K12a541

Knotscape

Old German army general's shoulder epaulette braiding

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a541

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^{10}-4 q^9+9 q^8-14 q^7+19 q^6-23 q^5+23 q^4-21 q^3+17 q^2-11 q+7-3 q^{-1} + q^{-2} }
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^4-7 t^3+19 t^2-31 t+37-31 t^{-1} +19 t^{-2} -7 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+z^6-3 z^4-2 z^2+1}
Determinant	153
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^8 a^{-4} -2 z^6 a^{-2} +5 z^6 a^{-4} -2 z^6 a^{-6} -8 z^4 a^{-2} +10 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +z^4-9 z^2 a^{-2} +9 z^2 a^{-4} -7 z^2 a^{-6} +2 z^2 a^{-8} +3 z^2-2 a^{-2} +2 a^{-4} -2 a^{-6} + a^{-8} +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^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +7 z^{10} a^{-4} +4 z^{10} a^{-6} +3 z^9 a^{-1} +7 z^9 a^{-3} +13 z^9 a^{-5} +9 z^9 a^{-7} -8 z^8 a^{-2} -11 z^8 a^{-4} +11 z^8 a^{-6} +13 z^8 a^{-8} +z^8-14 z^7 a^{-1} -37 z^7 a^{-3} -40 z^7 a^{-5} -4 z^7 a^{-7} +13 z^7 a^{-9} -5 z^6 a^{-2} -24 z^6 a^{-4} -50 z^6 a^{-6} -17 z^6 a^{-8} +9 z^6 a^{-10} -5 z^6+21 z^5 a^{-1} +44 z^5 a^{-3} +23 z^5 a^{-5} -21 z^5 a^{-7} -17 z^5 a^{-9} +4 z^5 a^{-11} +26 z^4 a^{-2} +46 z^4 a^{-4} +43 z^4 a^{-6} +5 z^4 a^{-8} -8 z^4 a^{-10} +z^4 a^{-12} +9 z^4-10 z^3 a^{-1} -12 z^3 a^{-3} +z^3 a^{-5} +13 z^3 a^{-7} +9 z^3 a^{-9} -z^3 a^{-11} -17 z^2 a^{-2} -19 z^2 a^{-4} -16 z^2 a^{-6} -4 z^2 a^{-8} +3 z^2 a^{-10} -7 z^2-2 z a^{-7} -2 z a^{-9} +2 a^{-2} +2 a^{-4} +2 a^{-6} + a^{-8} +2}

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