##### Department of Mathematics,

University of California San Diego

****************************

### Math 209 - Number Theory

## Ozlem Ejder

#### University of Southern California

## Torsion subgroups of elliptic curves in elementary abelian 2-extensions

##### Abstract:

Let $E$ be an elliptic curve defined over ${Q}$. The torsion subgroup of $E$ over the compositum of all quadratic extensions of ${Q}$ was studied by Michael Laska, Martin Lorenz, and Yasutsugu Fujita. Laska and Lorenz described a list of $31$ possible groups and Fujita proved that the list of $20$ different groups is complete. In this talk, we will generalize the results of Laska, Lorenz and Fujita to the elliptic curves defined over a quadratic cyclotomic field i.e. $Q(i)$ and $Q(\sqrt{-3})$.

Host: Kiran Kedlaya

### January 12, 2017

### 1:00 PM

### AP&M 7321

****************************