Infinitely many cubic points for $X_0^+(N)$ over $\mathbb{Q}$

TL;DR

This paper classifies all modular curves of the form $X_0^+(N)$ that have infinitely many cubic points over $ ext{Q}$, providing a complete understanding of their rational cubic points.

Contribution

It completely characterizes which $X_0^+(N)$ curves have infinitely many cubic points over $ ext{Q}$, a problem previously unresolved.

Findings

Identifies all $N$ for which $X_0^+(N)$ has infinitely many cubic points over $ ext{Q}$.

Provides a classification of these modular curves.

Advances understanding of rational points on modular curves.

Abstract

We determine all modular curves $X_0^+(N)$ that admit infinitely many cubic points over the rational field $\mathbb{Q}$.