K12a784
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-10 q^5+17 q^4-24 q^3+29 q^2-30 q+29-22 q^{-1} +15 q^{-2} -8 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+23 t^2-39 t+47-39 t^{-1} +23 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+9 z^4+4 z^2+1 }[/math] |
| Determinant | 193 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +5 z^6-4 a^2 z^4+5 z^4 a^{-2} -3 z^4 a^{-4} +11 z^4-6 a^2 z^2+z^2 a^{-2} -3 z^2 a^{-4} +12 z^2-3 a^2- a^{-2} - a^{-4} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +12 z^{10} a^{-2} +6 z^{10} a^{-4} +6 z^{10}+9 a z^9+14 z^9 a^{-1} +12 z^9 a^{-3} +7 z^9 a^{-5} +9 a^2 z^8-18 z^8 a^{-2} -8 z^8 a^{-4} +4 z^8 a^{-6} +3 z^8+6 a^3 z^7-10 a z^7-37 z^7 a^{-1} -41 z^7 a^{-3} -19 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-15 a^2 z^6-10 z^6 a^{-2} -11 z^6 a^{-4} -12 z^6 a^{-6} -29 z^6+a^5 z^5-8 a^3 z^5-a z^5+20 z^5 a^{-1} +28 z^5 a^{-3} +13 z^5 a^{-5} -3 z^5 a^{-7} -4 a^4 z^4+17 a^2 z^4+19 z^4 a^{-2} +12 z^4 a^{-4} +11 z^4 a^{-6} +39 z^4-2 a^5 z^3+5 a^3 z^3+13 a z^3+7 z^3 a^{-1} -4 z^3 a^{-3} -2 z^3 a^{-5} +3 z^3 a^{-7} +a^4 z^2-11 a^2 z^2-7 z^2 a^{-2} -z^2 a^{-4} -3 z^2 a^{-6} -21 z^2+a^5 z-2 a^3 z-7 a z-6 z a^{-1} -z a^{-3} -z a^{-7} +3 a^2+ a^{-2} - a^{-4} +6 }[/math] |
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