K12a1057

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1057

Polynomial invariants

Jones polynomial	$-q^{7}+5q^{6}-13q^{5}+22q^{4}-31q^{3}+38q^{2}-39q+37-29q^{-1}+19q^{-2}-10q^{-3}+4q^{-4}-q^{-5}$
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 -3 t^3+22 t^2-59 t+81-59 t^{-1} +22 t^{-2} -3 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 -3 z^6+4 z^4+2 z^2+1}
Determinant	249
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 -2 z^6 a^{-2} -z^6+2 a^2 z^4-3 z^4 a^{-2} +3 z^4 a^{-4} +2 z^4-a^4 z^2-2 z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} +4 z^2-a^2+ a^{-2} - a^{-4} +2}
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^{-1} +4 z^{11} a^{-3} +23 z^{10} a^{-2} +11 z^{10} a^{-4} +12 z^{10}+16 a z^9+23 z^9 a^{-1} +18 z^9 a^{-3} +11 z^9 a^{-5} +14 a^2 z^8-48 z^8 a^{-2} -21 z^8 a^{-4} +5 z^8 a^{-6} -8 z^8+9 a^3 z^7-24 a z^7-78 z^7 a^{-1} -76 z^7 a^{-3} -30 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-20 a^2 z^6+14 z^6 a^{-2} -2 z^6 a^{-4} -12 z^6 a^{-6} -20 z^6+a^5 z^5-11 a^3 z^5+14 a z^5+75 z^5 a^{-1} +75 z^5 a^{-3} +24 z^5 a^{-5} -2 z^5 a^{-7} -4 a^4 z^4+14 a^2 z^4+14 z^4 a^{-2} +12 z^4 a^{-4} +8 z^4 a^{-6} +28 z^4-a^5 z^3+6 a^3 z^3-2 a z^3-29 z^3 a^{-1} -30 z^3 a^{-3} -9 z^3 a^{-5} +z^3 a^{-7} +a^4 z^2-5 a^2 z^2-6 z^2 a^{-2} -2 z^2 a^{-4} -2 z^2 a^{-6} -12 z^2-a^3 z+4 z a^{-1} +6 z a^{-3} +3 z a^{-5} +a^2- a^{-2} - a^{-4} +2}

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