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Intermediate modular curves with infinitely many quartic points | Synapse

January 18, 2026

Intermediate modular curves with infinitely many quartic points

Key Points

The research aims to identify intermediate modular curves having infinitely many quartic points.
Developed a method to compute degrees of rational morphisms.
Investigated properties of modular curves and their relation to elliptic curves.
Analyzed group structures to categorize curves with specified quartic points.
Identified specific curves with infinitely many quartic points of defined degree.
Demonstrated a systematic method for relating modular curves to elliptic curves.
Established a connection between group characteristics and the properties of modular curves.

Abstract

For every group Formula: see text, there exists an intermediate modular curve Formula: see text. In this paper we determine all curves Formula: see text with infinitely many points of degree Formula: see text over Formula: see text. To do that, we developed a method to compute possible degrees of rational morphisms from Formula: see text to an elliptic curve.

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Cite This Study

Derickx et al. (Thu,) studied this question.

synapsesocial.com/papers/696c774feb60fb80d1395827 https://doi.org/https://doi.org/10.1142/s1793042126500557