K12a1073

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1073

Polynomial invariants

Jones polynomial	$q^{12}-4q^{11}+10q^{10}-18q^{9}+25q^{8}-32q^{7}+34q^{6}-31q^{5}+26q^{4}-17q^{3}+10q^{2}-4q+1$
Alexander 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 t^3+22 t^2-49 t+63-49 t^{-1} +22 t^{-2} -4 t^{-3} }
Conway 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^6-2 z^4+3 z^2+1}
Determinant	213
Signature	4
HOMFLY-PT 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^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -3 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +z^2 a^{-2} +3 z^2 a^{-4} -2 z^2 a^{-8} +z^2 a^{-10} +2 a^{-4} + a^{-6} -3 a^{-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 3 z^{11} a^{-7} +3 z^{11} a^{-9} +8 z^{10} a^{-6} +17 z^{10} a^{-8} +9 z^{10} a^{-10} +10 z^9 a^{-5} +13 z^9 a^{-7} +14 z^9 a^{-9} +11 z^9 a^{-11} +8 z^8 a^{-4} -9 z^8 a^{-6} -41 z^8 a^{-8} -16 z^8 a^{-10} +8 z^8 a^{-12} +4 z^7 a^{-3} -20 z^7 a^{-5} -52 z^7 a^{-7} -58 z^7 a^{-9} -26 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -17 z^6 a^{-4} -9 z^6 a^{-6} +35 z^6 a^{-8} +9 z^6 a^{-10} -16 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +13 z^5 a^{-5} +69 z^5 a^{-7} +82 z^5 a^{-9} +26 z^5 a^{-11} -8 z^5 a^{-13} -2 z^4 a^{-2} +11 z^4 a^{-4} +19 z^4 a^{-6} -3 z^4 a^{-8} +7 z^4 a^{-12} -2 z^4 a^{-14} +3 z^3 a^{-3} -7 z^3 a^{-5} -38 z^3 a^{-7} -50 z^3 a^{-9} -19 z^3 a^{-11} +3 z^3 a^{-13} +z^2 a^{-2} -7 z^2 a^{-4} -8 z^2 a^{-6} +z^2 a^{-8} -2 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} +z a^{-5} +10 z a^{-7} +14 z a^{-9} +5 z a^{-11} +2 a^{-4} - a^{-6} -3 a^{-8} - a^{-10} }

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