Selmer groups in twist families of elliptic curves
Quaestiones Mathematicae, vol.35, no.4, pp.471-487, 2012 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 35 Issue: 4
- Publication Date: 2012
- Doi Number: 10.2989/16073606.2012.742255
- Journal Name: Quaestiones Mathematicae
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.471-487
- Keywords: Birch, Elliptic curves, Swinnerton-Dyer conjecture, zeta-functions and related questions
- Bilecik Şeyh Edebali University Affiliated: Yes
Abstract
The aim of this article is to give some numerical data related to the order of the Selmer groups in twist families of elliptic curves. To do this we assume the Birch and Swinnerton-Dyer conjecture is true and we use a celebrated theorem of Waldspurger to get a fast algorithm to compute LE (1). Having an extensive amount of data we compare the distribution of the order of the Selmer groups by functions of type with ε small. We discuss how the "best choice" of α is depending on the conductor of the chosen elliptic curves and the congruence classes of twist factors. © 2012 Copyright NISC Pty Ltd.