8 citations · 12 across the 5 of their papers we have counts for
7 papers
Equationless quadratic Chabauty for non-split Cartan modular curves
Sachi Hashimoto, Guido Maria Lido, Davide Lombardo +2
The aim of this article is to describe an equationless method for determining the rational points on the non-split Cartan curve of prime level .…
Semistable reduction of modular curves associated with maximal subgroups in prime level
Bas Edixhoven, Pierre Parent
We complete the description of semistable models for modular curves associated with maximal subgroups of (for any prime, ). That is, in th…
Heights on square of modular curves
Pierre Parent, with an Appendix by Pascal Autissier
We develop a strategy for bounding from above the height of rational points of modular curves with values in number fields, by functions which are polynomial in the curve's level.…
Rational points on X_0^+ (p^r)
Yu. Bilu, P. Parent, M. Rebolledo
We show how the recent isogeny bounds due to É. Gaudron and G. Rémond allow to obtain the triviality of X_0^+ (p^r)(Q), for r>1 and p a prime exceeding 2.10^{11}. This includes the…
Runge's Method and Modular Curves
Yuri Bilu, Pierre Parent
We bound the j-invariant of S-integral points on arbitrary modular curves over arbitrary fields, in terms of the congruence group defining the curve, assuming a certain Runge condi…
Bounds for Integral j -Invariants and Cartan Structures on Elliptic Curves
Yuri Bilu, Pierre Parent
We bound the j -invariant of integral points on a modular curve in terms of the congruence group defining the curve. We apply this to prove that the modular curve Xsplit (p3) has n…