K12a506
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-15 q^3+22 q^2-27 q+29-27 q^{-1} +22 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^2-39 t+49-39 t^{-1} +21 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-z^4-2 z^2+1 }[/math] |
| Determinant | 185 |
| 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^2-8 z^2 a^{-2} +2 z^2 a^{-4} +10 z^2+a^4-2 a^2-2 a^{-2} + a^{-4} +3 }[/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+15 a z^9+15 z^9 a^{-1} +7 z^9 a^{-3} +7 a^4 z^8+7 a^2 z^8+7 z^8 a^{-2} +7 z^8 a^{-4} +4 a^5 z^7-9 a^3 z^7-36 a z^7-36 z^7 a^{-1} -9 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-15 a^4 z^6-34 a^2 z^6-34 z^6 a^{-2} -15 z^6 a^{-4} +z^6 a^{-6} -36 z^6-9 a^5 z^5-4 a^3 z^5+26 a z^5+26 z^5 a^{-1} -4 z^5 a^{-3} -9 z^5 a^{-5} -2 a^6 z^4+9 a^4 z^4+37 a^2 z^4+37 z^4 a^{-2} +9 z^4 a^{-4} -2 z^4 a^{-6} +52 z^4+5 a^5 z^3+6 a^3 z^3+6 z^3 a^{-3} +5 z^3 a^{-5} +a^6 z^2-4 a^4 z^2-16 a^2 z^2-16 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} -22 z^2-a^5 z-2 a^3 z-3 a z-3 z a^{-1} -2 z a^{-3} -z a^{-5} +a^4+2 a^2+2 a^{-2} + a^{-4} +3 }[/math] |
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