Michaud-Rodgers, Philippe (2022) Quadratic points on non-split Cartan modular curves. International Journal of Number Theory, 18 (2). pp. 245-267. doi:10.1142/S1793042122500178 ISSN 1793-0421.

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Abstract

In this paper, we study quadratic points on the non-split Cartan modular curves Xns(p), for p=7,11, and 13. Recently, Siksek proved that all quadratic points on Xns(7) arise as pullbacks of rational points on X+ns(7). Using similar techniques for p=11, and employing a version of Chabauty for symmetric powers of curves for p=13, we show that the same holds for Xns(11) and Xns(13). As a consequence, we prove that certain classes of elliptic curves over quadratic fields are modular.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Equations, Quadratic, Modular curves
Journal or Publication Title:	International Journal of Number Theory
Publisher:	World Scientific Publishing Co. Pte. Ltd.
ISSN:	1793-0421
Official Date:	March 2022
Dates:	Date Event March 2022 Published 17 July 2021 Available 10 May 2021 Accepted
Volume:	18
Number:	2
Page Range:	pp. 245-267
DOI:	10.1142/S1793042122500178
Status:	Peer Reviewed
Publication Status:	Published
Reuse Statement (publisher, data, author rights):	Electronic version of an article published as International Journal of Number Theory, Volume, Issue, Year, Pages] [Article DOI] © [copyright World Scientific Publishing Company] [Journal URL]
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	18 May 2021
Date of first compliant Open Access:	17 July 2022
Related URLs:	Publisher

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