K12n115
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+q^2-q+1+ q^{-1} - q^{-2} +3 q^{-3} -3 q^{-4} +3 q^{-5} -2 q^{-6} + q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-t^3-t^2+4 t-5+4 t^{-1} - t^{-2} - t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+7 z^6+13 z^4+7 z^2+1 }[/math] |
| Determinant | 11 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+8 a^2 z^6-z^6-a^6 z^4-a^4 z^4+21 a^2 z^4-6 z^4-3 a^6 z^2-2 a^4 z^2+22 a^2 z^2-10 z^2-2 a^6-a^4+8 a^2-4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+a^3 z^9+2 a z^9+z^9 a^{-1} +a^6 z^8-9 a^2 z^8-8 z^8+a^7 z^7+a^5 z^7-9 a^3 z^7-17 a z^7-8 z^7 a^{-1} +a^8 z^6-5 a^6 z^6+27 a^2 z^6+21 z^6+a^9 z^5-3 a^7 z^5-4 a^5 z^5+25 a^3 z^5+46 a z^5+21 z^5 a^{-1} -3 a^8 z^4+10 a^6 z^4-36 a^2 z^4-23 z^4-4 a^9 z^3+2 a^7 z^3+7 a^5 z^3-25 a^3 z^3-47 a z^3-21 z^3 a^{-1} +a^8 z^2-8 a^6 z^2+3 a^4 z^2+25 a^2 z^2+13 z^2+3 a^9 z-a^7 z-3 a^5 z+9 a^3 z+15 a z+7 z a^{-1} +2 a^6-a^4-8 a^2-4 }[/math] |
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