## Elementary matrix decomposition and the computation of Darmon points with higher conductor

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- by Xavier Guitart and Marc Masdeu PDF
- Math. Comp.
**84**(2015), 875-893 Request permission

## Abstract:

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.## References

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## Additional Information

**Xavier Guitart**- Affiliation: Universitat Politècnica de Catalunya, Departament de Matematica Aplicada II, C/Jordi Girona, 1-3, 08034 Barcelona (Spain)
- MR Author ID: 887813
- Email: xevi.guitart@gmail.com
**Marc Masdeu**- Affiliation: Columbia University, Department of Mathematics, Room 415, MC 4441, 2990 Broadway, New York, New York 10027
- MR Author ID: 772165
- Email: masdeu@math.columbia.edu
- Received by editor(s): May 14, 2013
- Received by editor(s) in revised form: June 5, 2013
- Published electronically: July 17, 2014
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**84**(2015), 875-893 - MSC (2010): Primary 11G40; Secondary 11F41, 11Y99
- DOI: https://doi.org/10.1090/S0025-5718-2014-02853-6
- MathSciNet review: 3290967