K12n458

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^6-5 q^5+10 q^4-15 q^3+20 q^2-21 q+21-17 q^{-1} +11 q^{-2} -6 q^{-3} +2 q^{-4} }[/math]
Alexander polynomial	[math]\displaystyle{ t^4-6 t^3+16 t^2-26 t+31-26 t^{-1} +16 t^{-2} -6 t^{-3} + t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ z^8+2 z^6+1 }[/math]
Determinant	129
Signature	0
HOMFLY-PT polynomial	[math]\displaystyle{ z^8-a^2 z^6-2 z^6 a^{-2} +5 z^6-4 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +9 z^4+a^4 z^2-5 a^2 z^2-3 z^2 a^{-2} +z^2 a^{-4} +6 z^2+a^4-2 a^2+2 a^{-2} - a^{-4} +1 }[/math]
Kauffman polynomial	[math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+5 a z^9+12 z^9 a^{-1} +7 z^9 a^{-3} +4 a^2 z^8+14 z^8 a^{-2} +9 z^8 a^{-4} +9 z^8+a^3 z^7-9 a z^7-23 z^7 a^{-1} -8 z^7 a^{-3} +5 z^7 a^{-5} -6 a^2 z^6-45 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -29 z^6+5 a^3 z^5+18 a z^5+13 z^5 a^{-1} -10 z^5 a^{-3} -10 z^5 a^{-5} +3 a^4 z^4+14 a^2 z^4+36 z^4 a^{-2} +11 z^4 a^{-4} -z^4 a^{-6} +35 z^4-8 a^3 z^3-16 a z^3-5 z^3 a^{-1} +6 z^3 a^{-3} +3 z^3 a^{-5} -4 a^4 z^2-12 a^2 z^2-8 z^2 a^{-2} -z^2 a^{-4} -15 z^2+3 a^3 z+6 a z+4 z a^{-1} +2 z a^{-3} +z a^{-5} +a^4+2 a^2-2 a^{-2} - a^{-4} +1 }[/math]

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