K12n578
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+6 q^4-10 q^3+14 q^2-15 q+15-13 q^{-1} +9 q^{-2} -5 q^{-3} +2 q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+11 t^2-20 t+25-20 t^{-1} +11 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-7 z^4-3 z^2+1 }[/math] |
| Determinant | 93 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -2 z^6+2 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} -8 z^4+5 a^2 z^2+z^2 a^{-2} +2 z^2 a^{-4} -11 z^2+3 a^2+3 a^{-2} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+2 a z^9+5 z^9 a^{-1} +3 z^9 a^{-3} +2 a^2 z^8+4 z^8 a^{-2} +4 z^8 a^{-4} +2 z^8+a^3 z^7+a z^7-7 z^7 a^{-1} -4 z^7 a^{-3} +3 z^7 a^{-5} +2 a^2 z^6-7 z^6 a^{-2} -10 z^6 a^{-4} +z^6 a^{-6} +6 z^6+3 a^3 z^5+7 z^5 a^{-1} +z^5 a^{-3} -9 z^5 a^{-5} +3 a^4 z^4-6 a^2 z^4-3 z^4 a^{-2} +7 z^4 a^{-4} -3 z^4 a^{-6} -22 z^4-5 a^3 z^3-3 a z^3-9 z^3 a^{-1} -4 z^3 a^{-3} +7 z^3 a^{-5} -4 a^4 z^2+7 a^2 z^2+5 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2 a^{-6} +20 z^2+2 a^3 z+3 a z+3 z a^{-1} +2 z a^{-3} -3 a^2-3 a^{-2} -5 }[/math] |
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