Lamé's special quartic
Lamé's special quartic, named after Gabriel Lamé, is the graph of the equation
where. It looks like a rounded square with "sides" of length and centered on the origin. This curve is a squircle centered on the origin, and it is a special case of a superellipse.
Because of Pierre de Fermat's only surviving proof, that of the n = 4 case of Fermat's Last Theorem, if r is rational there is no non-trivial rational point on this curve.
