Cartesian equation: . In the frame OXY derived from Oxy by rotation of -p/4: . Elliptic cubic.

The Lamé cubic is the Lamé curve: .
It looks like the witch of Agnesi, but one is rational while the other one is not.
The equation in the frame OXY shows that it is a special case of cubic hyperbola.
 

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© Robert FERRÉOL  2017