# An Elementary Computation of the $F$-Pure Threshold of an Elliptic Curve

## TL;DR

This paper presents an elementary method to compute the $F$-pure threshold of degree three homogeneous polynomials with isolated singularities, confirming a known result for elliptic curves.

## Contribution

It provides a simplified, elementary proof for the $F$-pure threshold of elliptic curves, previously established by Bhatt and Singh.

## Key findings

- Successfully computes the $F$-pure threshold using elementary methods.
- Confirms the known threshold value for elliptic curves.
- Simplifies the understanding of $F$-pure thresholds in this context.

## Abstract

We compute the $F$-pure threshold of a degree three homogeneous polynomial in three variables with an isolated singularity. The computation uses elementary methods to prove a known result of Bhatt and Singh.