K12a1005

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1005

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^5+4 q^4-10 q^3+19 q^2-28 q+36-38 q^{-1} +36 q^{-2} -30 q^{-3} +21 q^{-4} -12 q^{-5} +5 q^{-6} - q^{-7} }
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 2 t^4-11 t^3+29 t^2-49 t+59-49 t^{-1} +29 t^{-2} -11 t^{-3} +2 t^{-4} }
Conway polynomial	$2z^{8}+5z^{6}+3z^{4}+1$
Determinant	241
Signature	0
HOMFLY-PT polynomial	$a^{2}z^{8}+z^{8}-a^{4}z^{6}+3a^{2}z^{6}-z^{6}a^{-2}+4z^{6}-2a^{4}z^{4}+a^{2}z^{4}-3z^{4}a^{-2}+7z^{4}-4a^{2}z^{2}-3z^{2}a^{-2}+7z^{2}+a^{4}-3a^{2}-a^{-2}+4$
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 a^3 z^{11}+4 a z^{11}+10 a^4 z^{10}+22 a^2 z^{10}+12 z^{10}+10 a^5 z^9+13 a^3 z^9+20 a z^9+17 z^9 a^{-1} +5 a^6 z^8-20 a^4 z^8-50 a^2 z^8+15 z^8 a^{-2} -10 z^8+a^7 z^7-27 a^5 z^7-57 a^3 z^7-70 a z^7-32 z^7 a^{-1} +9 z^7 a^{-3} -13 a^6 z^6+4 a^4 z^6+27 a^2 z^6-27 z^6 a^{-2} +4 z^6 a^{-4} -21 z^6-2 a^7 z^5+20 a^5 z^5+51 a^3 z^5+66 a z^5+25 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +9 a^6 z^4+2 a^4 z^4+3 a^2 z^4+24 z^4 a^{-2} -4 z^4 a^{-4} +38 z^4+a^7 z^3-4 a^5 z^3-18 a^3 z^3-21 a z^3-3 z^3 a^{-1} +4 z^3 a^{-3} -z^3 a^{-5} -a^4 z^2-10 a^2 z^2-9 z^2 a^{-2} -18 z^2+a^3 z+a z-z a^{-1} -z a^{-3} +a^4+3 a^2+ a^{-2} +4}

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