K12a1116

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1116

Polynomial invariants

Jones polynomial	$-q+3-7q^{-1}+14q^{-2}-20q^{-3}+27q^{-4}-29q^{-5}+28q^{-6}-24q^{-7}+17q^{-8}-10q^{-9}+4q^{-10}-q^{-11}$
Alexander polynomial	$2t^{4}-9t^{3}+23t^{2}-37t+43-37t^{-1}+23t^{-2}-9t^{-3}+2t^{-4}$
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 2 z^8+7 z^6+9 z^4+6 z^2+1}
Determinant	185
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^8-3 z^4 a^8-3 z^2 a^8-a^8+z^8 a^6+4 z^6 a^6+5 z^4 a^6+z^2 a^6-2 a^6+z^8 a^4+5 z^6 a^4+11 z^4 a^4+13 z^2 a^4+6 a^4-z^6 a^2-4 z^4 a^2-5 z^2 a^2-2 a^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 z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-4 z^4 a^{12}+9 z^7 a^{11}-13 z^5 a^{11}+7 z^3 a^{11}-2 z a^{11}+13 z^8 a^{10}-23 z^6 a^{10}+17 z^4 a^{10}-4 z^2 a^{10}+12 z^9 a^9-19 z^7 a^9+12 z^5 a^9-3 z^3 a^9+2 z a^9+7 z^{10} a^8-3 z^8 a^8-8 z^6 a^8+4 z^4 a^8+3 z^2 a^8-a^8+2 z^{11} a^7+12 z^9 a^7-34 z^7 a^7+34 z^5 a^7-20 z^3 a^7+4 z a^7+11 z^{10} a^6-25 z^8 a^6+25 z^6 a^6-17 z^4 a^6+2 a^6+2 z^{11} a^5+4 z^9 a^5-16 z^7 a^5+11 z^5 a^5-3 z^3 a^5-2 z a^5+4 z^{10} a^4-6 z^8 a^4-5 z^6 a^4+13 z^4 a^4-13 z^2 a^4+6 a^4+4 z^9 a^3-9 z^7 a^3-z^5 a^3+11 z^3 a^3-4 z a^3+3 z^8 a^2-11 z^6 a^2+13 z^4 a^2-6 z^2 a^2+2 a^2+z^7 a-4 z^5 a+5 z^3 a-2 z a}

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