As an algebraic geometer, I have a minor correction: The graphic "examples of elliptic curves" features the singular curve y^2 = x^3. This is not an elliptic curves, because by definition elliptic curves are smooth.
Good spotting. I actually based that animation on the grid of sample curves at https://en.wikipedia.org/wiki/Elliptic_curve , which includes A=B=0 in the illustration but makes the point it's not a valid curve.
I didn't think anyone would notice/care, but I'll tweak it to skip over that example.
As an algebraic geometer, I have a minor correction: The graphic "examples of elliptic curves" features the singular curve y^2 = x^3. This is not an elliptic curves, because by definition elliptic curves are smooth.