Gonality of the modular curve X1(N)
Number Theory
2018-05-03 v3
Abstract
In this paper we compute the gonality over Q of the modular curve X1(N) for all N <= 40 and give upper bounds for each N <= 250. This allows us to determine all N for which X1(N) has infinitely points of degree <= 8. We conjecture that the modular units of Q(X1(N)) are freely generated by f_2,...,f_{[N/2]+1} where f_k is obtained from the equation for X1(k).
Cite
@article{arxiv.1307.5719,
title = {Gonality of the modular curve X1(N)},
author = {Maarten Derickx and Mark van Hoeij},
journal= {arXiv preprint arXiv:1307.5719},
year = {2018}
}
Comments
17 pages. In this version, Theorem 3 is extended from d <= 6 to d <= 8