K13a248

Knotscape

Three trefoil knots along a closed loop, mutually interlinked.

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K13a248

Polynomial invariants

Jones polynomial	Data:K13a248/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 9 t^3-38 t^2+79 t-99+79 t^{-1} -38 t^{-2} +9 t^{-3} }
Conway polynomial	Data:K13a248/Conway Polynomial
Determinant	351
Signature	6
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^{-6} +4 z^6 a^{-8} +4 z^6 a^{-10} +2 z^4 a^{-6} +12 z^4 a^{-8} +10 z^4 a^{-10} -8 z^4 a^{-12} +z^2 a^{-6} +12 z^2 a^{-8} +8 z^2 a^{-10} -18 z^2 a^{-12} +5 z^2 a^{-14} +4 a^{-8} +2 a^{-10} -10 a^{-12} +6 a^{-14} - a^{-16} }
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^{12} a^{-12} +z^{12} a^{-14} +6 z^{11} a^{-11} +11 z^{11} a^{-13} +5 z^{11} a^{-15} +13 z^{10} a^{-10} +32 z^{10} a^{-12} +29 z^{10} a^{-14} +10 z^{10} a^{-16} +14 z^9 a^{-9} +26 z^9 a^{-11} +26 z^9 a^{-13} +24 z^9 a^{-15} +10 z^9 a^{-17} +10 z^8 a^{-8} -10 z^8 a^{-10} -66 z^8 a^{-12} -60 z^8 a^{-14} -9 z^8 a^{-16} +5 z^8 a^{-18} +4 z^7 a^{-7} -22 z^7 a^{-9} -88 z^7 a^{-11} -134 z^7 a^{-13} -98 z^7 a^{-15} -25 z^7 a^{-17} +z^7 a^{-19} +z^6 a^{-6} -20 z^6 a^{-8} -9 z^6 a^{-10} +43 z^6 a^{-12} +17 z^6 a^{-14} -27 z^6 a^{-16} -13 z^6 a^{-18} -6 z^5 a^{-7} +12 z^5 a^{-9} +103 z^5 a^{-11} +179 z^5 a^{-13} +117 z^5 a^{-15} +21 z^5 a^{-17} -2 z^5 a^{-19} -2 z^4 a^{-6} +21 z^4 a^{-8} +10 z^4 a^{-10} -21 z^4 a^{-12} +20 z^4 a^{-14} +39 z^4 a^{-16} +11 z^4 a^{-18} +2 z^3 a^{-7} -62 z^3 a^{-11} -118 z^3 a^{-13} -68 z^3 a^{-15} -9 z^3 a^{-17} +z^3 a^{-19} +z^2 a^{-6} -14 z^2 a^{-8} +21 z^2 a^{-12} -4 z^2 a^{-14} -13 z^2 a^{-16} -3 z^2 a^{-18} -2 z a^{-9} +17 z a^{-11} +35 z a^{-13} +19 z a^{-15} +3 z a^{-17} +4 a^{-8} -2 a^{-10} -10 a^{-12} -6 a^{-14} - a^{-16} }

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