Just in case somebody else wonders about a reference, its here: https://en.wikipedia.org/wiki/Elliptic_integral https://en.wikipedia.org/wiki/Elliptic_integral

Just in case somebody else wonders about a reference, its here: https://en.wikipedia.org/wiki/Elliptic_integral https://en.wikipedia.org/wiki/Elliptic_integral -- as the WP page on elliptic curve says: "An elliptic curve is not an ellipse: see elliptic integral for the origin of the term." The confusing fact which Mark Dominus means is however, probably the fact that the term "Elliptic curve" seems to be a merger of the name "algebraic curve" and the defining equation y^2 = x^3 + ax + b which is however not the defining equation of an ellipse. That would be instead, in its simplest form 1 = (x/a)^2 + (y/b)^2 That's in fact confusing.