K12a447
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+3 q^4-6 q^3+10 q^2-14 q+18-18 q^{-1} +17 q^{-2} -14 q^{-3} +10 q^{-4} -6 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+12 t^2-28 t+37-28 t^{-1} +12 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+2 z^2+1 }[/math] |
| Determinant | 121 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+4 z^2 a^4+2 a^4-z^6 a^2-2 z^4 a^2-2 z^2 a^2-a^2-z^6-2 z^4-2 z^2+2 z^4 a^{-2} +4 z^2 a^{-2} +2 a^{-2} -z^2 a^{-4} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+4 a^5 z^9+5 a^3 z^9+5 a z^9+4 z^9 a^{-1} +3 a^6 z^8-6 a^4 z^8-17 a^2 z^8+4 z^8 a^{-2} -4 z^8+a^7 z^7-14 a^5 z^7-28 a^3 z^7-22 a z^7-5 z^7 a^{-1} +4 z^7 a^{-3} -12 a^6 z^6-7 a^4 z^6+13 a^2 z^6-2 z^6 a^{-2} +3 z^6 a^{-4} +3 z^6-4 a^7 z^5+12 a^5 z^5+40 a^3 z^5+33 a z^5+3 z^5 a^{-1} -5 z^5 a^{-3} +z^5 a^{-5} +13 a^6 z^4+17 a^4 z^4+4 a^2 z^4-7 z^4 a^{-2} -6 z^4 a^{-4} -z^4+4 a^7 z^3-4 a^5 z^3-25 a^3 z^3-19 a z^3-z^3 a^{-1} -z^3 a^{-3} -2 z^3 a^{-5} -5 a^6 z^2-11 a^4 z^2-7 a^2 z^2+7 z^2 a^{-2} +3 z^2 a^{-4} +3 z^2-a^7 z+a^5 z+5 a^3 z+4 a z+z a^{-1} +z a^{-3} +z a^{-5} +a^6+2 a^4+a^2-2 a^{-2} - a^{-4} }[/math] |
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