K12n761
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^7+5 q^6-7 q^5+9 q^4-10 q^3+10 q^2-8 q+6-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+10 t^2-10 t+9-10 t^{-1} +10 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+z^2+1 }[/math] |
| Determinant | 61 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -9 z^4 a^{-2} +13 z^4 a^{-4} -5 z^4 a^{-6} +z^4-11 z^2 a^{-2} +14 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} +3 z^2-4 a^{-2} +5 a^{-4} -2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +3 z^9 a^{-1} +9 z^9 a^{-3} +6 z^9 a^{-5} -4 z^8 a^{-2} +z^8 a^{-4} +6 z^8 a^{-6} +z^8-15 z^7 a^{-1} -42 z^7 a^{-3} -25 z^7 a^{-5} +2 z^7 a^{-7} -15 z^6 a^{-2} -35 z^6 a^{-4} -25 z^6 a^{-6} -5 z^6+23 z^5 a^{-1} +56 z^5 a^{-3} +28 z^5 a^{-5} -5 z^5 a^{-7} +38 z^4 a^{-2} +57 z^4 a^{-4} +29 z^4 a^{-6} +z^4 a^{-8} +9 z^4-12 z^3 a^{-1} -26 z^3 a^{-3} -13 z^3 a^{-5} +z^3 a^{-7} -24 z^2 a^{-2} -30 z^2 a^{-4} -13 z^2 a^{-6} -7 z^2+2 z a^{-1} +4 z a^{-3} +2 z a^{-5} +z a^{-7} +z a^{-9} +4 a^{-2} +5 a^{-4} +2 a^{-6} +2 }[/math] |
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