I'd like to put my hands on some polynomial defining a curve of genus $4$, living in the plane or in the 3D space.
Do you know about any? Is there any procedure to build one?
The best would be one which is:
with many real points ( I want to plot it and see it! )
More specifically, it would be great to be able to compute the canonical embedding (or map in the hyperelliptic case) of the curve.