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January 18, 2026International Journal of Number Theory0 citations

Intermediate modular curves with infinitely many quartic points

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MDMaarten DerickxPOPetar Orlić

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. (2026) studied this question.

synapsesocial.com/papers/696c774feb60fb80d1395827https://doi.org/10.1142/s1793042126500557
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