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.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca