Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms

Bartosz Naskręcki

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arXiv · 1609.04715

Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms

Bartosz Naskręcki

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Abstract

We prove results on the Mordell--Weil rank of elliptic curves $y^2=x(x-\alpha a^2)(x-\beta b^2)$ parametrized by binary quadratic forms $\alpha a^2+\beta b^2=\gamma c^2$. We express our explicit lower bounds over number fields and offer a detailed description of the corresponding Mordell-Weil group structure in the function field case.

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Bartosz Naskręcki. 2016-09-15. Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms. https://arxiv.org/abs/1609.04715

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