Guitart Morales, XavierMasdeu, Marc2023-03-142023-03-142015-030025-5718https://hdl.handle.net/2445/195282We extend the algorithm of Darmon-Green and Darmon-Pollack for computing $p$-adic Darmon points on elliptic curves to the case of composite conductor. We also extend the algorithm of Darmon-Logan for computing ATR Darmon points to treat curves of nontrivial conductor. Both cases involve an algorithmic decomposition into elementary matrices in congruence subgroups $\Gamma_1(\mathfrak{N})$ for ideals $\mathfrak{N}$ in certain rings of $S$-integers. We use these extensions to provide additional evidence in support of the conjectures on the rationality of Darmon points.19 p.application/pdfengcc-by-nc-nd (c) American Mathematical Society (AMS), 2015https://creativecommons.org/licenses/by-nc-nd/4.0/Funcions LÀlgebra linealTeoria de la matriu STeoria de nombresL-functionsLinear algebraS-matrix theoryNumber theoryinfo:eu-repo/semantics/article6500492023-03-14info:eu-repo/semantics/openAccess