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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/195282
Elementary matrix decomposition and the computation of Darmon points with higher conductor
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We 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.
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GUITART MORALES, Xavier and MASDEU, Marc. Elementary matrix decomposition and the computation of Darmon points with higher conductor. Mathematics of Computation. 2015. Vol. 84, num. 292, pags. 875-893. ISSN 0025-5718. [consulted: 11 of October of 2026]. Available at: https://hdl.handle.net/2445/195282