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Rank parity for congruent supersingular elliptic curves


Author: Jeffrey Hatley
Journal: Proc. Amer. Math. Soc. 145 (2017), 3775-3786
MSC (2010): Primary 14H52; Secondary 11F80, 11R23
DOI: https://doi.org/10.1090/proc/13545
Published electronically: January 23, 2017
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Abstract: A recent paper of Shekhar compares the ranks of elliptic curves $ E_1$ and $ E_2$ for which there is an isomorphism $ E_1[p] \simeq E_2[p]$ as $ \mathrm {Gal}(\bar {\mathbf {Q}}/\mathbf {Q})$-modules, where $ p$ is a prime of good ordinary reduction for both curves. In this paper we prove an analogous result in the case where $ p$ is a prime of good supersingular reduction.


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Additional Information

Jeffrey Hatley
Affiliation: Department of Mathematics, Bailey Hall 202, Union College, Schenectady, New York 12308
Email: hatleyj@union.edu

DOI: https://doi.org/10.1090/proc/13545
Received by editor(s): May 26, 2016
Received by editor(s) in revised form: May 30, 2016, June 6, 2016, August 3, 2016, September 6, 2016, September 9, 2016, October 5, 2016, and October 14, 2016
Published electronically: January 23, 2017
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2017 American Mathematical Society

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