##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Allechar Serrano Lopez

#### University of Utah

## Counting elliptic curves with prescribed torsion over imaginary quadratic fields

##### Abstract:

A generalization of Mazur's theorem states that there are 26 possibilities for the torsion subgroup of an elliptic curve over a quadratic extension of $\mathbb{Q}$. If $G$ is one of these groups, we count the number of elliptic curves of bounded naive height whose torsion subgroup is isomorphic to $G$ in the case of imaginary quadratic fields.

Host: Kiran Kedlaya

### February 11, 2021

### 1:00 PM

### See https://www.math.ucsd.edu/\~{}nts/

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