K12n643
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^9+4 q^8-6 q^7+8 q^6-8 q^5+8 q^4-6 q^3+4 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+8 t^2-10 t+9-10 t^{-1} +8 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-4 z^4+4 z^2+1 }[/math] |
| Determinant | 49 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} +z^4 a^{-2} -3 z^4 a^{-4} -3 z^4 a^{-6} +z^4 a^{-8} +3 z^2 a^{-2} -z^2 a^{-4} -z^2 a^{-6} +3 z^2 a^{-8} + a^{-2} + a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +3 z^9 a^{-7} +z^9 a^{-9} +2 z^8 a^{-4} -3 z^8 a^{-6} -5 z^8 a^{-8} +2 z^7 a^{-3} -7 z^7 a^{-5} -14 z^7 a^{-7} -5 z^7 a^{-9} +z^6 a^{-2} -5 z^6 a^{-4} +5 z^6 a^{-6} +12 z^6 a^{-8} +z^6 a^{-10} -7 z^5 a^{-3} +10 z^5 a^{-5} +30 z^5 a^{-7} +13 z^5 a^{-9} -4 z^4 a^{-2} -4 z^4 a^{-6} -7 z^4 a^{-8} +z^4 a^{-10} +5 z^3 a^{-3} -9 z^3 a^{-5} -25 z^3 a^{-7} -9 z^3 a^{-9} +2 z^3 a^{-11} +4 z^2 a^{-2} +2 z^2 a^{-4} -2 z^2 a^{-10} +2 z a^{-5} +6 z a^{-7} +2 z a^{-9} -2 z a^{-11} - a^{-2} + a^{-8} + a^{-10} }[/math] |
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