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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On an elliptic curve defined over $ \mathbb{Q}(\sqrt{-23})$


Authors: L. V. Dieulefait, M. Mink and B. Z. Moroz
Original publication: Algebra i Analiz, tom 24 (2012), nomer 4.
Journal: St. Petersburg Math. J. 24 (2013), 575-589
MSC (2010): Primary 11G05, 11G40, 14G10
Published electronically: May 24, 2013
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Abstract: Recently, the first three examples were found of elliptic curves without complex multiplication and defined over an imaginary quadratic field that have been proved to satisfy the Hasse-Weil conjecture. In the paper, the same algorithm is employed to prove the modularity and thereby the Hasse-Weil conjecture for the fourth elliptic curve without CM defined over the imaginary quadratic field $ \mathbb{Q}(\sqrt {-23})$.


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Additional Information

L. V. Dieulefait
Affiliation: Departament D’Álgebra Geometria, Facultat de Matemátiques, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain
Email: ldieulefait@ub.edu

M. Mink
Affiliation: Seminar für Mathematik und ihre Didaktik, Universität zu Köln, Gronewaldstr 2, D-50931 Köln, Germany
Email: mmink@uni-koeln.de

B. Z. Moroz
Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany
Email: moroz@mpim-bonn.mpg.de

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01254-4
PII: S 1061-0022(2013)01254-4
Keywords: Hasse--Weil conjecture, elliptic curve
Received by editor(s): June 10, 2011
Published electronically: May 24, 2013
Article copyright: © Copyright 2013 American Mathematical Society