Distribution of Mordell-Weil ranks of families of elliptic curves

• Autorzy: Bartosz Naskręcki
• Języki publikacji: EN

Abstrakty

EN

We discuss the distribution of Mordell-Weil ranks of the family of elliptic curves y² = (x + αf²)(x + βbg²)(x + γh²) where f,g,h are coprime polynomials that parametrize the projective smooth conic a² + b² = c² and α,β,γ are elements from ℚ̅. 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.

Kategorie tematyczne

• 11D25: Cubic and quartic equations
• 11D45: Counting solutions of Diophantine equations
• 11G05: Elliptic curves over global fields
• 14H52: Elliptic curves

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2016
• Tom: 108
• Numer: 1
• Strony: 201-229

Daty

wydano

2016

Twórcy

autor

Bartosz Naskręcki

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

Identyfikatory

DOI

10.4064/bc108-0-16