K12a778
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+13 q^4-23 q^3+33 q^2-40 q+43-39 q^{-1} +31 q^{-2} -21 q^{-3} +11 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+30 t^2-57 t+71-57 t^{-1} +30 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-4 z^4-2 z^2+1 }[/math] |
| Determinant | 265 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +3 z^6+a^4 z^4-5 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +3 z^4+2 a^4 z^2-4 a^2 z^2-z^2 a^{-2} +z^2 a^{-4} +a^4-a^2+ a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +9 a^2 z^{10}+11 z^{10} a^{-2} +20 z^{10}+12 a^3 z^9+25 a z^9+29 z^9 a^{-1} +16 z^9 a^{-3} +9 a^4 z^8+2 a^2 z^8-z^8 a^{-2} +12 z^8 a^{-4} -20 z^8+4 a^5 z^7-19 a^3 z^7-64 a z^7-75 z^7 a^{-1} -29 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-17 a^4 z^6-33 a^2 z^6-33 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} -25 z^6-7 a^5 z^5+11 a^3 z^5+51 a z^5+57 z^5 a^{-1} +17 z^5 a^{-3} -7 z^5 a^{-5} -2 a^6 z^4+14 a^4 z^4+36 a^2 z^4+29 z^4 a^{-2} +13 z^4 a^{-4} -z^4 a^{-6} +35 z^4+4 a^5 z^3-4 a^3 z^3-16 a z^3-16 z^3 a^{-1} -6 z^3 a^{-3} +2 z^3 a^{-5} +a^6 z^2-7 a^4 z^2-14 a^2 z^2-6 z^2 a^{-2} -4 z^2 a^{-4} -8 z^2-a^5 z+2 a z+2 z a^{-1} +z a^{-3} +a^4+a^2- a^{-2} }[/math] |
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