We prove a necessary and sufficient condition for isogenous elliptic curves based on the algebraic dependence of p-adic elliptic functions. As a consequence, we give a short proof of the p-adic analogue of Schneider’s theorem on the linear independence of p-adic elliptic logarithms of algebraic points on two nonisogenous elliptic curves defined over the field of algebraic numbers.

中文翻译：

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椭圆曲线和-ADIC 椭圆超越

我们基于代数相关性证明了等生椭圆曲线的充要条件p-adic 椭圆函数。因此，我们给出一个简短的证明p- Schneider 定理关于线性独立性的进数类似物p-在代数数域上定义的两条非同质椭圆曲线上代数点的进数椭圆对数。