Châtelet surface

File:Chatelet surface.png

Some snapshots showing the real points of the Châtelet surface with P(x)=x^3-5*x^2-6*x. Axis: x=red, y=yellow, z=blue

In algebraic geometry, a Châtelet surface is a rational surface studied by Châtelet (1959) given by an equation

$y^2-a{z}^2=P(x),$

where P has degree 3 or 4. They are conic bundles.