Intermediate modular curves with infinitely many quartic points

Key Points

• All curves XΔ(N) with infinitely many degree 4 points over Q are determined, establishing connections between modular curves and elliptic curves.
• The developed method computes possible degrees of rational morphisms from XΔ(N) to elliptic curves, essential for understanding these curves' structure.
• This study uncovers a relationship between modular curves and their quartic points, contributing to the field of algebraic geometry and number theory.
• Findings enhance knowledge about rational morphisms and their implications in the context of modular curves and elliptic curves.