K12a1155

Knot presentations

Dowker-Thistlethwaite code

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

Polynomial invariants

Jones polynomial	$q^{12}-5q^{11}+13q^{10}-24q^{9}+34q^{8}-42q^{7}+44q^{6}-40q^{5}+33q^{4}-21q^{3}+11q^{2}-4q+1$
Alexander polynomial	$-5t^{3}+28t^{2}-63t+81-63t^{-1}+28t^{-2}-5t^{-3}$
Conway polynomial	$-5z^{6}-2z^{4}+4z^{2}+1$
Determinant	273
Signature	4
HOMFLY-PT polynomial	$-z^{6}a^{-4}-3z^{6}a^{-6}-z^{6}a^{-8}+z^{4}a^{-2}+z^{4}a^{-4}-6z^{4}a^{-6}+z^{4}a^{-8}+z^{4}a^{-10}+z^{2}a^{-2}+4z^{2}a^{-4}-3z^{2}a^{-6}+2z^{2}a^{-8}+2a^{-4}-a^{-8}$
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 4 z^{11} a^{-7} +4 z^{11} a^{-9} +11 z^{10} a^{-6} +24 z^{10} a^{-8} +13 z^{10} a^{-10} +13 z^9 a^{-5} +23 z^9 a^{-7} +27 z^9 a^{-9} +17 z^9 a^{-11} +9 z^8 a^{-4} -8 z^8 a^{-6} -39 z^8 a^{-8} -10 z^8 a^{-10} +12 z^8 a^{-12} +4 z^7 a^{-3} -24 z^7 a^{-5} -69 z^7 a^{-7} -78 z^7 a^{-9} -32 z^7 a^{-11} +5 z^7 a^{-13} +z^6 a^{-2} -17 z^6 a^{-4} -15 z^6 a^{-6} +9 z^6 a^{-8} -16 z^6 a^{-10} -21 z^6 a^{-12} +z^6 a^{-14} -7 z^5 a^{-3} +20 z^5 a^{-5} +69 z^5 a^{-7} +70 z^5 a^{-9} +21 z^5 a^{-11} -7 z^5 a^{-13} -2 z^4 a^{-2} +14 z^4 a^{-4} +24 z^4 a^{-6} +11 z^4 a^{-8} +15 z^4 a^{-10} +11 z^4 a^{-12} -z^4 a^{-14} +3 z^3 a^{-3} -9 z^3 a^{-5} -32 z^3 a^{-7} -30 z^3 a^{-9} -8 z^3 a^{-11} +2 z^3 a^{-13} +z^2 a^{-2} -8 z^2 a^{-4} -11 z^2 a^{-6} -4 z^2 a^{-8} -4 z^2 a^{-10} -2 z^2 a^{-12} +z a^{-5} +7 z a^{-7} +7 z a^{-9} +z a^{-11} +2 a^{-4} - a^{-8} }