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

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.

I second frutiger's recommendation of Elliptic Tales: Curves, Counting, and Number Theory. There should be more science and math books at this level but it's rare—either you're assumed to be starting from scratch or to be at least a graduate student in the field. I also recommend Jim Baggott's Perfect Symmetry: The Accidental Discovery of Buckminsterfullerene as another example at this rarely seen intermediate level. (Arguably all of Scientific American was at this level 50 years ago, but that era is long gone.)