K12n825
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-2 q^7+4 q^6-6 q^5+6 q^4-7 q^3+7 q^2-5 q+4-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+6 t^2-9 t+11-9 t^{-1} +6 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-6 z^4-3 z^2+1 }[/math] |
| Determinant | 45 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6 a^{-4} -4 z^4 a^{-2} -4 z^4 a^{-4} +z^4 a^{-6} +z^4-4 z^2 a^{-2} -5 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2-3 a^{-4} +2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +2 z^9 a^{-3} +4 z^9 a^{-5} +2 z^9 a^{-7} +2 z^8 a^{-2} -z^8 a^{-4} -2 z^8 a^{-6} +z^8 a^{-8} +z^7 a^{-1} -5 z^7 a^{-3} -17 z^7 a^{-5} -11 z^7 a^{-7} -5 z^6 a^{-2} -6 z^6 a^{-4} -7 z^6 a^{-6} -6 z^6 a^{-8} -2 z^5 a^{-3} +17 z^5 a^{-5} +19 z^5 a^{-7} +3 z^4 a^{-2} +z^4 a^{-4} +14 z^4 a^{-6} +12 z^4 a^{-8} +4 z^4+2 a z^3-2 z^3 a^{-1} +5 z^3 a^{-3} -3 z^3 a^{-5} -12 z^3 a^{-7} +a^2 z^2-4 z^2 a^{-2} +8 z^2 a^{-4} -2 z^2 a^{-6} -8 z^2 a^{-8} -5 z^2-z a^{-1} -2 z a^{-3} +2 z a^{-5} +3 z a^{-7} -3 a^{-4} -2 a^{-6} +2 }[/math] |
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