Preface

This is an introductory graduate-level textbook about the Birch and Swinnerton-Dyer conjecture and modern approaches to the arithmetic of elliptic curves.

Other very relevant books: Darmon's Rational Points on Modular Elliptic Curves.




Acknowledgements. I would like to acknowledge the partial support of NSF Grant DMS 05-55776.




Notation and Conventions.



William 2007-05-25