Guitart Morales, XavierRotger, VictorZhao, Yu2023-03-132023-03-132014-050002-9947https://hdl.handle.net/2445/195115Let $F / F_0$ be a quadratic extension of totally real number fields, and let $E$ be an elliptic curve over $F$ which is isogenous to its Galois conjugate over $F_0$. A quadratic extension $M / F$ is said to be almost totally complex (ATC) if all archimedean places of $F$ but one extend to a complex place of $M$. The main goal of this note is to provide a new construction for a supply of Darmon-like points on $E$, which are conjecturally defined over certain ring class fields of $M$. These points are constructed by means of an extension of Darmon's ATR method to higher-dimensional modular abelian varieties, from which they inherit the following features: they are algebraic provided Darmon's conjectures on ATR points hold true, and they are explicitly computable, as we illustrate with a detailed example that provides numerical evidence for the validity of our conjectures.30 p.application/pdfengcc-by-nc-nd (c) American Mathematical Society (AMS), 2014https://creativecommons.org/licenses/by-nc-nd/4.0/Funcions LGeometria algebraica aritmèticaTeoria de nombresCorbes el·líptiquesL-functionsArithmetical algebraic geometryNumber theoryElliptic curvesinfo:eu-repo/semantics/article6500472023-03-13info:eu-repo/semantics/openAccess