Reducibility and rational torsion in elliptic curves
by
Prof.Amod Agashe(Florida State University)
→
Asia/Kolkata
AG-77
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.
