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arXiv · 1609.04731

Distribution of Mordell--Weil ranks of families of elliptic curves

Bartosz Naskręcki
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Abstract

We discuss the distribution of Mordell--Weil ranks of the family of elliptic curves $y^2=(x+αf^2)(x+βb g^2)(x+γh^2)$ 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 $\overline{\mathbb{Q}}$. 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.

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Bartosz Naskręcki. 2016-09-15. Distribution of Mordell--Weil ranks of families of elliptic curves. https://doi.org/10.4064/bc108-0-16

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