K12a499
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+11 q^4-19 q^3+28 q^2-34 q+37-34 q^{-1} +28 q^{-2} -19 q^{-3} +11 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+25 t^2-51 t+65-51 t^{-1} +25 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+3 z^4+2 z^2+1 }[/math] |
| Determinant | 233 |
| 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^4-6 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +13 z^4+a^4 z^2-7 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} +14 z^2-2 a^2-2 a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +5 a^2 z^{10}+5 z^{10} a^{-2} +10 z^{10}+10 a^3 z^9+25 a z^9+25 z^9 a^{-1} +10 z^9 a^{-3} +10 a^4 z^8+19 a^2 z^8+19 z^8 a^{-2} +10 z^8 a^{-4} +18 z^8+5 a^5 z^7-9 a^3 z^7-45 a z^7-45 z^7 a^{-1} -9 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-20 a^4 z^6-64 a^2 z^6-64 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} -86 z^6-9 a^5 z^5-12 a^3 z^5+9 a z^5+9 z^5 a^{-1} -12 z^5 a^{-3} -9 z^5 a^{-5} -a^6 z^4+13 a^4 z^4+58 a^2 z^4+58 z^4 a^{-2} +13 z^4 a^{-4} -z^4 a^{-6} +88 z^4+4 a^5 z^3+14 a^3 z^3+17 a z^3+17 z^3 a^{-1} +14 z^3 a^{-3} +4 z^3 a^{-5} -3 a^4 z^2-20 a^2 z^2-20 z^2 a^{-2} -3 z^2 a^{-4} -34 z^2-3 a^3 z-7 a z-7 z a^{-1} -3 z a^{-3} +2 a^2+2 a^{-2} +5 }[/math] |
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