Rational points on quadratic elliptic surfaces

Sadek, Mohammad (2022) Rational points on quadratic elliptic surfaces. European Journal of Mathematics . ISSN 2199-675X (Print) 2199-6768 (Online) Published Online First https://dx.doi.org/10.1007/s40879-022-00577-x

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We consider elliptic surfaces whose coefficients are degree 2 polynomials in a variable T. It was recently shown, Kollár and Mella (Amer J Math 139(4):915–936 2017), that for infinitely many rational values of T the resulting elliptic curves have rank at least 1. We prove that the Mordell–Weil rank of each such elliptic surface is at most 6 over 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 Q.
Item Type: Article
Uncontrolled Keywords: Elliptic curves; Elliptic surfaces; Mordell–Weil rank; Nagao’s conjecture
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Mohammad Sadek
Date Deposited: 21 Sep 2022 11:36
Last Modified: 21 Sep 2022 11:36
URI: https://research.sabanciuniv.edu/id/eprint/44491

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