K12a1007

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1007

Polynomial invariants

Jones polynomial	$q^{5}-3q^{4}+6q^{3}-11q^{2}+16q-19+22q^{-1}-21q^{-2}+18q^{-3}-13q^{-4}+8q^{-5}-4q^{-6}+q^{-7}$
Alexander polynomial	$-2t^{4}+9t^{3}-19t^{2}+27t-29+27t^{-1}-19t^{-2}+9t^{-3}-2t^{-4}$
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 -2 z^8-7 z^6-5 z^4+1}
Determinant	143
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 -a^2 z^8-z^8+a^4 z^6-4 a^2 z^6+z^6 a^{-2} -5 z^6+3 a^4 z^4-3 a^2 z^4+4 z^4 a^{-2} -9 z^4+a^4 z^2+3 a^2 z^2+4 z^2 a^{-2} -8 z^2-a^4+3 a^2+ 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 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+4 z^{10} a^{-2} +10 z^{10}+10 a^3 z^9+6 a z^9-z^9 a^{-1} +3 z^9 a^{-3} +12 a^4 z^8-7 a^2 z^8-18 z^8 a^{-2} +z^8 a^{-4} -38 z^8+11 a^5 z^7-17 a^3 z^7-34 a z^7-21 z^7 a^{-1} -15 z^7 a^{-3} +8 a^6 z^6-19 a^4 z^6-11 a^2 z^6+26 z^6 a^{-2} -5 z^6 a^{-4} +47 z^6+4 a^7 z^5-13 a^5 z^5+2 a^3 z^5+34 a z^5+39 z^5 a^{-1} +24 z^5 a^{-3} +a^8 z^4-7 a^6 z^4+7 a^4 z^4+8 a^2 z^4-16 z^4 a^{-2} +7 z^4 a^{-4} -30 z^4-2 a^7 z^3+3 a^5 z^3+4 a^3 z^3-11 a z^3-24 z^3 a^{-1} -14 z^3 a^{-3} +a^6 z^2+5 a^2 z^2+5 z^2 a^{-2} -2 z^2 a^{-4} +13 z^2+2 a z+4 z a^{-1} +2 z a^{-3} -a^4-3 a^2- a^{-2} -2}

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