K12n586
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-8 q^3+13 q^2-16 q+17-16 q^{-1} +13 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+8 t^2-24 t+35-24 t^{-1} +8 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+2 z^4-z^2+1 }[/math] |
| Determinant | 101 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6+2 a^2 z^4+2 z^4 a^{-2} -2 z^4-a^4 z^2+2 a^2 z^2+2 z^2 a^{-2} -z^2 a^{-4} -3 z^2+a^2+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+a^3 z^9+5 a z^9+4 z^9 a^{-1} +7 z^8 a^{-2} +7 z^8-6 a z^7+z^7 a^{-1} +7 z^7 a^{-3} +4 a^4 z^6+7 a^2 z^6-8 z^6 a^{-2} +4 z^6 a^{-4} -9 z^6+a^5 z^5+4 a^3 z^5+7 a z^5-8 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} -7 a^4 z^4-13 a^2 z^4-2 z^4 a^{-2} -6 z^4 a^{-4} -2 z^4-2 a^5 z^3-8 a^3 z^3-8 a z^3+3 z^3 a^{-1} +4 z^3 a^{-3} -z^3 a^{-5} +3 a^4 z^2+6 a^2 z^2+4 z^2 a^{-2} +2 z^2 a^{-4} +5 z^2+a^5 z+3 a^3 z+2 a z-a^2- a^{-2} -1 }[/math] |
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