Counting elliptic curves with a rational $N$-isogeny

Abstract: The classical problem of counting elliptic curves with a rational N-isogeny can be phrased in terms of counting rational points on certain moduli stacks of elliptic curves. Counting points on stacks poses various challenges, and I will discuss these along with a few ways to overcome them. I will also talk about the theory of heights on stacks developed in recent work of Ellenberg, Satriano and Zureick-Brown and use it to count elliptic curves with an $N$-isogeny for certain $N$. The talk assumes no prior knowledge of stacks and is based on joint work with Brandon Boggess.

number theory

Audience: researchers in the topic

Comments: There will be a 30 minute pre-talk for graduate students and postdocs preceding the main talk.

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.