 a+6 z^3 a-z a+4 z^6-4 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }