# Number Theory Seminar: 2011-11-10

In Padelford C401 at 3:35pm on Thursday, November 10, 2011.

## Speaker: Ralph Greenberg (University of Washington)

## Title: The image of Galois representations attached to elliptic curves with an isogeny

## Abstract

If E is an elliptic curve defined over Q, then the Tate module for E provides an interesting Galois representation. If E has an isogeny defined over Q, then the image of this Galois representation is constrained in a certain way. The theme of the results described in this talk is that this image will often be as large as allowed by the above constraint. One of the results to be described is joint work with Karl Rubin, Alice Silverberg, and Michael Stoll.