Collinear CM-points
Number Theory
2018-02-28 v4
Abstract
Andr\'e's celebrated Theorem of 1998 implies that each complex straight line (apart from obvious exceptions) contains at most finitely many points whose both coordinates are j-invariants of elliptic curves with complex multiplication. We show that there are only a finite number of such lines which contain more than two such points. As there is a line through any two complex points, this is best possible.
Cite
@article{arxiv.1503.08378,
title = {Collinear CM-points},
author = {Yuri Bilu and Florian Luca and David Masser},
journal= {arXiv preprint arXiv:1503.08378},
year = {2018}
}
Comments
Minor changes suggested by the referee