K12n504

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ 2 q^4-6 q^3+11 q^2-16 q+20-20 q^{-1} +18 q^{-2} -14 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math]
Alexander polynomial	[math]\displaystyle{ t^4-6 t^3+15 t^2-24 t+29-24 t^{-1} +15 t^{-2} -6 t^{-3} + t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ z^8+2 z^6-z^4-2 z^2+1 }[/math]
Determinant	121
Signature	0
HOMFLY-PT polynomial	[math]\displaystyle{ z^8-2 a^2 z^6-z^6 a^{-2} +5 z^6+a^4 z^4-7 a^2 z^4-4 z^4 a^{-2} +9 z^4+2 a^4 z^2-7 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} +7 z^2+a^4-2 a^2-2 a^{-2} + a^{-4} +3 }[/math]
Kauffman polynomial	[math]\displaystyle{ 2 a^2 z^{10}+2 z^{10}+6 a^3 z^9+11 a z^9+5 z^9 a^{-1} +7 a^4 z^8+10 a^2 z^8+4 z^8 a^{-2} +7 z^8+4 a^5 z^7-8 a^3 z^7-23 a z^7-10 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-16 a^4 z^6-35 a^2 z^6-6 z^6 a^{-2} -24 z^6-9 a^5 z^5-6 a^3 z^5+16 a z^5+18 z^5 a^{-1} +5 z^5 a^{-3} -2 a^6 z^4+9 a^4 z^4+32 a^2 z^4+12 z^4 a^{-2} +3 z^4 a^{-4} +30 z^4+5 a^5 z^3+6 a^3 z^3-4 a z^3-13 z^3 a^{-1} -8 z^3 a^{-3} +a^6 z^2-4 a^4 z^2-13 a^2 z^2-10 z^2 a^{-2} -4 z^2 a^{-4} -14 z^2-a^5 z-a^3 z+a z+3 z a^{-1} +2 z a^{-3} +a^4+2 a^2+2 a^{-2} + a^{-4} +3 }[/math]

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