椭圆曲线的再现性评价标准
Critères d'irréductibilité pour les représentations des courbes elliptiques
摘要：
令$E$是在数域$K$上定义的椭圆曲线。如果$E$允许在$K$上定义一个$p$ -，则我们说素数$p$对于$(E,K)$是例外的.所有这样的素数的所谓例外集是有限的当且仅当$E$在K上没有复乘。本文证明了例外集包含在一个显式整数表的素除子因子集中（取决于$E$和$K$），它的无穷多个素因子都是非零的.它提供了一个有效的算法计算它在有限的情况下。其他不太一般，但相当有用的标准，以及几个数值例子。
英文摘要：
Let $E$ be an elliptic curve defined over a number field $K$. We say that a prime number $p$ is exceptional for $(E,K)$ if $E$ admits a $p$-isogeny defined over $K$. The so-called exceptional set of all such prime numbers is finite if and only if $E$ does not have complex multiplication over K. In this paper, we prove that the exceptional set is included in the set of prime divisors of an explicit list of integers (depending on $E$ and $K$), whose infinitely many of them are non-zero. It provides an efficient algorithm for computing it in the finite case. Other less general but rather useful criteria are given, as well as several numerical examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
