Singular Units and Isogenies Between CM Elliptic Curves

31 Oct 2018 · Yingkun Li ·

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.