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Suppose you had an undergraduate friend who's looking to take an introductory course on Elliptic Curves over $\mathbb Q$, in the context of Number Theory. The difficulty is around the level of Silverman and Tate's Rational Points on Elliptic Curves. What topics in algebra and analysis would you advise him to self-study prior to the course in order to better follow and understand it better? Any help is appreciated!

(PS: I've seen this question as well as this, but they seem to be about Elliptic Curves over $\mathbb C$, which I think is quite different and requires different prerequisites compared to Elliptic Curves over $\mathbb Q$. Please do correct me if I'm wrong about this.)

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    $\begingroup$ The first thing I'd suggest reading at least the first chapter to see if he is comfortable with the material. Perhaps even try reading the course notes of MIT OCW 2004 to at least get a feel of what is expected. $\endgroup$ – user10354138 Dec 6 '18 at 9:25

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