K12a216

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^{10}-3 q^9+6 q^8-11 q^7+15 q^6-18 q^5+19 q^4-17 q^3+15 q^2-10 q+6-3 q^{-1} + q^{-2} }[/math]
Alexander polynomial	[math]\displaystyle{ t^4-7 t^3+18 t^2-24 t+25-24 t^{-1} +18 t^{-2} -7 t^{-3} + t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ z^8+z^6-4 z^4+z^2+1 }[/math]
Determinant	125
Signature	4
HOMFLY-PT polynomial	[math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +5 z^6 a^{-4} -2 z^6 a^{-6} -8 z^4 a^{-2} +10 z^4 a^{-4} -8 z^4 a^{-6} +z^4 a^{-8} +z^4-8 z^2 a^{-2} +12 z^2 a^{-4} -9 z^2 a^{-6} +3 z^2 a^{-8} +3 z^2-2 a^{-2} +5 a^{-4} -4 a^{-6} + a^{-8} +1 }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +7 z^{10} a^{-4} +4 z^{10} a^{-6} +3 z^9 a^{-1} +6 z^9 a^{-3} +10 z^9 a^{-5} +7 z^9 a^{-7} -10 z^8 a^{-2} -20 z^8 a^{-4} -z^8 a^{-6} +8 z^8 a^{-8} +z^8-15 z^7 a^{-1} -40 z^7 a^{-3} -44 z^7 a^{-5} -12 z^7 a^{-7} +7 z^7 a^{-9} +2 z^6 a^{-2} +3 z^6 a^{-4} -22 z^6 a^{-6} -13 z^6 a^{-8} +5 z^6 a^{-10} -5 z^6+24 z^5 a^{-1} +60 z^5 a^{-3} +50 z^5 a^{-5} +3 z^5 a^{-7} -8 z^5 a^{-9} +3 z^5 a^{-11} +15 z^4 a^{-2} +21 z^4 a^{-4} +27 z^4 a^{-6} +8 z^4 a^{-8} -4 z^4 a^{-10} +z^4 a^{-12} +8 z^4-14 z^3 a^{-1} -31 z^3 a^{-3} -22 z^3 a^{-5} +z^3 a^{-7} +3 z^3 a^{-9} -3 z^3 a^{-11} -11 z^2 a^{-2} -16 z^2 a^{-4} -15 z^2 a^{-6} -3 z^2 a^{-8} +z^2 a^{-10} -z^2 a^{-12} -5 z^2+2 z a^{-1} +5 z a^{-3} +2 z a^{-5} -z a^{-7} +z a^{-9} +z a^{-11} +2 a^{-2} +5 a^{-4} +4 a^{-6} + a^{-8} +1 }[/math]

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