K12n593
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^9+4 q^8-7 q^7+10 q^6-10 q^5+10 q^4-8 q^3+6 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+9 t^2-13 t+13-13 t^{-1} +9 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-3 z^4+5 z^2+1 }[/math] |
| Determinant | 61 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} +z^4 a^{-2} -2 z^4 a^{-4} -3 z^4 a^{-6} +z^4 a^{-8} +2 z^2 a^{-2} +2 z^2 a^{-4} -2 z^2 a^{-6} +3 z^2 a^{-8} +2 a^{-4} - a^{-6} + a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +3 z^9 a^{-5} +4 z^9 a^{-7} +z^9 a^{-9} +4 z^8 a^{-4} +z^8 a^{-6} -3 z^8 a^{-8} +3 z^7 a^{-3} -8 z^7 a^{-5} -15 z^7 a^{-7} -4 z^7 a^{-9} +z^6 a^{-2} -12 z^6 a^{-4} -10 z^6 a^{-6} +4 z^6 a^{-8} +z^6 a^{-10} -9 z^5 a^{-3} +6 z^5 a^{-5} +24 z^5 a^{-7} +9 z^5 a^{-9} -3 z^4 a^{-2} +9 z^4 a^{-4} +14 z^4 a^{-6} +3 z^4 a^{-8} +z^4 a^{-10} +5 z^3 a^{-3} -5 z^3 a^{-5} -15 z^3 a^{-7} -3 z^3 a^{-9} +2 z^3 a^{-11} +2 z^2 a^{-2} -6 z^2 a^{-4} -8 z^2 a^{-6} -2 z^2 a^{-8} -2 z^2 a^{-10} +z a^{-5} +4 z a^{-7} -3 z a^{-11} +2 a^{-4} + a^{-6} + a^{-8} + a^{-10} }[/math] |
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