Here is another version, with a and b controlling the holes/handles.

Parabolic cyclide:
_FxGraph3D (a*u*u+b*v*v)/(1+u*u+v*v);(a-(b-a)*v*v)*u/(1+u*u+v*v);(b-(a-b)*u*u)*v/(1+u*u+v*v);-10;10;-10;10;50;50;1;-1;1;UV

The _ArcToCircle script is a slightly tested quick modification of the LineWeb script, which converts a bunch of circular arcs to circles.
It was utilized to create a very nice parabolic cyclide.
Run the above Parabolic cyclide script once, outputting U curves.
Change colors, and run the script again, outputting V curves.
Select the U curves and run _ArcToCircle. Do Loft of the U circles. The U arcs can be (color) deleted.
Select the V curves and run _ArcToCircle. Do Loft of the V circles. Color delete the V arcs.
Hide the circles, except for the outer circle of the U curves.
Use the outer circle of the U curves to trim and delete the overlapping portions of the V lofted surface.
Join the lofted U surface with the remaining lofted V surface. Make the resulting double hole/double handle surface the same color.
In Right view, select the origin, and make a new circle to trim away outer lobes, preserving the center holes/handles.
This is a brief synopsis of the creation of the .3dm. Most or all of the steps are here.
Of course, periodically save the interim work, just in case of a problem.

- Brian