K12a185

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^8+5 q^7-13 q^6+22 q^5-31 q^4+38 q^3-39 q^2+36 q-28+19 q^{-1} -10 q^{-2} +4 q^{-3} - q^{-4} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^4+8 t^3-27 t^2+54 t-67+54 t^{-1} -27 t^{-2} +8 t^{-3} - t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -z^8+z^4+2 z^2+1 }[/math]
Determinant	247
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-8 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +6 z^4-2 a^2 z^2-7 z^2 a^{-2} +5 z^2 a^{-4} -z^2 a^{-6} +7 z^2-a^2-2 a^{-2} +2 a^{-4} - a^{-6} +3 }[/math]
Kauffman polynomial	[math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +15 z^{10} a^{-2} +9 z^{10} a^{-4} +6 z^{10}+7 a z^9+20 z^9 a^{-1} +31 z^9 a^{-3} +18 z^9 a^{-5} +4 a^2 z^8-5 z^8 a^{-2} +20 z^8 a^{-4} +20 z^8 a^{-6} -z^8+a^3 z^7-17 a z^7-58 z^7 a^{-1} -68 z^7 a^{-3} -15 z^7 a^{-5} +13 z^7 a^{-7} -12 a^2 z^6-59 z^6 a^{-2} -74 z^6 a^{-4} -29 z^6 a^{-6} +5 z^6 a^{-8} -31 z^6-3 a^3 z^5+11 a z^5+41 z^5 a^{-1} +29 z^5 a^{-3} -13 z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4+68 z^4 a^{-2} +58 z^4 a^{-4} +17 z^4 a^{-6} -2 z^4 a^{-8} +42 z^4+3 a^3 z^3+a z^3-4 z^3 a^{-1} +5 z^3 a^{-3} +13 z^3 a^{-5} +6 z^3 a^{-7} -6 a^2 z^2-24 z^2 a^{-2} -17 z^2 a^{-4} -6 z^2 a^{-6} -19 z^2-a^3 z-2 a z-2 z a^{-1} -2 z a^{-3} -3 z a^{-5} -2 z a^{-7} +a^2+2 a^{-2} +2 a^{-4} + a^{-6} +3 }[/math]

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