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Local invariants of isogenous elliptic curves


Authors: Tim Dokchitser and Vladimir Dokchitser
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
Published electronically: October 10, 2014
MathSciNet review: 3324930
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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.


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Additional Information

Tim Dokchitser
Affiliation: Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom
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
Email: v.dokchitser@dpmms.cam.ac.uk, v.dokchitser@warwick.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-2014-06271-5
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.