K12a622

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^5+4 q^4-10 q^3+18 q^2-25 q+30-31 q^{-1} +29 q^{-2} -22 q^{-3} +15 q^{-4} -8 q^{-5} +3 q^{-6} - q^{-7} }[/math]
Alexander polynomial	[math]\displaystyle{ -2 t^3+17 t^2-47 t+65-47 t^{-1} +17 t^{-2} -2 t^{-3} }[/math]
Conway polynomial	[math]\displaystyle{ -2 z^6+5 z^4+3 z^2+1 }[/math]
Determinant	197
Signature	0
HOMFLY-PT polynomial	[math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+2 z^2 a^4+a^4-z^6 a^2-z^6+z^4+3 z^2+2+2 z^4 a^{-2} - a^{-2} -z^2 a^{-4} }[/math]
Kauffman polynomial	[math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+12 a^2 z^{10}+7 z^{10}+5 a^5 z^9+9 a^3 z^9+16 a z^9+12 z^9 a^{-1} +3 a^6 z^8-9 a^4 z^8-21 a^2 z^8+13 z^8 a^{-2} +4 z^8+a^7 z^7-14 a^5 z^7-36 a^3 z^7-43 a z^7-13 z^7 a^{-1} +9 z^7 a^{-3} -10 a^6 z^6-a^4 z^6+2 a^2 z^6-20 z^6 a^{-2} +4 z^6 a^{-4} -31 z^6-4 a^7 z^5+11 a^5 z^5+39 a^3 z^5+34 a z^5-3 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +10 a^6 z^4+6 a^4 z^4+10 a^2 z^4+14 z^4 a^{-2} -4 z^4 a^{-4} +32 z^4+5 a^7 z^3-3 a^5 z^3-20 a^3 z^3-11 a z^3+9 z^3 a^{-1} +7 z^3 a^{-3} -z^3 a^{-5} -4 a^6 z^2-3 a^4 z^2-5 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} -13 z^2-2 a^7 z+4 a^3 z+a z-3 z a^{-1} -2 z a^{-3} +a^6+a^4+ a^{-2} +2 }[/math]

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