K12a323
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+10 q^4-20 q^3+30 q^2-37 q+41-38 q^{-1} +32 q^{-2} -22 q^{-3} +12 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+28 t^2-55 t+69-55 t^{-1} +28 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^2+1 }[/math] |
| Determinant | 253 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-5 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +9 z^4+a^4 z^2-5 a^2 z^2-8 z^2 a^{-2} +2 z^2 a^{-4} +11 z^2-2 a^2-4 a^{-2} + a^{-4} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +8 a^2 z^{10}+7 z^{10} a^{-2} +15 z^{10}+13 a^3 z^9+28 a z^9+25 z^9 a^{-1} +10 z^9 a^{-3} +11 a^4 z^8+12 a^2 z^8+9 z^8 a^{-2} +8 z^8 a^{-4} +2 z^8+5 a^5 z^7-16 a^3 z^7-57 a z^7-51 z^7 a^{-1} -11 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-20 a^4 z^6-53 a^2 z^6-42 z^6 a^{-2} -14 z^6 a^{-4} +z^6 a^{-6} -59 z^6-8 a^5 z^5-3 a^3 z^5+23 a z^5+22 z^5 a^{-1} -4 z^5 a^{-3} -8 z^5 a^{-5} -a^6 z^4+13 a^4 z^4+44 a^2 z^4+43 z^4 a^{-2} +10 z^4 a^{-4} -2 z^4 a^{-6} +61 z^4+4 a^5 z^3+8 a^3 z^3+6 a z^3+9 z^3 a^{-1} +13 z^3 a^{-3} +6 z^3 a^{-5} -3 a^4 z^2-15 a^2 z^2-19 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} -26 z^2-2 a^3 z-5 a z-7 z a^{-1} -6 z a^{-3} -2 z a^{-5} +2 a^2+4 a^{-2} + a^{-4} +6 }[/math] |
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