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Parity of ranks of elliptic curves with equivalent mod $ p$ Galois representations


Author: Sudhanshu Shekhar
Journal: Proc. Amer. Math. Soc. 144 (2016), 3255-3266
MSC (2010): Primary 14H52, 11F33, 11R23
DOI: https://doi.org/10.1090/proc/12993
Published electronically: February 3, 2016
MathSciNet review: 3503694
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Abstract: Given two elliptic curves $ E_1$ and $ E_2$ defined over the field of rational numbers $ \mathbb{Q}$ that have good and ordinary reduction at an odd prime $ p$, and have equivalent, irreducible mod $ p$ Galois representations, we study the variation of the parity of Selmer ranks and analytic ranks of $ E_1$ and $ E_2$ over certain number fields.


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Additional Information

Sudhanshu Shekhar
Affiliation: Mathematics Center Heidelberg – and – Indian Institute of Science education and Research, Mohali
Email: sudhanshu@mathi.uni-heidelberg.de, sshekhars2012@gmail.com

DOI: https://doi.org/10.1090/proc/12993
Keywords: Iwasawa theory, congruences, Selmer groups, elliptic curves
Received by editor(s): June 9, 2015
Received by editor(s) in revised form: August 21, 2015, and September 23, 2015
Published electronically: February 3, 2016
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2016 American Mathematical Society

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