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