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Re:Elliptic Curves: The Great Mystery by Karrot_Kream on Tuesday January 17, 2023 @03:23AM (#34410298)
Subsequently, if you've taken an undergraduate level algebra class (or just have mathematical maturity and can work through some algebraic definitions) I suggest Tate and Silverman's Rational Points on Elliptic Curves. It's not super rigorous but it's good at introducing elliptic curves.

https://link.springer.com/book/10.1007/978-3-319-18588-0

Re:Elliptic Curves: The Great Mystery by robinhouston on Tuesday January 17, 2023 @03:44AM (#34410410)
I also really like Cassels' _Lectures on Elliptic Curves_, which is written very lucidly and actually describes in detail how to do a lot of the calculations that tend to be glossed over a bit by more theory-inclined authors.