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.)