Math 844, Elliptic Curves and Modular Forms - Spring 2006

Nigel Boston

Contact Information

303 Van Vleck Hall

Telephone: 263-4753.



Office Hours: Mondays 2-3:30 (in 303 VV), Wednesdays 10:45-12:15 (in 3619 EH).


Useful Web Materials

Elliptic curves resources
Elliptic curve resources
Elliptic curve research articles
Elliptic curves and cryptology links
Elliptic curve rank records
List of useful elliptic curve links
Rusin's elliptic curve links
More elliptic curve links
Elkies' Computational Number Theory Page

Course Description

This course is an introduction to elliptic curves and modular forms. These play a central role in modern arithmetical geometry and even in applications to cryptography. On the elliptic curve side, we shall cover elliptic curves over finite fields, over the complex numbers, and over the rationals. We shall prove the Mordell-Weil theorem, discuss torsion, Tate-Shafarevich groups, elliptic curves with CM, and integer points on elliptic curves and Diophantine approximation. On the modular form side, we shall discuss Fourier expansions and Hecke theory. On both sides, we introduce L-functions, leading to the notion of modularity of an elliptic curve. Applications and open problems will be mentioned throughout.


1st Homework due Feb 2
2nd Homework due Feb 9
3rd Homework due Feb 16
4th Homework due Feb 23
5th Homework due Mar 2
6th Homework due Mar 9
7th Homework due Mar 23
8th Homework due Mar 30
9th Homework due Apr 6
10th Homework due Apr 13
11th Homework due Apr 20