K12n558
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^9+q^8-q^7+3 q^5-5 q^4+7 q^3-7 q^2+7 q-5+3 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-3 t^2+8 t-11+8 t^{-1} -3 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+3 z^4+5 z^2+1 }[/math] |
| Determinant | 35 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +4 z^4 a^{-2} -z^4 a^{-4} +z^4 a^{-6} -z^4+6 z^2 a^{-2} -2 z^2 a^{-4} +4 z^2 a^{-6} -z^2 a^{-8} -2 z^2+3 a^{-2} -2 a^{-4} +3 a^{-6} -2 a^{-8} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +z^9 a^{-5} +2 z^9 a^{-7} +z^9 a^{-9} +z^8 a^{-2} -9 z^8 a^{-6} -8 z^8 a^{-8} +3 z^7 a^{-1} +4 z^7 a^{-3} -9 z^7 a^{-5} -18 z^7 a^{-7} -8 z^7 a^{-9} +5 z^6 a^{-2} +6 z^6 a^{-4} +24 z^6 a^{-6} +20 z^6 a^{-8} +3 z^6+a z^5-4 z^5 a^{-1} -4 z^5 a^{-3} +28 z^5 a^{-5} +48 z^5 a^{-7} +21 z^5 a^{-9} -16 z^4 a^{-2} -11 z^4 a^{-4} -22 z^4 a^{-6} -20 z^4 a^{-8} -7 z^4-2 a z^3-3 z^3 a^{-1} -3 z^3 a^{-3} -25 z^3 a^{-5} -45 z^3 a^{-7} -22 z^3 a^{-9} +11 z^2 a^{-2} +9 z^2 a^{-4} +11 z^2 a^{-6} +9 z^2 a^{-8} +4 z^2+a z+2 z a^{-1} +3 z a^{-3} +7 z a^{-5} +13 z a^{-7} +8 z a^{-9} -3 a^{-2} -2 a^{-4} -3 a^{-6} -2 a^{-8} -1 }[/math] |
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