K12a1021

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1021

Polynomial invariants

Jones polynomial	$q^{9}-5q^{8}+13q^{7}-26q^{6}+40q^{5}-50q^{4}+55q^{3}-52q^{2}+43q-30+17q^{-1}-6q^{-2}+q^{-3}$
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^3-35 t^2+76 t-97+76 t^{-1} -35 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-z^4+z^2+1}
Determinant	339
Signature	2
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 a^{-2} -3 z^6 a^{-2} +3 z^6 a^{-4} +z^6-5 z^4 a^{-2} +6 z^4 a^{-4} -3 z^4 a^{-6} +z^4-3 z^2 a^{-2} +5 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} +z^2- a^{-2} +2 a^{-4} - a^{-6} +1}
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 6 z^{11} a^{-3} +6 z^{11} a^{-5} +20 z^{10} a^{-2} +36 z^{10} a^{-4} +16 z^{10} a^{-6} +26 z^9 a^{-1} +43 z^9 a^{-3} +35 z^9 a^{-5} +18 z^9 a^{-7} -12 z^8 a^{-2} -50 z^8 a^{-4} -9 z^8 a^{-6} +12 z^8 a^{-8} +17 z^8+6 a z^7-45 z^7 a^{-1} -115 z^7 a^{-3} -97 z^7 a^{-5} -28 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-33 z^6 a^{-2} -13 z^6 a^{-4} -25 z^6 a^{-6} -19 z^6 a^{-8} +z^6 a^{-10} -24 z^6-4 a z^5+23 z^5 a^{-1} +79 z^5 a^{-3} +75 z^5 a^{-5} +16 z^5 a^{-7} -7 z^5 a^{-9} +26 z^4 a^{-2} +35 z^4 a^{-4} +31 z^4 a^{-6} +12 z^4 a^{-8} -z^4 a^{-10} +9 z^4-6 z^3 a^{-1} -19 z^3 a^{-3} -18 z^3 a^{-5} -2 z^3 a^{-7} +3 z^3 a^{-9} -7 z^2 a^{-2} -13 z^2 a^{-4} -11 z^2 a^{-6} -3 z^2 a^{-8} -2 z^2+z a^{-1} +2 z a^{-3} -z a^{-7} + a^{-2} +2 a^{-4} + a^{-6} +1}

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