In this paper, we show that an action on the set of elliptic curves with j=1728j=1728 preserves a certain kind of symmetry on the local root number of Hecke characters attached to such elliptic curves. As a consequence, we give results on the distribution of the root numbers and their average of the aforementioned Hecke characters.

中文翻译：

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附加在某些椭圆曲线上的Hecke字符的根数分布

在本文中，我们证明了对具有j = 1728j = 1728的椭圆曲线集的动作在附着到此类椭圆曲线的Hecke字符的局部根数上保留了某种对称性。结果，我们给出了根数的分布及其上述Hecke字符的平均值的结果。