Families of elliptic curves of rank ≥5 over ℚ(t)

Moody, Dustin and Sadek, Mohammad and Zargar, Arman Shamsi (2019) Families of elliptic curves of rank ≥5 over ℚ(t). Rocky Mountain Journal of Mathematics, 49 (7). pp. 2253-2266. ISSN 0035-7596 (Print) 1945-3795 (Online)

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We construct two infinite families of curves with high rank. The first is defined by the equation y2 = x(x − a2)(x − b2) + a2b2, where a, b ∈ ℚ(t). The second family arises from a system of rational cuboids, i.e., a rectangular box for which the lengths of the edges and face diagonals are all rational. We create a second family with defining equation y2 = (x − a2)(x − b2)(x − c2) + a2b2c2, where a, b, c ∈ Q(t) are the edge lengths of a rational cuboid. We show that the rank of both families is ≥ 5 over Q(t). We conclude by studying corresponding families of curves defined by other known solutions to the rational cuboid problem, and find some specific examples of curves from these various families with high rank.
Item Type: Article
Uncontrolled Keywords: And phrases. Elliptic curves; Rank; Rational cuboids
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Mohammad Sadek
Date Deposited: 29 Jul 2023 14:16
Last Modified: 29 Jul 2023 14:16
URI: https://research.sabanciuniv.edu/id/eprint/46415

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