2-torsion of elliptic curves on twists of X(3)

Faculty Member

Patrick Allen

Project Image

Elliptic curves are a fundamental object of study in modern number theory. Elliptic curves are parametrized by another class of curves known as modular curves. That is, each point on a modular curve corresponds to an elliptic curve together with additional level structure.

This IGL project will consider some specific examples of modular curves and attempt to understand information about the 2-torsion of the elliptic curves in these families.

Team Meetings

Once every two weeks (the graduate student will meet with them weekly).

Project Difficulty

Advanced

Undergrad Prerequisites

Math 417 or 427 (Abstract Algebra and at least an understanding of Galois Theory)