K12n531
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^5+5 q^4-9 q^3+13 q^2-15 q+17-14 q^{-1} +11 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+11 t^2-20 t+25-20 t^{-1} +11 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+7 z^4+4 z^2+1 }[/math] |
| Determinant | 97 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +6 z^6-4 a^2 z^4-3 z^4 a^{-2} +14 z^4-6 a^2 z^2-3 z^2 a^{-2} -z^2 a^{-4} +14 z^2-3 a^2- a^{-2} - a^{-4} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+4 a z^9+6 z^9 a^{-1} +2 z^9 a^{-3} +6 a^2 z^8+4 z^8 a^{-2} +z^8 a^{-4} +9 z^8+5 a^3 z^7-3 a z^7-10 z^7 a^{-1} -2 z^7 a^{-3} +3 a^4 z^6-12 a^2 z^6-13 z^6 a^{-2} +2 z^6 a^{-4} -30 z^6+a^5 z^5-8 a^3 z^5-6 a z^5+z^5 a^{-1} +z^5 a^{-3} +3 z^5 a^{-5} -5 a^4 z^4+13 a^2 z^4+14 z^4 a^{-2} -8 z^4 a^{-4} +40 z^4-2 a^5 z^3+3 a^3 z^3+14 a z^3+11 z^3 a^{-1} -5 z^3 a^{-3} -7 z^3 a^{-5} +a^4 z^2-10 a^2 z^2-7 z^2 a^{-2} +3 z^2 a^{-4} -21 z^2+a^5 z-2 a^3 z-7 a z-5 z a^{-1} +2 z a^{-3} +3 z a^{-5} +3 a^2+ a^{-2} - a^{-4} +6 }[/math] |
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