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. 22532266. ISSN 00357596 (Print) 19453795 (Online)
This is the latest version of this item.
Official URL: https://dx.doi.org/10.1216/RMJ20194972253
Abstract
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 
Available Versions of this Item

On families of elliptic curves of rank >= 5 over Q(t). (deposited 28 Jul 2019 22:32)
 Families of elliptic curves of rank ≥5 over ℚ(t). (deposited 29 Jul 2023 14:16) [Currently Displayed]