# name
Almost totally complex points on elliptic curves

# metadata.dc.description.abstract[].value
Let $F / F_0$ 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.

# metadata.dc.relation.ispartof[].value
Transactions of the American Mathematical Society, 2014, vol. 366, num. 5, p. 2773-2802

# metadata.dc.rights[].value
cc-by-nc-nd (c) American Mathematical Society (AMS), 2014

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Almost totally complex points on elliptic curves