K12a234

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^7+3 q^6-7 q^5+11 q^4-16 q^3+21 q^2-21 q+21-17 q^{-1} +12 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math]
Alexander polynomial	[math]\displaystyle{ 2 t^4-8 t^3+18 t^2-27 t+31-27 t^{-1} +18 t^{-2} -8 t^{-3} +2 t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ 2 z^8+8 z^6+10 z^4+5 z^2+1 }[/math]
Determinant	141
Signature	0
HOMFLY-PT polynomial	[math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+5 z^6 a^{-2} -z^6 a^{-4} +5 z^6-4 a^2 z^4+9 z^4 a^{-2} -4 z^4 a^{-4} +9 z^4-5 a^2 z^2+8 z^2 a^{-2} -5 z^2 a^{-4} +7 z^2-2 a^2+4 a^{-2} -3 a^{-4} +2 }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +7 z^{10} a^{-2} +4 z^{10} a^{-4} +3 z^{10}+5 a z^9+8 z^9 a^{-1} +8 z^9 a^{-3} +5 z^9 a^{-5} +6 a^2 z^8-17 z^8 a^{-2} -11 z^8 a^{-4} +3 z^8 a^{-6} +3 z^8+5 a^3 z^7-3 a z^7-25 z^7 a^{-1} -37 z^7 a^{-3} -19 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-8 a^2 z^6+15 z^6 a^{-2} +8 z^6 a^{-4} -11 z^6 a^{-6} -15 z^6+a^5 z^5-7 a^3 z^5-4 a z^5+30 z^5 a^{-1} +53 z^5 a^{-3} +23 z^5 a^{-5} -4 z^5 a^{-7} -5 a^4 z^4+6 a^2 z^4-9 z^4 a^{-2} -6 z^4 a^{-4} +10 z^4 a^{-6} +18 z^4-2 a^5 z^3+3 a^3 z^3+6 a z^3-18 z^3 a^{-1} -37 z^3 a^{-3} -14 z^3 a^{-5} +4 z^3 a^{-7} +2 a^4 z^2-5 a^2 z^2+6 z^2 a^{-2} +6 z^2 a^{-4} -2 z^2 a^{-6} -9 z^2+a^5 z-a^3 z-2 a z+5 z a^{-1} +11 z a^{-3} +5 z a^{-5} -z a^{-7} +2 a^2-4 a^{-2} -3 a^{-4} +2 }[/math]

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