Low Degree Places on the Modular Curve X1(N)
Mark van Hoeij
TL;DR
This paper explores points on the modular curve X1(N) over number fields with degrees lower than the gonality, providing questions and examples to deepen understanding of these special points.
Contribution
It introduces new questions and examples of low-degree points on X1(N), highlighting phenomena not explained by gonality alone.
Findings
Examples of points with degree less than gonality on X1(N)
Questions raised about the nature of these points
Insights into the structure of modular curves
Abstract
This short note gives questions and examples of points on X1(N) defined over number fields whose degrees are lower than the gonality.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Analytic Number Theory Research