K12a335

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^8+5 q^7-14 q^6+24 q^5-34 q^4+42 q^3-43 q^2+40 q-31+21 q^{-1} -11 q^{-2} +4 q^{-3} - q^{-4} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^4+9 t^3-30 t^2+59 t-73+59 t^{-1} -30 t^{-2} +9 t^{-3} - t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -z^8+z^6+4 z^4+4 z^2+1 }[/math]
Determinant	271
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ -z^8 a^{-2} -3 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-3 z^4 a^{-2} +4 z^4 a^{-4} -z^4 a^{-6} +5 z^4-2 a^2 z^2+z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} +4 z^2-a^2+2 a^{-2} - a^{-6} +1 }[/math]
Kauffman polynomial	[math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +21 z^{10} a^{-2} +13 z^{10} a^{-4} +8 z^{10}+8 a z^9+22 z^9 a^{-1} +37 z^9 a^{-3} +23 z^9 a^{-5} +4 a^2 z^8-25 z^8 a^{-2} +10 z^8 a^{-4} +23 z^8 a^{-6} -8 z^8+a^3 z^7-20 a z^7-74 z^7 a^{-1} -95 z^7 a^{-3} -28 z^7 a^{-5} +14 z^7 a^{-7} -11 a^2 z^6-29 z^6 a^{-2} -60 z^6 a^{-4} -33 z^6 a^{-6} +5 z^6 a^{-8} -18 z^6-3 a^3 z^5+17 a z^5+71 z^5 a^{-1} +68 z^5 a^{-3} +2 z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4+39 z^4 a^{-2} +41 z^4 a^{-4} +18 z^4 a^{-6} -z^4 a^{-8} +28 z^4+3 a^3 z^3-6 a z^3-29 z^3 a^{-1} -23 z^3 a^{-3} +4 z^3 a^{-5} +7 z^3 a^{-7} -5 a^2 z^2-8 z^2 a^{-2} -7 z^2 a^{-4} -5 z^2 a^{-6} -11 z^2-a^3 z+a z+6 z a^{-1} +6 z a^{-3} -z a^{-5} -3 z a^{-7} +a^2-2 a^{-2} + a^{-6} +1 }[/math]

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