K12a1277
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-11 q^3+15 q^2-18 q+19-17 q^{-1} +13 q^{-2} -9 q^{-3} +5 q^{-4} -2 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+14 t^2-26 t+33-26 t^{-1} +14 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-10 z^4-6 z^2+1 }[/math] |
| Determinant | 121 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-3 a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} -7 z^4+3 a^4 z^2-3 a^2 z^2+2 z^2 a^{-4} -8 z^2+2 a^4-a^2+ a^{-2} + a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+3 z^{10} a^{-2} +5 z^{10}+3 a^3 z^9+a z^9+3 z^9 a^{-1} +5 z^9 a^{-3} +3 a^4 z^8-2 a^2 z^8-4 z^8 a^{-2} +5 z^8 a^{-4} -14 z^8+2 a^5 z^7-8 a^3 z^7-3 a z^7-9 z^7 a^{-1} -13 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-9 a^4 z^6-a^2 z^6-14 z^6 a^{-4} +z^6 a^{-6} +24 z^6-6 a^5 z^5+13 a^3 z^5+5 a z^5+7 z^5 a^{-1} +13 z^5 a^{-3} -8 z^5 a^{-5} -4 a^6 z^4+11 a^4 z^4+7 a^2 z^4+z^4 a^{-2} +12 z^4 a^{-4} -3 z^4 a^{-6} -22 z^4+4 a^5 z^3-14 a^3 z^3-2 a z^3+3 z^3 a^{-1} -9 z^3 a^{-3} +4 z^3 a^{-5} +4 a^6 z^2-9 a^4 z^2-8 a^2 z^2+z^2 a^{-2} -7 z^2 a^{-4} +2 z^2 a^{-6} +15 z^2+3 a^3 z+a z-z a^{-1} +z a^{-3} +2 a^4+a^2- a^{-2} + a^{-4} -2 }[/math] |
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