# A note on rank zero quadratic twists of a Mordell curve

## TL;DR

This paper constructs two specific families of quadratic twists of the Mordell curve with rank zero and provides numerical evidence to support their properties.

## Contribution

It introduces explicit families of rank zero quadratic twists of a Mordell curve and supports the findings with numerical examples.

## Key findings

- Two families of rank zero quadratic twists are constructed.
- Numerical examples support the theoretical results.

## Abstract

We produce two families of rank zero quadratic twists of the Mordell curve $y^2=x^3+2$. At the end, we give numerical examples supporting the result.