K12n492
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+8 q^4-11 q^3+14 q^2-15 q+14-11 q^{-1} +7 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+9 t^2-20 t+27-20 t^{-1} +9 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-3 z^4-2 z^2+1 }[/math] |
| Determinant | 89 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} -3 z^4+2 a^2 z^2+z^2 a^{-4} -5 z^2+2 a^2+2 a^{-2} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+a z^9+5 z^9 a^{-1} +4 z^9 a^{-3} +6 z^8 a^{-2} +6 z^8 a^{-4} +a z^7-8 z^7 a^{-1} -5 z^7 a^{-3} +4 z^7 a^{-5} +6 a^2 z^6-15 z^6 a^{-2} -15 z^6 a^{-4} +z^6 a^{-6} +7 z^6+3 a^3 z^5+3 a z^5+5 z^5 a^{-1} -5 z^5 a^{-3} -10 z^5 a^{-5} +a^4 z^4-8 a^2 z^4+3 z^4 a^{-2} +7 z^4 a^{-4} -2 z^4 a^{-6} -15 z^4-3 a^3 z^3-3 a z^3-3 z^3 a^{-1} +2 z^3 a^{-3} +5 z^3 a^{-5} -a^4 z^2+6 a^2 z^2+5 z^2 a^{-2} +z^2 a^{-6} +13 z^2+a^3 z+a z+z a^{-1} +z a^{-3} -2 a^2-2 a^{-2} -3 }[/math] |
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