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arXiv · 2207.00114

Rational points on quadratic elliptic surfaces

Mohammad Sadek
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Abstract

We consider elliptic surfaces whose coefficients are degree $2$ polynomials in a variable $T$. It was recently shown that for infinitely many rational values of $T$ the resulting elliptic curves have rank at least $1$. In this article, we prove that the Mordell-Weil rank of each such elliptic surface is at most $6$ over $\mathbb Q$. In fact, we show that the Mordell-Weil rank of these elliptic surfaces is controlled by the number of zeros of a certain polynomial over $\mathbb Q$.

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Mohammad Sadek. 2022-06-30. Rational points on quadratic elliptic surfaces. https://arxiv.org/abs/2207.00114

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