8 citations · 9 across the 3 of their papers we have counts for
5 papers
Computing with necklaces on elliptic curves
Marusia Rebolledo, Christian Wuthrich
We present computational algorithms to work with points on the modular curve associated to the normaliser of a non-split Cartan group of prime level . Rather than working with e…
Large Galois images for Jacobian varieties of genus 3 curves
Sara Arias-de-Reyna, Cécile Armana, Valentijn Karemaker +3
Given a prime number l greater than or equal to 5, we construct an infinite family of three-dimensional abelian varieties over Q such that, for any A/Q in the family, the Galois re…
Galois representations and Galois groups over Q
Sara Arias-de-Reyna, Cécile Armana, Valentijn Karemaker +3
In this paper we generalize results of P. Le Duff to genus n hyperelliptic curves. More precisely, let C/Q be a hyperelliptic genus n curve and let J(C) be the associated Jacobian…
A moduli interpretation for the non-split Cartan modular curve
Marusia Rebolledo, Christian Wuthrich
Modular curves like X_0(N) and X_1(N) appear very frequently in arithmetic geometry. While their complex points are obtained as a quotient of the upper half plane by some subgroups…
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…