Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)



On quadratic families of CM elliptic curves

Author: Ritabrata Munshi
Journal: Trans. Amer. Math. Soc. 363 (2011), 4337-4358
MSC (2000): Primary 11F67; Secondary 11M41, 11G40
Published electronically: March 4, 2011
MathSciNet review: 2792990
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Given a CM elliptic curve with Weierstrass equation $ y^2=f(x)$, and a positive definite binary quadratic form $ Q(u,v)$, we show that there are infinitely many reduced integer pairs $ (u,v)$ such that the twisted elliptic curve $ Q(u,v)y^2=f(x)$ has analytic rank (and consequently Mordell-Weil rank) one. In fact it follows that the number of such pairs with $ \vert u\vert, \vert v\vert \leq X$ is at least $ X^{2-\varepsilon}$ for any $ \varepsilon>0$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 11F67, 11M41, 11G40

Retrieve articles in all journals with MSC (2000): 11F67, 11M41, 11G40

Additional Information

Ritabrata Munshi
Affiliation: Institute for Advanced Study, Einstein Drive, Princeton New Jersey 08540
Address at time of publication: School of Mathematics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai 400005, India

Keywords: CM elliptic curves, $L$-functions, nonvanishing
Received by editor(s): December 1, 2009
Published electronically: March 4, 2011
Additional Notes: The author was supported by NSF grant No. DMS-0635607.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia