Alt-C is supposed to close a curve and fill it so it can be rendered. It does close it but it doesn’t seem to fill it or make it visible to the camera. If I convert it to a mesh I’d have to create all the faces.
The curve needs to be a 2D curve
I added bezier curve, rotated one of the control arms enough to make it concave and tried it… closes but no fill.
As I said, the curve needs to be 2D for it to fill. A bezier curve by default is a 3D curve. Change it to 2D in the curve properties.
That worked. My def of 2d meant coplanar. Didn’t realize there was a button. (isn’t there always?)