Regulators of rank one quadratic twists

Christophe Delaunay, Xavier-François Roblot

Type: Article

Publication Date: 2008-01-01

Citations: 2

DOI: https://doi.org/10.5802/jtnb.643

Abstract

We investigate the regulators of elliptic curves with rank 1 in some families of quadratic twists of a fixed elliptic curve. In particular, we formulate some conjectures on the average size of these regulators. We also describe an efficient algorithm to compute explicitly some of the invariants of a rank one quadratic twist of an elliptic curve (regulator, order of the Tate-Shafarevich group, etc.) and we discuss the numerical data that we obtain and compare it with our predictions.

Locations

Journal de Théorie des Nombres de Bordeaux - View - PDF
arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF

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Works Cited by This (18)

Action	Title	Year	Authors
+	A Course in Computational Algebraic Number Theory	1993	Henri Cohen
+	On the Distribution of Analytic Values on Quadratic Twists of Elliptic Curves	2006	Patricia L. Quattrini
+	Heegner point computations	1994	Noam D. Elkies
+	Discretisation for odd quadratic twists	2005	J. Brian Conrey Michael Rubinstein N. C. Snaith Mark E. Watkins
+	On the frequency of vanishing of quadratic twists of modular L-functions	2000	JB Conrey JP Keating MO Rubinstein N C Snaith
+	Random Matrix Theory and L-Functions at s = 1/2	2000	Jonathan P. Keating N. C. Snaith
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+ PDF Chat	Derivatives of random matrix characteristic polynomials with applications to elliptic curves	2005	N C Snaith
+	Numerical Investigations Related to the Derivatives of the<i>L</i>-Series of Certain Elliptic Curves	2003	Christophe Delaunay Sylvain Duquesne