K12a1065

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1065

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^7+5 q^6-13 q^5+24 q^4-36 q^3+45 q^2-48 q+46-37 q^{-1} +26 q^{-2} -14 q^{-3} +5 q^{-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 t^4-8 t^3+31 t^2-67 t+87-67 t^{-1} +31 t^{-2} -8 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+3 z^4+z^2+1}
Determinant	301
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-a^2 z^6-3 z^6 a^{-2} +4 z^6-2 a^2 z^4-7 z^4 a^{-2} +3 z^4 a^{-4} +9 z^4-3 a^2 z^2-6 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +8 z^2-a^2- a^{-2} +3}
Kauffman polynomial	$5z^{11}a^{-1}+5z^{11}a^{-3}+30z^{10}a^{-2}+12z^{10}a^{-4}+18z^{10}+28az^{9}+39z^{9}a^{-1}+22z^{9}a^{-3}+11z^{9}a^{-5}+25a^{2}z^{8}-53z^{8}a^{-2}-20z^{8}a^{-4}+5z^{8}a^{-6}-3z^{8}+14a^{3}z^{7}-42az^{7}-111z^{7}a^{-1}-84z^{7}a^{-3}-28z^{7}a^{-5}+z^{7}a^{-7}+5a^{4}z^{6}-36a^{2}z^{6}+z^{6}a^{-2}-3z^{6}a^{-4}-12z^{6}a^{-6}-49z^{6}+a^{5}z^{5}-12a^{3}z^{5}+18az^{5}+82z^{5}a^{-1}+77z^{5}a^{-3}+24z^{5}a^{-5}-2z^{5}a^{-7}-a^{4}z^{4}+22a^{2}z^{4}+25z^{4}a^{-2}+15z^{4}a^{-4}+9z^{4}a^{-6}+42z^{4}+5a^{3}z^{3}-2az^{3}-22z^{3}a^{-1}-24z^{3}a^{-3}-8z^{3}a^{-5}+z^{3}a^{-7}-7a^{2}z^{2}-9z^{2}a^{-2}-4z^{2}a^{-4}-2z^{2}a^{-6}-14z^{2}-a^{3}z-az+za^{-1}+2za^{-3}+za^{-5}+a^{2}+a^{-2}+3$

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