K12a1123

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1123

Polynomial invariants

Jones polynomial	$q^{6}-4q^{5}+11q^{4}-22q^{3}+32q^{2}-39q+43-39q^{-1}+32q^{-2}-22q^{-3}+11q^{-4}-4q^{-5}+q^{-6}$
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 t^4-9 t^3+30 t^2-56 t+69-56 t^{-1} +30 t^{-2} -9 t^{-3} + t^{-4} }
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 z^8-z^6-4 z^4-z^2+1}
Determinant	261
Signature	0
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^8-2 a^2 z^6-2 z^6 a^{-2} +3 z^6+a^4 z^4-5 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +4 z^4+2 a^4 z^2-5 a^2 z^2-5 z^2 a^{-2} +2 z^2 a^{-4} +5 z^2+a^4-3 a^2-3 a^{-2} + a^{-4} +5}
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 a z^{11}+3 z^{11} a^{-1} +10 a^2 z^{10}+10 z^{10} a^{-2} +20 z^{10}+13 a^3 z^9+27 a z^9+27 z^9 a^{-1} +13 z^9 a^{-3} +9 a^4 z^8-2 a^2 z^8-2 z^8 a^{-2} +9 z^8 a^{-4} -22 z^8+4 a^5 z^7-23 a^3 z^7-74 a z^7-74 z^7 a^{-1} -23 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-16 a^4 z^6-26 a^2 z^6-26 z^6 a^{-2} -16 z^6 a^{-4} +z^6 a^{-6} -18 z^6-7 a^5 z^5+18 a^3 z^5+70 a z^5+70 z^5 a^{-1} +18 z^5 a^{-3} -7 z^5 a^{-5} -2 a^6 z^4+12 a^4 z^4+29 a^2 z^4+29 z^4 a^{-2} +12 z^4 a^{-4} -2 z^4 a^{-6} +30 z^4+4 a^5 z^3-8 a^3 z^3-32 a z^3-32 z^3 a^{-1} -8 z^3 a^{-3} +4 z^3 a^{-5} +a^6 z^2-5 a^4 z^2-13 a^2 z^2-13 z^2 a^{-2} -5 z^2 a^{-4} +z^2 a^{-6} -14 z^2-a^5 z+4 a z+4 z a^{-1} -z a^{-5} +a^4+3 a^2+3 a^{-2} + a^{-4} +5}

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