K12n689

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^{15}-2 q^{14}+2 q^{13}-3 q^{12}+2 q^{11}-2 q^{10}+q^9+q^8-q^7+2 q^6-q^5+q^4 }[/math]
Alexander polynomial	[math]\displaystyle{ 2 t^4-3 t^3+5 t-7+5 t^{-1} -3 t^{-3} +2 t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ 2 z^8+13 z^6+22 z^4+10 z^2+1 }[/math]
Determinant	7
Signature	6
HOMFLY-PT polynomial	[math]\displaystyle{ z^8 a^{-8} +z^8 a^{-10} +7 z^6 a^{-8} +7 z^6 a^{-10} -z^6 a^{-12} +15 z^4 a^{-8} +15 z^4 a^{-10} -8 z^4 a^{-12} +11 z^2 a^{-8} +13 z^2 a^{-10} -16 z^2 a^{-12} +2 z^2 a^{-14} +2 a^{-8} +5 a^{-10} -9 a^{-12} +3 a^{-14} }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-9} +2 z^9 a^{-11} +z^9 a^{-13} +z^8 a^{-8} -7 z^8 a^{-10} -9 z^8 a^{-12} +z^8 a^{-16} -6 z^7 a^{-9} -15 z^7 a^{-11} -9 z^7 a^{-13} +2 z^7 a^{-15} +2 z^7 a^{-17} -7 z^6 a^{-8} +16 z^6 a^{-10} +28 z^6 a^{-12} +z^6 a^{-14} -3 z^6 a^{-16} +z^6 a^{-18} +9 z^5 a^{-9} +34 z^5 a^{-11} +25 z^5 a^{-13} -9 z^5 a^{-15} -9 z^5 a^{-17} +15 z^4 a^{-8} -19 z^4 a^{-10} -43 z^4 a^{-12} -6 z^4 a^{-14} -z^4 a^{-16} -4 z^4 a^{-18} -2 z^3 a^{-9} -30 z^3 a^{-11} -28 z^3 a^{-13} +10 z^3 a^{-15} +10 z^3 a^{-17} -11 z^2 a^{-8} +15 z^2 a^{-10} +33 z^2 a^{-12} +7 z^2 a^{-14} +3 z^2 a^{-16} +3 z^2 a^{-18} -z a^{-9} +10 z a^{-11} +10 z a^{-13} -4 z a^{-15} -3 z a^{-17} +2 a^{-8} -5 a^{-10} -9 a^{-12} -3 a^{-14} }[/math]

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