K12n711
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^5+6 q^4-10 q^3+15 q^2-18 q+19-17 q^{-1} +13 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+13 t^2-23 t+29-23 t^{-1} +13 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+3 z^4+1 }[/math] |
| Determinant | 113 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +5 z^6-3 a^2 z^4-2 z^4 a^{-2} +8 z^4-2 a^2 z^2+z^2 a^{-2} -z^2 a^{-4} +2 z^2+a^2+3 a^{-2} - a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+6 a z^9+9 z^9 a^{-1} +3 z^9 a^{-3} +8 a^2 z^8-z^8 a^{-2} +z^8 a^{-4} +6 z^8+7 a^3 z^7-8 a z^7-21 z^7 a^{-1} -6 z^7 a^{-3} +4 a^4 z^6-13 a^2 z^6+4 z^6 a^{-2} +4 z^6 a^{-4} -17 z^6+a^5 z^5-11 a^3 z^5+4 a z^5+23 z^5 a^{-1} +10 z^5 a^{-3} +3 z^5 a^{-5} -6 a^4 z^4+6 a^2 z^4-13 z^4 a^{-2} -13 z^4 a^{-4} +12 z^4-a^5 z^3+3 a^3 z^3-11 z^3 a^{-1} -13 z^3 a^{-3} -6 z^3 a^{-5} +a^4 z^2+11 z^2 a^{-2} +7 z^2 a^{-4} +3 z^2+2 z a^{-1} +4 z a^{-3} +2 z a^{-5} -a^2-3 a^{-2} - a^{-4} -2 }[/math] |
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