K12a139
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-6 q^5+14 q^4-23 q^3+33 q^2-39 q+41-37 q^{-1} +29 q^{-2} -19 q^{-3} +10 q^{-4} -4 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^4-6 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +8 z^4+2 a^4 z^2-7 a^2 z^2-z^2 a^{-2} +6 z^2+a^4-2 a^2+2 a^{-2} - a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +7 a^2 z^{10}+9 z^{10} a^{-2} +16 z^{10}+10 a^3 z^9+26 a z^9+32 z^9 a^{-1} +16 z^9 a^{-3} +8 a^4 z^8+7 a^2 z^8+13 z^8 a^{-2} +14 z^8 a^{-4} -2 z^8+4 a^5 z^7-14 a^3 z^7-62 a z^7-73 z^7 a^{-1} -23 z^7 a^{-3} +6 z^7 a^{-5} +a^6 z^6-15 a^4 z^6-39 a^2 z^6-61 z^6 a^{-2} -25 z^6 a^{-4} +z^6 a^{-6} -58 z^6-8 a^5 z^5+5 a^3 z^5+48 a z^5+43 z^5 a^{-1} +z^5 a^{-3} -7 z^5 a^{-5} -2 a^6 z^4+11 a^4 z^4+44 a^2 z^4+44 z^4 a^{-2} +10 z^4 a^{-4} +65 z^4+5 a^5 z^3+a^3 z^3-11 a z^3-5 z^3 a^{-1} +2 z^3 a^{-3} +a^6 z^2-5 a^4 z^2-19 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} -20 z^2-a^5 z-a^3 z+z a^{-3} +z a^{-5} +a^4+2 a^2-2 a^{-2} - a^{-4} +1 }[/math] |
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