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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Local invariants of isogenous elliptic curves
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by Tim Dokchitser and Vladimir Dokchitser PDF
Trans. Amer. Math. Soc. 367 (2015), 4339-4358 Request permission

Abstract:

We investigate how various invariants of elliptic curves, such as the discriminant, Kodaira type, Tamagawa number and real and complex periods, change under an isogeny of prime degree $p$. For elliptic curves over $l$-adic fields, the classification is almost complete (the exception is wild potentially supersingular reduction when $l=p$), and is summarised in a table.
References
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Additional Information
  • Tim Dokchitser
  • Affiliation: Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
  • MR Author ID: 733080
  • Email: tim.dokchitser@bristol.ac.uk
  • Vladimir Dokchitser
  • Affiliation: Department of Pure Mathematics and Mathematical Statistics, Emmanuel College, Cambridge CB2 3AP, United Kingdom
  • Address at time of publication: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
  • MR Author ID: 768165
  • Email: v.dokchitser@dpmms.cam.ac.uk, v.dokchitser@warwick.ac.uk
  • Received by editor(s): January 17, 2013
  • Received by editor(s) in revised form: August 4, 2013
  • Published electronically: October 10, 2014
  • Additional Notes: The first author was supported by a Royal Society University Research Fellowship
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 4339-4358
  • MSC (2010): Primary 11G07; Secondary 11G05, 11G40
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06271-5
  • MathSciNet review: 3324930