K12a111

Knot presentations

Dowker-Thistlethwaite code

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

Polynomial invariants

Jones polynomial	$-q^{11}+4q^{10}-9q^{9}+17q^{8}-26q^{7}+32q^{6}-35q^{5}+33q^{4}-27q^{3}+20q^{2}-11q+5-q^{-1}$
Alexander polynomial	$t^{4}-8t^{3}+26t^{2}-47t+57-47t^{-1}+26t^{-2}-8t^{-3}+t^{-4}$
Conway polynomial	$z^{8}-2z^{4}+z^{2}+1$
Determinant	221
Signature	4
HOMFLY-PT polynomial	$z^{8}a^{-4}-z^{6}a^{-2}+4z^{6}a^{-4}-3z^{6}a^{-6}-2z^{4}a^{-2}+7z^{4}a^{-4}-10z^{4}a^{-6}+3z^{4}a^{-8}+7z^{2}a^{-4}-12z^{2}a^{-6}+7z^{2}a^{-8}-z^{2}a^{-10}+a^{-2}+3a^{-4}-6a^{-6}+4a^{-8}-a^{-10}$
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 2 z^{11} a^{-5} +2 z^{11} a^{-7} +7 z^{10} a^{-4} +14 z^{10} a^{-6} +7 z^{10} a^{-8} +9 z^9 a^{-3} +20 z^9 a^{-5} +22 z^9 a^{-7} +11 z^9 a^{-9} +5 z^8 a^{-2} -4 z^8 a^{-4} -11 z^8 a^{-6} +9 z^8 a^{-8} +11 z^8 a^{-10} +z^7 a^{-1} -24 z^7 a^{-3} -64 z^7 a^{-5} -54 z^7 a^{-7} -7 z^7 a^{-9} +8 z^7 a^{-11} -14 z^6 a^{-2} -32 z^6 a^{-4} -45 z^6 a^{-6} -43 z^6 a^{-8} -12 z^6 a^{-10} +4 z^6 a^{-12} -2 z^5 a^{-1} +17 z^5 a^{-3} +49 z^5 a^{-5} +29 z^5 a^{-7} -12 z^5 a^{-9} -10 z^5 a^{-11} +z^5 a^{-13} +12 z^4 a^{-2} +41 z^4 a^{-4} +63 z^4 a^{-6} +43 z^4 a^{-8} +4 z^4 a^{-10} -5 z^4 a^{-12} +z^3 a^{-1} -3 z^3 a^{-3} -10 z^3 a^{-5} +5 z^3 a^{-7} +18 z^3 a^{-9} +6 z^3 a^{-11} -z^3 a^{-13} -2 z^2 a^{-2} -17 z^2 a^{-4} -31 z^2 a^{-6} -18 z^2 a^{-8} +2 z^2 a^{-12} +z a^{-3} -z a^{-5} -6 z a^{-7} -6 z a^{-9} -2 z a^{-11} - a^{-2} +3 a^{-4} +6 a^{-6} +4 a^{-8} + a^{-10} }