K12a1137
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-2 q^7+5 q^6-10 q^5+14 q^4-19 q^3+22 q^2-21 q+19-14 q^{-1} +9 q^{-2} -4 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+16 t^2-31 t+39-31 t^{-1} +16 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-8 z^4-3 z^2+1 }[/math] |
| Determinant | 141 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-6 z^4 a^{-2} -3 z^4 a^{-4} +z^4 a^{-6} -z^4+a^2 z^2-5 z^2 a^{-2} -4 z^2 a^{-4} +3 z^2 a^{-6} +2 z^2-3 a^{-4} +2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +4 z^{10} a^{-2} +6 z^{10} a^{-4} +2 z^{10} a^{-6} +9 z^9 a^{-1} +9 z^9 a^{-3} +2 z^9 a^{-5} +2 z^9 a^{-7} +5 z^8 a^{-2} -15 z^8 a^{-4} -6 z^8 a^{-6} +z^8 a^{-8} +13 z^8+13 a z^7-9 z^7 a^{-1} -28 z^7 a^{-3} -16 z^7 a^{-5} -10 z^7 a^{-7} +9 a^2 z^6-29 z^6 a^{-2} +6 z^6 a^{-4} +z^6 a^{-6} -6 z^6 a^{-8} -19 z^6+4 a^3 z^5-17 a z^5-6 z^5 a^{-1} +17 z^5 a^{-3} +19 z^5 a^{-5} +17 z^5 a^{-7} +a^4 z^4-8 a^2 z^4+21 z^4 a^{-2} -z^4 a^{-4} +7 z^4 a^{-6} +12 z^4 a^{-8} +8 z^4-a^3 z^3+7 a z^3+z^3 a^{-1} -3 z^3 a^{-3} -8 z^3 a^{-5} -12 z^3 a^{-7} +3 a^2 z^2-7 z^2 a^{-2} +7 z^2 a^{-4} -z^2 a^{-6} -8 z^2 a^{-8} -4 z^2+z a^{-3} +5 z a^{-5} +4 z a^{-7} -3 a^{-4} -2 a^{-6} +2 }[/math] |
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