K12a235

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^8+4 q^7-10 q^6+16 q^5-22 q^4+27 q^3-27 q^2+25 q-19+13 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math]
Alexander polynomial	[math]\displaystyle{ 4 t^3-18 t^2+40 t-51+40 t^{-1} -18 t^{-2} +4 t^{-3} }[/math]
Conway polynomial	[math]\displaystyle{ 4 z^6+6 z^4+4 z^2+1 }[/math]
Determinant	175
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+5 z^4 a^{-2} +z^4 a^{-4} -z^4 a^{-6} +2 z^4-2 a^2 z^2+5 z^2 a^{-2} -z^2 a^{-6} +2 z^2-a^2+2 a^{-2} - a^{-6} +1 }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +5 z^{10} a^{-4} +3 z^{10}+4 a z^9+10 z^9 a^{-1} +16 z^9 a^{-3} +10 z^9 a^{-5} +3 a^2 z^8-9 z^8 a^{-2} +6 z^8 a^{-4} +12 z^8 a^{-6} +a^3 z^7-10 a z^7-32 z^7 a^{-1} -42 z^7 a^{-3} -12 z^7 a^{-5} +9 z^7 a^{-7} -11 a^2 z^6-10 z^6 a^{-2} -27 z^6 a^{-4} -21 z^6 a^{-6} +4 z^6 a^{-8} -19 z^6-4 a^3 z^5+3 a z^5+30 z^5 a^{-1} +40 z^5 a^{-3} +2 z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4+13 z^4 a^{-2} +23 z^4 a^{-4} +16 z^4 a^{-6} -4 z^4 a^{-8} +23 z^4+5 a^3 z^3+5 a z^3-14 z^3 a^{-1} -20 z^3 a^{-3} +3 z^3 a^{-5} +8 z^3 a^{-7} -z^3 a^{-9} -6 a^2 z^2-2 z^2 a^{-2} -5 z^2 a^{-4} -6 z^2 a^{-6} -9 z^2-2 a^3 z-2 a z+3 z a^{-1} +5 z a^{-3} -z a^{-5} -3 z a^{-7} +a^2-2 a^{-2} + a^{-6} +1 }[/math]

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