K12a1217
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-21 q^3+30 q^2-36 q+38-34 q^{-1} +28 q^{-2} -18 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+23 t^2-55 t+73-55 t^{-1} +23 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-z^4+z^2+1 }[/math] |
| Determinant | 237 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-a^2 z^4+z^4 a^{-4} -2 z^4+a^4 z^2-2 a^2 z^2+2 z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a z^{11}+4 z^{11} a^{-1} +10 a^2 z^{10}+11 z^{10} a^{-2} +21 z^{10}+11 a^3 z^9+11 a z^9+14 z^9 a^{-1} +14 z^9 a^{-3} +8 a^4 z^8-19 a^2 z^8-14 z^8 a^{-2} +11 z^8 a^{-4} -52 z^8+4 a^5 z^7-25 a^3 z^7-46 a z^7-48 z^7 a^{-1} -26 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-18 a^4 z^6+14 a^2 z^6-21 z^6 a^{-4} +z^6 a^{-6} +55 z^6-9 a^5 z^5+21 a^3 z^5+58 a z^5+47 z^5 a^{-1} +11 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+12 a^4 z^4+2 a^2 z^4+9 z^4 a^{-4} -z^4 a^{-6} -22 z^4+4 a^5 z^3-5 a^3 z^3-24 a z^3-18 z^3 a^{-1} -z^3 a^{-3} +2 z^3 a^{-5} -3 a^4 z^2-6 a^2 z^2-3 z^2+a z+z a^{-1} +a^2+ a^{-2} +3 }[/math] |
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