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@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 ?