K12n873
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 3 q^4-7 q^3+11 q^2-14 q+15-14 q^{-1} +11 q^{-2} -7 q^{-3} +3 q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+10 t^2-16 t+21-16 t^{-1} +10 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6-5 z^2+1 }[/math] |
| Determinant | 85 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +5 z^6-4 a^2 z^4-4 z^4 a^{-2} +8 z^4+a^4 z^2-6 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} +5 z^2+2 a^4-3 a^2-3 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^9+3 z^9 a^{-1} +6 a^2 z^8+6 z^8 a^{-2} +12 z^8+3 a^3 z^7+a z^7+z^7 a^{-1} +3 z^7 a^{-3} -14 a^2 z^6-14 z^6 a^{-2} -28 z^6-8 a z^5-8 z^5 a^{-1} +6 a^4 z^4+20 a^2 z^4+20 z^4 a^{-2} +6 z^4 a^{-4} +28 z^4-5 a^3 z^3+7 a z^3+7 z^3 a^{-1} -5 z^3 a^{-3} -9 a^4 z^2-15 a^2 z^2-15 z^2 a^{-2} -9 z^2 a^{-4} -12 z^2+a^3 z-2 a z-2 z a^{-1} +z a^{-3} +2 a^4+3 a^2+3 a^{-2} +2 a^{-4} +3 }[/math] |
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