Speaker: Amod Agashe
Affiliation: Florida State University
Title of Talk: Reducibility and rational torsion in elliptic curves
Date: January 04, 2023
Time: 14:30:00 Hours
Venue: AG-77

Abstract: Let $A$ be an optimal elliptic curve over $\mathbb{Q}$ and let $N$ denote its conductor. Suppose $N$ is square-free and $r$ is a prime such that $r$ does not divide $6N$. We show that if $A[r]$ is reducible, then $A$ has a rational $r$-torsion point. We give an application of this result to the second part of the Birch and Swinnerton-Dyer conjecture for $A$. This is joint work with Matthew Winters.