Rational sequences on different models of elliptic curves

Çelik, Gamze Savaş and Sadek, Mohammad and Soydan, Gökhan (2019) Rational sequences on different models of elliptic curves. Glasnik Matematicki, 54 (1). pp. 53-64. ISSN 0017-095X (Print) 1846-7989 (Online)

[thumbnail of rational_sequences_on_different_models_of_elliptic_curves.pdf] PDF
rational_sequences_on_different_models_of_elliptic_curves.pdf

Download (140kB)

Abstract

Given a set S of elements in a number field k, we discuss the existence of planar algebraic curves over k which possess rational points whose x-coordinates are exactly the elements of S. If the size vertical bar S vertical bar of S is either 4, 5, or 6, we exhibit infinite families of (twisted) Edwards curves and (general) Huff curves for which the elements of S are realized as the x-coordinates of rational points on these curves. This generalizes earlier work on progressions of certain types on some algebraic curves.
Item Type: Article
Uncontrolled Keywords: Elliptic curve; Edwards curve; Huff curve; rational sequence; rational point
Subjects: Q Science > QA Mathematics > QA150-272.5 Algebra
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Mohammad Sadek
Date Deposited: 24 Aug 2019 22:54
Last Modified: 26 Apr 2022 10:05
URI: https://research.sabanciuniv.edu/id/eprint/37315

Actions (login required)

View Item
View Item