K12a716

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a716

Polynomial invariants

Jones 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 -1+2 q^{-1} -2 q^{-2} +4 q^{-3} -4 q^{-4} +5 q^{-5} -5 q^{-6} +5 q^{-7} -5 q^{-8} +4 q^{-9} -3 q^{-10} +2 q^{-11} - q^{-12} }
Alexander polynomial	$t^{5}-3t^{4}+5t^{3}-5t^{2}+5t-5+5t^{-1}-5t^{-2}+5t^{-3}-3t^{-4}+t^{-5}$
Conway polynomial	$z^{10}+7z^{8}+16z^{6}+15z^{4}+7z^{2}+1$
Determinant	43
Signature	-6
HOMFLY-PT polynomial	$a^{6}z^{10}-a^{8}z^{8}+9a^{6}z^{8}-a^{4}z^{8}-7a^{8}z^{6}+30a^{6}z^{6}-7a^{4}z^{6}-16a^{8}z^{4}+46a^{6}z^{4}-15a^{4}z^{4}-14a^{8}z^{2}+31a^{6}z^{2}-10a^{4}z^{2}-4a^{8}+6a^{6}-a^{4}$
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^3 a^{15}-z a^{15}+2 z^4 a^{14}-2 z^2 a^{14}+2 z^5 a^{13}-z^3 a^{13}+2 z^6 a^{12}-2 z^4 a^{12}+z^2 a^{12}+2 z^7 a^{11}-4 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+2 z^8 a^{10}-6 z^6 a^{10}+5 z^4 a^{10}-2 z^2 a^{10}+2 z^9 a^9-8 z^7 a^9+9 z^5 a^9-5 z^3 a^9+z a^9+2 z^{10} a^8-11 z^8 a^8+22 z^6 a^8-26 z^4 a^8+17 z^2 a^8-4 a^8+z^{11} a^7-4 z^9 a^7+12 z^5 a^7-13 z^3 a^7+4 z a^7+4 z^{10} a^6-28 z^8 a^6+68 z^6 a^6-74 z^4 a^6+37 z^2 a^6-6 a^6+z^{11} a^5-5 z^9 a^5+3 z^7 a^5+12 z^5 a^5-13 z^3 a^5+2 z a^5+2 z^{10} a^4-15 z^8 a^4+38 z^6 a^4-39 z^4 a^4+15 z^2 a^4-a^4+z^9 a^3-7 z^7 a^3+15 z^5 a^3-10 z^3 a^3+z a^3}

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