K12a516

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^9-5 q^8+11 q^7-19 q^6+27 q^5-32 q^4+34 q^3-31 q^2+25 q-16+9 q^{-1} -4 q^{-2} + q^{-3} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^4+7 t^3-23 t^2+47 t-59+47 t^{-1} -23 t^{-2} +7 t^{-3} - t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -z^8-z^6-z^4+2 z^2+1 }[/math]
Determinant	215
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +3 z^6 a^{-4} +z^6-11 z^4 a^{-2} +10 z^4 a^{-4} -3 z^4 a^{-6} +3 z^4-9 z^2 a^{-2} +12 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} +3 z^2-2 a^{-2} +4 a^{-4} -2 a^{-6} +1 }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +4 z^{10} a^{-2} +9 z^{10} a^{-4} +5 z^{10} a^{-6} +7 z^9 a^{-1} +19 z^9 a^{-3} +22 z^9 a^{-5} +10 z^9 a^{-7} +13 z^8 a^{-2} +12 z^8 a^{-4} +16 z^8 a^{-6} +10 z^8 a^{-8} +7 z^8+4 a z^7-5 z^7 a^{-1} -35 z^7 a^{-3} -41 z^7 a^{-5} -10 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-45 z^6 a^{-2} -67 z^6 a^{-4} -58 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -14 z^6-9 a z^5-10 z^5 a^{-1} +11 z^5 a^{-3} +9 z^5 a^{-5} -12 z^5 a^{-7} -9 z^5 a^{-9} -2 a^2 z^4+46 z^4 a^{-2} +73 z^4 a^{-4} +52 z^4 a^{-6} +12 z^4 a^{-8} -z^4 a^{-10} +10 z^4+6 a z^3+11 z^3 a^{-1} +11 z^3 a^{-3} +16 z^3 a^{-5} +14 z^3 a^{-7} +4 z^3 a^{-9} +a^2 z^2-19 z^2 a^{-2} -29 z^2 a^{-4} -18 z^2 a^{-6} -3 z^2 a^{-8} -4 z^2-a z-3 z a^{-1} -5 z a^{-3} -7 z a^{-5} -4 z a^{-7} +2 a^{-2} +4 a^{-4} +2 a^{-6} +1 }[/math]

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