# Counting elliptic curves with an isogeny of degree three

## TL;DR

This paper estimates the number of rational elliptic curves with a degree three isogeny by height, providing insights into their distribution.

## Contribution

It introduces a method to count elliptic curves with a specific isogeny degree over the rationals based on height.

## Key findings

- Quantifies the density of elliptic curves with a degree three isogeny.
- Provides asymptotic estimates for the count based on height.
- Enhances understanding of the structure of elliptic curves with prescribed isogenies.

## Abstract

We count by height the number of elliptic curves over the rationals that possess an isogeny of degree three.