K12a214
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-21 q^3+31 q^2-38 q+41-38 q^{-1} +31 q^{-2} -21 q^{-3} +12 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+28 t^2-56 t+71-56 t^{-1} +28 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+1 }[/math] |
| Determinant | 257 |
| 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^4-5 z^4 a^{-2} +z^4 a^{-4} +8 z^4+a^4 z^2-4 a^2 z^2-4 z^2 a^{-2} +z^2 a^{-4} +6 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +8 a^2 z^{10}+8 z^{10} a^{-2} +16 z^{10}+13 a^3 z^9+29 a z^9+29 z^9 a^{-1} +13 z^9 a^{-3} +11 a^4 z^8+10 a^2 z^8+10 z^8 a^{-2} +11 z^8 a^{-4} -2 z^8+5 a^5 z^7-19 a^3 z^7-67 a z^7-67 z^7 a^{-1} -19 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-21 a^4 z^6-50 a^2 z^6-50 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -56 z^6-8 a^5 z^5+4 a^3 z^5+45 a z^5+45 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+44 z^4 a^{-2} +13 z^4 a^{-4} -z^4 a^{-6} +60 z^4+3 a^5 z^3+2 a^3 z^3-9 a z^3-9 z^3 a^{-1} +2 z^3 a^{-3} +3 z^3 a^{-5} -3 a^4 z^2-12 a^2 z^2-12 z^2 a^{-2} -3 z^2 a^{-4} -18 z^2+1 }[/math] |
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