@phryk @ArneBab The wiki article actually answers that:
> correspond to embeddings of the torus into the complex projective plane
and
> An elliptic curve is not an ellipse in the sense of a projective conic, ... However, there is a natural representation of real elliptic curves with shape invariant j ≥ 1 as ellipses in the hyperbolic plane
(and that's enough math language for a month) Anyway have you seen https://www.youtube.com/watch?v=NF1pwjL9-DE ?