Elliptic curves with rational subgroups of order three
Number Theory
2007-05-23 v2
Abstract
In this article we present a characterization of elliptic curves defined over a finite field Fq which possess a rational subgroup of order three. There are two posible cases depending on the rationality of the points in these groups. We show that for finite fields Fq, q= -1 mod 3, all elliptic curves with a point of order 3, they have another rational subgroup whose points are not defined over the finite field. If q = 1 mod 3, this is no true; but there exits a one to one correspondence between curves with points of order 3 and curves with rational subgroups whose points are not rational.
Cite
@article{arxiv.math/0506327,
title = {Elliptic curves with rational subgroups of order three},
author = {D. Sadornil},
journal= {arXiv preprint arXiv:math/0506327},
year = {2007}
}
Comments
Submitted to publication. Corrige version