K12n821
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-2 q^4+3 q^3-4 q^2+5 q-5+5 q^{-1} -4 q^{-2} +3 q^{-3} -2 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+3 t^3-5 t^2+6 t-5+6 t^{-1} -5 t^{-2} +3 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-5 z^6-7 z^4-3 z^2+1 }[/math] |
| Determinant | 35 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8+a^2 z^6+z^6 a^{-2} -7 z^6+5 a^2 z^4+5 z^4 a^{-2} -17 z^4+7 a^2 z^2+7 z^2 a^{-2} -17 z^2+3 a^2+3 a^{-2} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+a z^9+3 z^9 a^{-1} +2 z^9 a^{-3} -4 z^8 a^{-2} +z^8 a^{-4} -5 z^8-3 a z^7-15 z^7 a^{-1} -12 z^7 a^{-3} +5 a^2 z^6+2 z^6 a^{-2} -6 z^6 a^{-4} +13 z^6+4 a^3 z^5+4 a z^5+22 z^5 a^{-1} +22 z^5 a^{-3} +3 a^4 z^4-14 a^2 z^4+2 z^4 a^{-2} +11 z^4 a^{-4} -26 z^4+2 a^5 z^3-7 a^3 z^3-8 a z^3-12 z^3 a^{-1} -13 z^3 a^{-3} +a^6 z^2-2 a^4 z^2+9 a^2 z^2+4 z^2 a^{-2} -6 z^2 a^{-4} +22 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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