K12a84

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^4+4 q^3-9 q^2+16 q-23+29 q^{-1} -31 q^{-2} +30 q^{-3} -24 q^{-4} +17 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^4+7 t^3-22 t^2+43 t-53+43 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -z^8-z^6+2 z^2+1 }[/math]
Determinant	199
Signature	-2
HOMFLY-PT polynomial	[math]\displaystyle{ -a^2 z^8+2 a^4 z^6-5 a^2 z^6+2 z^6-a^6 z^4+7 a^4 z^4-12 a^2 z^4-z^4 a^{-2} +7 z^4-2 a^6 z^2+10 a^4 z^2-13 a^2 z^2-2 z^2 a^{-2} +9 z^2-2 a^6+5 a^4-5 a^2- a^{-2} +4 }[/math]
Kauffman polynomial	[math]\displaystyle{ a^3 z^{11}+a z^{11}+5 a^4 z^{10}+9 a^2 z^{10}+4 z^{10}+10 a^5 z^9+21 a^3 z^9+17 a z^9+6 z^9 a^{-1} +12 a^6 z^8+15 a^4 z^8+3 a^2 z^8+4 z^8 a^{-2} +4 z^8+9 a^7 z^7-4 a^5 z^7-46 a^3 z^7-49 a z^7-15 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-17 a^6 z^6-50 a^4 z^6-56 a^2 z^6-13 z^6 a^{-2} -40 z^6+a^9 z^5-13 a^7 z^5-15 a^5 z^5+25 a^3 z^5+36 a z^5+7 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+12 a^6 z^4+47 a^4 z^4+67 a^2 z^4+14 z^4 a^{-2} +50 z^4-a^9 z^3+9 a^7 z^3+15 a^5 z^3-2 a^3 z^3-6 a z^3+4 z^3 a^{-1} +3 z^3 a^{-3} +a^8 z^2-6 a^6 z^2-22 a^4 z^2-31 a^2 z^2-6 z^2 a^{-2} -22 z^2-3 a^7 z-4 a^5 z-a^3 z-a z-2 z a^{-1} -z a^{-3} +2 a^6+5 a^4+5 a^2+ a^{-2} +4 }[/math]

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