54 citations · 220 across the 21 of their papers we have counts for
4 papers · 1 filter
Computing Galois representations and equations for modular curves
Maarten Derickx, Mark van Hoeij, Jinxiang Zeng
We construct plane models of the modular curve , and use their explicit equations to compute Galois representations associated to modular forms for values of that…
Computing Puiseux Expansions at Cusps of the Modular Curve X0(N)
Mark van Hoeij
The goal in this preprint is to give an efficient algorithm to compute Puiseux expansions at cusps of X0(N). It is based on a relation with a hypergeometric function that holds for…
Gonality of the modular curve X1(N)
Maarten Derickx, Mark van Hoeij
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) h…
Algorithms and differential relations for Belyi functions
Mark van Hoeij, Raimundas Vidunas
A tool package for computing genus 0 Belyi functions is presented, including simplification routines, computation of moduli fields, decompositions, dessins d'enfant. The main algor…