Mordell Curves with Ordinates in Arithmetic Progression

Sakha A. Alkabouss; Benjamin Earp-Lynch; Simon Earp-Lynch; Omar Kihel

Mordell Curves with Ordinates in Arithmetic Progression

Number Theory 2026-07-08 v1

Authors: Sakha A. Alkabouss , Benjamin Earp-Lynch , Simon Earp-Lynch , Omar Kihel

Abstract

We show that Mordell curves with arithmetic progressions in the $y$ -coordinate of length $7$ have not been ruled out by previous work, and we give non-isomorphic families of Mordell curves with $y$ -arithmetic progressions of length $6$ . We also construct parametric families of elliptic curves of moderate rank, with subfamilies possessing rational points in arithmetic progression.

Cite

@article{arxiv.2607.06998,
  title  = {Mordell Curves with Ordinates in Arithmetic Progression},
  author = {Sakha A. Alkabouss and Benjamin Earp-Lynch and Simon Earp-Lynch and Omar Kihel},
  journal= {arXiv preprint arXiv:2607.06998},
  year   = {2026}
}