K12a1100

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1100

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+5 q^4-13 q^3+23 q^2-33 q+40-41 q^{-1} +39 q^{-2} -30 q^{-3} +20 q^{-4} -11 q^{-5} +4 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+31 t^2-54 t+65-54 t^{-1} +31 t^{-2} -11 t^{-3} +2 t^{-4} }
Conway polynomial	$2z^{8}+5z^{6}+5z^{4}+3z^{2}+1$
Determinant	261
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 a^2 z^8+z^8-a^4 z^6+4 a^2 z^6-z^6 a^{-2} +3 z^6-3 a^4 z^4+8 a^2 z^4-2 z^4 a^{-2} +2 z^4-4 a^4 z^2+10 a^2 z^2-z^2 a^{-2} -2 z^2-3 a^4+6 a^2-2}
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 4 a^3 z^{11}+4 a z^{11}+9 a^4 z^{10}+23 a^2 z^{10}+14 z^{10}+8 a^5 z^9+13 a^3 z^9+27 a z^9+22 z^9 a^{-1} +4 a^6 z^8-18 a^4 z^8-48 a^2 z^8+21 z^8 a^{-2} -5 z^8+a^7 z^7-21 a^5 z^7-56 a^3 z^7-79 a z^7-32 z^7 a^{-1} +13 z^7 a^{-3} -11 a^6 z^6+8 a^4 z^6+28 a^2 z^6-30 z^6 a^{-2} +5 z^6 a^{-4} -26 z^6-3 a^7 z^5+18 a^5 z^5+60 a^3 z^5+67 a z^5+14 z^5 a^{-1} -13 z^5 a^{-3} +z^5 a^{-5} +9 a^6 z^4-3 a^4 z^4-13 a^2 z^4+15 z^4 a^{-2} -2 z^4 a^{-4} +16 z^4+3 a^7 z^3-8 a^5 z^3-31 a^3 z^3-30 a z^3-6 z^3 a^{-1} +4 z^3 a^{-3} -2 a^6 z^2+6 a^4 z^2+12 a^2 z^2-3 z^2 a^{-2} +z^2-a^7 z+3 a^5 z+9 a^3 z+8 a z+3 z a^{-1} -3 a^4-6 a^2-2}

Modifying This Page

Read me first: Modifying Knot Pages See/edit the Large Knot Page master template. Back to the top.