CM elliptic curves and the Coates-Wiles Theorem

This project will take place in the field of elliptic curves and more precisely it will focus on the study of a particular instance of a known case of the Birch and Swinnerton-Dyer Conjecture (BSD Conjecture). This case consists of the study of elliptic curves defined over an imaginary quadratic field K with complex multiplication by (an order in) K, and analytic rank equal to 0. More precisely, the aim will be to understand Rubin’s proof of the fact that, under the previous conditions, the group of K-rational points of an ellitpic curve is finite. This result had also been proven by Coates and Wiles using another method.Outgoin