Singular Units and Isogenies Between CM Elliptic Curves
Number Theory
2021-07-01 v4
Abstract
In this note, we will apply the results of Gross-Zagier, Gross-Kohnen-Zagier and their generalizations to give a short proof that the differences of singular moduli are not units. As a consequence, we obtain a result on isogenies between reductions of CM elliptic curves.
Cite
@article{arxiv.1810.13214,
title = {Singular Units and Isogenies Between CM Elliptic Curves},
author = {Yingkun Li},
journal= {arXiv preprint arXiv:1810.13214},
year = {2021}
}
Comments
Final version. To appear in Compositio Math