English

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

R2 v1 2026-06-23T04:58:54.705Z