What question did this study set out to answer?

The research aims to identify intermediate modular curves having infinitely many quartic points.

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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Authors

Maarten Derickx

University of Zagreb

Petar Orlić

University of Zagreb

Journals

International Journal of Number Theory

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Building similarity graph...

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Intermediate modular curves with infinitely many quartic points

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

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Discussion

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