K12n775

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^6+6 q^5-12 q^4+17 q^3-21 q^2+22 q-20+16 q^{-1} -10 q^{-2} +5 q^{-3} - q^{-4} }[/math]
Alexander polynomial	[math]\displaystyle{ -t^4+6 t^3-17 t^2+27 t-29+27 t^{-1} -17 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	131
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^4-10 z^4 a^{-2} +4 z^4 a^{-4} +6 z^4-a^2 z^2-10 z^2 a^{-2} +5 z^2 a^{-4} -z^2 a^{-6} +4 z^2+a^2-3 a^{-2} +2 a^{-4} +1 }[/math]
Kauffman polynomial	[math]\displaystyle{ 4 z^{10} a^{-2} +4 z^{10}+8 a z^9+19 z^9 a^{-1} +11 z^9 a^{-3} +5 a^2 z^8+8 z^8 a^{-2} +10 z^8 a^{-4} +3 z^8+a^3 z^7-24 a z^7-58 z^7 a^{-1} -30 z^7 a^{-3} +3 z^7 a^{-5} -15 a^2 z^6-51 z^6 a^{-2} -25 z^6 a^{-4} -41 z^6-2 a^3 z^5+17 a z^5+50 z^5 a^{-1} +34 z^5 a^{-3} +3 z^5 a^{-5} +12 a^2 z^4+57 z^4 a^{-2} +32 z^4 a^{-4} +6 z^4 a^{-6} +43 z^4+a^3 z^3-2 a z^3-21 z^3 a^{-1} -20 z^3 a^{-3} -z^3 a^{-5} +z^3 a^{-7} -a^2 z^2-26 z^2 a^{-2} -15 z^2 a^{-4} -z^2 a^{-6} -13 z^2+a z+5 z a^{-1} +4 z a^{-3} -a^2+3 a^{-2} +2 a^{-4} +1 }[/math]

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