K13a4532

Knotscape

Angular decorative knot

Angular decorative knot with central pentagram

Knot presentations

Dowker-Thistlethwaite code

6 16 14 18 20 24 22 4 2 8 26 12 10

Notes on presentations of K13a4532

Polynomial invariants

Jones polynomial	Data:K13a4532/Jones Polynomial
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 4 t^3-16 t^2+25 t-25+25 t^{-1} -16 t^{-2} +4 t^{-3} }
Conway polynomial	Data:K13a4532/Conway Polynomial
Determinant	115
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^2 a^6+2 a^6-2 z^4 a^4-6 z^2 a^4-3 a^4+z^6 a^2+2 z^4 a^2-z^2 a^2+2 z^6+7 z^4+6 z^2+2+z^6 a^{-2} +2 z^4 a^{-2} -z^2 a^{-2} -z^4 a^{-4} -2 z^2 a^{-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 a^4 z^{12}+a^2 z^{12}+2 a^5 z^{11}+5 a^3 z^{11}+3 a z^{11}+a^6 z^{10}-3 a^4 z^{10}+2 a^2 z^{10}+6 z^{10}-15 a^5 z^9-29 a^3 z^9-4 a z^9+10 z^9 a^{-1} -8 a^6 z^8-10 a^4 z^8-28 a^2 z^8+12 z^8 a^{-2} -14 z^8+40 a^5 z^7+54 a^3 z^7-28 a z^7-30 z^7 a^{-1} +12 z^7 a^{-3} +23 a^6 z^6+47 a^4 z^6+50 a^2 z^6-30 z^6 a^{-2} +10 z^6 a^{-4} -14 z^6-45 a^5 z^5-35 a^3 z^5+62 a z^5+22 z^5 a^{-1} -24 z^5 a^{-3} +6 z^5 a^{-5} -28 a^6 z^4-57 a^4 z^4-22 a^2 z^4+15 z^4 a^{-2} -15 z^4 a^{-4} +3 z^4 a^{-6} +40 z^4+20 a^5 z^3+6 a^3 z^3-38 a z^3-11 z^3 a^{-1} +9 z^3 a^{-3} -3 z^3 a^{-5} +z^3 a^{-7} +13 a^6 z^2+25 a^4 z^2+a^2 z^2-3 z^2 a^{-2} +6 z^2 a^{-4} -20 z^2-3 a^5 z+a^3 z+8 a z+4 z a^{-1} -2 a^6-3 a^4+2}

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