K12a579
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+8 q^4-14 q^3+21 q^2-25 q+28-26 q^{-1} +21 q^{-2} -15 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+21 t^2-37 t+45-37 t^{-1} +21 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-z^4+1 }[/math] |
| Determinant | 177 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +5 z^6+a^4 z^4-7 a^2 z^4-7 z^4 a^{-2} +z^4 a^{-4} +11 z^4+2 a^4 z^2-8 a^2 z^2-7 z^2 a^{-2} +2 z^2 a^{-4} +11 z^2+a^4-3 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+4 z^{10} a^{-2} +8 z^{10}+7 a^3 z^9+14 a z^9+14 z^9 a^{-1} +7 z^9 a^{-3} +7 a^4 z^8+5 a^2 z^8+4 z^8 a^{-2} +7 z^8 a^{-4} -5 z^8+4 a^5 z^7-10 a^3 z^7-37 a z^7-40 z^7 a^{-1} -13 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-15 a^4 z^6-28 a^2 z^6-30 z^6 a^{-2} -18 z^6 a^{-4} +z^6 a^{-6} -23 z^6-9 a^5 z^5-2 a^3 z^5+35 a z^5+42 z^5 a^{-1} +4 z^5 a^{-3} -10 z^5 a^{-5} -2 a^6 z^4+8 a^4 z^4+30 a^2 z^4+39 z^4 a^{-2} +14 z^4 a^{-4} -2 z^4 a^{-6} +43 z^4+5 a^5 z^3+4 a^3 z^3-12 a z^3-14 z^3 a^{-1} +2 z^3 a^{-3} +5 z^3 a^{-5} +a^6 z^2-3 a^4 z^2-15 a^2 z^2-17 z^2 a^{-2} -5 z^2 a^{-4} -23 z^2-a^5 z-a^3 z+a z+z a^{-1} +a^4+3 a^2+ a^{-2} +4 }[/math] |
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