Distribution of Mordell–Weil ranks of families of elliptic curves

Tom 108 / 2016

Bartosz Naskręcki Banach Center Publications 108 (2016), 201-229 MSC: Primary 14H52; Secondary 11D25, 11D45, 11G05. DOI: 10.4064/bc108-0-16


We discuss the distribution of Mordell–Weil ranks of the family of elliptic curves $y^2=(x+\alpha f^2)(x+\beta b g^2)(x+\gamma h^2)$ where $f,g,h$ are coprime polynomials that parametrize the projective smooth conic $a^2+b^2=c^2$ and $\alpha,\beta,\gamma$ are elements from $\overline{\mathbb{Q}}$. 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.


  • Bartosz NaskręckiFaculty of Mathematics and Computer Science
    Adam Mickiewicz University
    Umultowska 87
    61-614 Poznań, Poland
    Lehrstuhl für Computeralgebra
    Mathematisches Institut
    Universität Bayreuth
    95440 Bayreuth, Germany

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