2014/02/26 by Xavier Guitart, Guitart, Xavier, Marc Masdeu +1
Mathematics · #11G05 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G05
paper · pdf · doi:10.48550/arxiv.1402.6531
Final version, accepted in Publicacions Matematiques
openalex publication_date 2014/02/26 · arxiv created 2014/09/17 · arxiv updated 2014/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we consider certain elliptic curves defined over real quadratic fields isogenous to their Galois conjugate. We give a construction of algebraic points on these curves defined over almost totally real number fields. The main ingredient is the system of Heegner points arising from Shimura curve uniformizations. In addition, we provide an explicit p-adic analytic formula which allows for the effective, algorithmic calculation of such points.