K12n615

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^6+5 q^5-9 q^4+13 q^3-16 q^2+16 q-15+12 q^{-1} -7 q^{-2} +4 q^{-3} - q^{-4} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^4+6 t^3-15 t^2+19 t-17+19 t^{-1} -15 t^{-2} +6 t^{-3} - t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -z^8-2 z^6+z^4-3 z^2+1 }[/math]
Determinant	99
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-9 z^4 a^{-2} +4 z^4 a^{-4} +7 z^4-2 a^2 z^2-9 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +5 z^2+a^2-3 a^{-2} +2 a^{-4} +1 }[/math]
Kauffman polynomial	[math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+5 a z^9+11 z^9 a^{-1} +6 z^9 a^{-3} +4 a^2 z^8+7 z^8 a^{-2} +6 z^8 a^{-4} +5 z^8+a^3 z^7-16 a z^7-35 z^7 a^{-1} -16 z^7 a^{-3} +2 z^7 a^{-5} -15 a^2 z^6-38 z^6 a^{-2} -16 z^6 a^{-4} -37 z^6-3 a^3 z^5+12 a z^5+34 z^5 a^{-1} +21 z^5 a^{-3} +2 z^5 a^{-5} +16 a^2 z^4+48 z^4 a^{-2} +25 z^4 a^{-4} +5 z^4 a^{-6} +44 z^4+2 a^3 z^3-3 a z^3-21 z^3 a^{-1} -18 z^3 a^{-3} -z^3 a^{-5} +z^3 a^{-7} -4 a^2 z^2-26 z^2 a^{-2} -15 z^2 a^{-4} -2 z^2 a^{-6} -17 z^2+2 a z+8 z a^{-1} +7 z a^{-3} +z a^{-5} -a^2+3 a^{-2} +2 a^{-4} +1 }[/math]

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