Distribution of Mordell-Weil ranks of families of elliptic curves

Bartosz Naskrecki

Research output: Contribution to journalArticle (Academic Journal)

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Abstract

We discuss the distribution of Mordell–Weil ranks of the family of elliptic curves y^2 = (x + αf^2)(x + βg^2)(x + γh^2) where f, g, h are coprime polynomials that parametrize the projective smooth conic a^2 + b^2 = c^2 and α, β, γ are elements from Qbar. In our previous papers we discussed certain special cases of this problem and in this article we complete the picture by proving the general results.
Original languageEnglish
Pages (from-to)201-229
Number of pages29
JournalBanach Center Publications
Volume108
Early online date14 Jun 2016
DOIs
Publication statusPublished - 2016

Keywords

  • elliptic curve
  • Mordell-Weil rank
  • elliptic surface

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