K12a1018

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1018

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 -q^8+3 q^7-7 q^6+13 q^5-18 q^4+23 q^3-25 q^2+23 q-19+14 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }
Alexander polynomial	$4t^{3}-18t^{2}+36t-43+36t^{-1}-18t^{-2}+4t^{-3}$
Conway polynomial	$4z^{6}+6z^{4}+1$
Determinant	159
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 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+5 z^4 a^{-2} +2 z^4 a^{-4} -z^4 a^{-6} +z^4-a^2 z^2+3 z^2 a^{-2} +2 z^2 a^{-4} -2 z^2 a^{-6} -2 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 2 z^{11} a^{-1} +2 z^{11} a^{-3} +11 z^{10} a^{-2} +6 z^{10} a^{-4} +5 z^{10}+6 a z^9+5 z^9 a^{-1} +8 z^9 a^{-3} +9 z^9 a^{-5} +4 a^2 z^8-34 z^8 a^{-2} -10 z^8 a^{-4} +9 z^8 a^{-6} -11 z^8+a^3 z^7-19 a z^7-30 z^7 a^{-1} -40 z^7 a^{-3} -24 z^7 a^{-5} +6 z^7 a^{-7} -14 a^2 z^6+41 z^6 a^{-2} -z^6 a^{-4} -24 z^6 a^{-6} +3 z^6 a^{-8} +z^6-3 a^3 z^5+15 a z^5+39 z^5 a^{-1} +64 z^5 a^{-3} +30 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4-24 z^4 a^{-2} +22 z^4 a^{-4} +29 z^4 a^{-6} -5 z^4 a^{-8} +z^4+2 a^3 z^3-4 a z^3-29 z^3 a^{-1} -44 z^3 a^{-3} -12 z^3 a^{-5} +7 z^3 a^{-7} -2 z^3 a^{-9} -2 a^2 z^2+2 z^2 a^{-2} -15 z^2 a^{-4} -12 z^2 a^{-6} +3 z^2+2 a z+9 z a^{-1} +11 z a^{-3} +3 z a^{-5} -z a^{-7} -a^2+2 a^{-4} + a^{-6} -1}

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