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 @b4c50e1b 
You now have me reading the Wikipedia articles on elliptic curves and, most usefully, the Weierstrass elliptic functions, which are new to me.
I liked the motivational section which made an analogy between the circle and the eliptic curve, with sin and the p function taking analogous roles.
I am starting to get a sense of it at least.
Many thanks. 
 @913f1b00 - excellent!   You might like my own explanation of the Weierstrass elliptic function, which is an attempt to cut through the nonsense and get to the point:

https://math.ucr.edu/home/baez/week13.html