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’