Selmer groups in twist families of elliptic curves

İNAM İ.

Quaestiones Mathematicae, cilt.35, sa.4, ss.471-487, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 4
  • Basım Tarihi: 2012
  • Doi Numarası: 10.2989/16073606.2012.742255
  • Dergi Adı: Quaestiones Mathematicae
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.471-487
  • Anahtar Kelimeler: Birch, Elliptic curves, Swinnerton-Dyer conjecture, zeta-functions and related questions
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

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.