2-Selmer groups of quadratic twists of elliptic curves

Authors:
George Boxer and Peter Diao

Journal:
Proc. Amer. Math. Soc. **138** (2010), 1969-1978

MSC (2010):
Primary 11G05, 11G40

Published electronically:
February 11, 2010

MathSciNet review:
2596031

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Abstract: In this paper we investigate families of quadratic twists of elliptic curves. Addressing a speculation of Ono, we identify a large class of elliptic curves for which the parities of the ``algebraic parts'' of the central values , as varies, have essentially the same multiplicative structure as the coefficients of . We achieve this by controlling the 2-Selmer rank (à la Mazur and Rubin) when the Tamagawa numbers do not already dictate the parity.

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Additional Information

**George Boxer**

Affiliation:
Department of Mathematics, Mailbox 2704, Frist Center, Princeton University, Princeton, New Jersey 08544

Email:
gboxer@princeton.edu

**Peter Diao**

Affiliation:
Department of Mathematics, Mailbox 2704, Frist Center, Princeton University, Princeton, New Jersey 08544

Email:
pdiao@princeton.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-10-10273-1

Received by editor(s):
October 27, 2009

Published electronically:
February 11, 2010

Communicated by:
Ken Ono

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.