There are two curves commonly known as the Lamé curve: the ellipse evolute and the superellipse.
Lamé Curve
See also
Ellipse Evolute, SuperellipseExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Lamé Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LameCurve.html