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Bounding the $ j$-invariant of integral points on $ X_{\mathrm{ns}}^{+}(p)$


Authors: Aurélien Bajolet and Min Sha
Journal: Proc. Amer. Math. Soc. 142 (2014), 3395-3410
MSC (2010): Primary 11G16, 11J86; Secondary 14G35, 11G50
Published electronically: June 25, 2014
MathSciNet review: 3238416
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Abstract: For any prime $ p\ge 7$, by using Baker's method we obtain two explicit bounds in terms of $ p$ for the $ j$-invariant of an integral point on $ X_{\mathrm {ns}}^{+}(p)$ which is the modular curve of level $ p$ corresponding to the normalizer of a non-split Cartan subgroup of $ \mathrm {GL}_2(\mathbb{Z}/p\mathbb{Z})$.


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Additional Information

Aurélien Bajolet
Affiliation: Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 33405 Talence cedex, France
Email: Aurelien.Bajolet@math.u-bordeaux1.fr

Min Sha
Affiliation: Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 33405 Talence cedex, France
Email: shamin2010@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-12100-9
Keywords: Modular curves, non-split Cartan, $j$-invariant, Baker's method
Received by editor(s): March 14, 2012
Received by editor(s) in revised form: August 13, 2012, and October 30, 2012
Published electronically: June 25, 2014
Additional Notes: The second author was supported by the China Scholarship Council.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.