Found in 2 comments on Hacker News
frutiger · 2019-10-08 · Original thread
I can recommend https://www.amazon.com/Elliptic-Tales-Curves-Counting-Number.... It goes in-depth into the motivating use cases for elliptic curves (as well as their group law) and explains some very elegant theorems (Bézout's theorem) as well as open problems in Maths (the Birch-Swinnerton-Dyer conjecture).
mrkgnao · 2017-08-07 · Original thread
For anyone looking to learn more about elliptic curves, which are astoundingly "well-connected" as math topics go, here's a good book that should be accessible to anyone with some calculus under their belt:

https://www.amazon.com/Elliptic-Tales-Curves-Counting-Number...

It's not a textbook, which is both good and bad. In my case, it did a good job whetting my appetite for more!

A really well-written and not-extremely-difficult undergrad textbook on elliptic curves:

https://www.amazon.com/Rational-Points-Elliptic-Undergraduat...

(Non-affiliate links, just so you know.)

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