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.

中文翻译：

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CM椭圆曲线之间的奇异单位和同构

在本说明中，我们将应用Gross–Zagier，Gross–Kohnen–Zagier的结果及其推广，以简短证明奇异模量的差异不是单位。结果，我们获得了CM椭圆曲线减小之间的同质性的结果。