Parity of ranks of elliptic curves with equivalent mod $p$ Galois representations
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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.References
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Additional Information
- Sudhanshu Shekhar
- Affiliation: Mathematics Center Heidelberg – and – Indian Institute of Science education and Research, Mohali
- MR Author ID: 1061352
- Email: sudhanshu@mathi.uni-heidelberg.de, sshekhars2012@gmail.com
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3255-3266
- MSC (2010): Primary 14H52, 11F33, 11R23
- DOI: https://doi.org/10.1090/proc/12993
- MathSciNet review: 3503694