Sadek, Mohammad (2022) Rational points on quadratic elliptic surfaces. European Journal of Mathematics, 8 (2). pp. 674-686. ISSN 2199-675X (Print) 2199-6768 (Online)
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Official URL: https://dx.doi.org/10.1007/s40879-022-00577-x
Abstract
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: | 07 Sep 2023 14:49 |
| Last Modified: | 07 Sep 2023 14:49 |
| URI: | https://research.sabanciuniv.edu/id/eprint/47809 |
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Rational points on quadratic elliptic surfaces. (deposited 21 Sep 2022 11:36)
- Rational points on quadratic elliptic surfaces. (deposited 07 Sep 2023 14:49) [Currently Displayed]
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