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
 Description 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.