Rank 0 Quadratic Twists of a Family of Elliptic Curves

Gang Yu

Type: Article

Publication Date: 2003-01-01

Citations: 19

DOI: https://doi.org/10.1023/a:1022258905572

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button. In this paper, we consider a family of elliptic curves over ${\open Q}$ with 2-torsion part ${\open Z}_2$. We prove that, for every such elliptic curve, a positive proportion of quadratic twists have Mordell–Weil rank 0.

Locations

Deep Blue (University of Michigan) - View - PDF
Compositio Mathematica - View - PDF

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+	OPEN PROBLEMS ON EXPONENTIAL AND CHARACTER SUMS	2009	Igor E. Shparlinski
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Works Cited by This (31)

Action	Title	Year	Authors
+	Rank zero quadratic twists of modular elliptic curves	1996	Ken Ono
+ PDF Chat	The Arithmetic of Elliptic Curves	1986	Joseph H. Silverman
+	Conjectures on elliptic curves over quadratic fields	1979	Dorian Goldfeld
+	Sur les coefficients de Fourier des formes modulaires de poids demi-entier	1981	J. L. Waldspurger
+	An Example of an Elliptic Curve with a Positive Density of Prime Quadratic Twists Which Have Rank Zero	1999	Kevin James
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+	None	1999	Siman Wong
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+	On Character Sums and <i>L</i> -Series. II	1963	D. A. Burgess