This course will be an introduction to the theory of elliptic curves. We will use the standard reference in the subject, "The Arithmetic of Elliptic Curves", by J. Silverman. The goal of the course will be to understand and calculate the set of all rational points on a given elliptic curve (i.e. calculate the torsion and the rank), and a number of refined invariants (such as the order of the Tate-Shafarevich group). The prerequisite for this course is a basic understanding of algebraic number theory and algebraic geometry, although I will adjust the material to the audience background as much as I can.

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