I can recommend https://www.amazon.com/Elliptic-Tales-Curves-Counting-Number/dp/0691151199 https://www.amazon.com/Elliptic-Tales-Curves-Counting-Number.... It

I can recommend https://www.amazon.com/Elliptic-Tales-Curves-Counting-Number/dp/0691151199 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).