**Title of the course:** Elliptic Curves

**Instructor:** Dr. Dino Festi

**Institution:** Mainz University

**Dates:** 7-13 August 2017

**Prerequisites:** Basic group theory and ring theory, basic complex analysis.

**Level:** Graduate, advanced undergraduate, beginning undergraduate

**Abstract:** The goal of this course is to introduce the concept of elliptic curves.

We will define elliptic curves on Q, number fields, C, and finite fields;

we will define the group operation on the set of rational points of the curve;

we will focus on the study of the rational points on an elliptic curves over Q;

we will show how to compute the torsion points of a given elliptic curve;

if time permits, we will illustrate a method to compute the rank of elliptic curves

admitting a rational 2-torsion point.

**Textbook or/and course webpage:**

Silverman, `the arithmetic of elliptic curves’

Silverman, Tate, `Rational points on elliptic curves’

**Language: **EN