View abstract

Session I.2 - Computational Number Theory

Wednesday, June 14, 14:00 ~ 15:00

Counting points on modular curves

Andrew Sutherland

Massachusetts Institute of Technology, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Let $H$ be an open subgroup of $\mathrm{GL}_2(\hat{\mathbb{Z}})$, let $X_H$ be the corresponding modular curve that parametrizes elliptic curves with $H$-level structure, and let~$\mathbb{F}_q$ be a finite field whose characteristic does not divide the level of $H$.

I will discuss improvements to the moduli-theoretic approach for computing $\#X_H(\mathbb{F}_q)$ that lead to an algorithm that is practically and asymptotically faster than existing approaches as $q$, the genus of $X_H$, and the level of $H$ vary.

View abstract PDF