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Torsion of elliptic curves over cyclic cubic fields


Authors: Maarten Derickx and Filip Najman
Journal: Math. Comp. 88 (2019), 2443-2459
MSC (2010): Primary 11G05
DOI: https://doi.org/10.1090/mcom/3408
Published electronically: December 27, 2018
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Abstract: We determine all the possible torsion groups of elliptic curves over cyclic cubic fields, over non-cyclic totally real cubic fields, and over complex cubic fields.


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Additional Information

Maarten Derickx
Affiliation: Johann Bernoulli Institute, Universiteit Groningen, Nijenborgh 9, 9747 AG Groningen, The Netherlands
Email: maarten@mderickx.nl

Filip Najman
Affiliation: Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
Email: fnajman@math.hr

DOI: https://doi.org/10.1090/mcom/3408
Keywords: Elliptic curves, modular curves, rational points
Received by editor(s): April 30, 2018
Received by editor(s) in revised form: September 28, 2018
Published electronically: December 27, 2018
Additional Notes: The second author was supported by the QuantiXLie Centre of Excellence, a project co-financed by the Croatian Government and European Union through the European Regional Development Fund—the Competitiveness and Cohesion Operational Programme (Grant KK.01.1.1.01.0004).
Article copyright: © Copyright 2018 American Mathematical Society