# Math 844, Elliptic Curves and Modular Forms - Spring 2006

# Nigel Boston

## Contact Information

303 Van Vleck Hall
Telephone: 263-4753.

E-mail: *boston@math.wisc.edu*

Homepage

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

## Sections

- Lecture: TR 1-2:15, B211 Van Vleck.

## 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

MAGMA
## 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.
## Homeworks

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