School of Mathematics Seminars and Lectures

Reducibility and rational torsion in elliptic curves

by Prof. Amod Agashe (Florida State University)

Wednesday, January 4, 2023 from to (Asia/Kolkata)
at 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.