论文标题
在椭圆形曲线上，$ p $ - 发病率上的二次磁场
On elliptic curves with $p$-isogenies over quadratic fields
论文作者
论文摘要
令$ k $为一个数字字段。对于哪个Primes $ p $，是否存在椭圆曲线$ e / k $承认$ k $ - 理性$ p $发育？尽管我们对理由的问题有一个答案，但将其扩展到其他数字字段是数字理论的基本开放问题。在本文中，我们研究了这个问题，即$ k $是一个二次领域，但假设$ e $可以在$ k $ the $ p $的$ k $上半固定。我们证明了二次场和特定二次场家族的结果。
Let $K$ be a number field. For which primes $p$ does there exist an elliptic curve $E / K$ admitting a $K$-rational $p$-isogeny? Although we have an answer to this question over the rationals, extending this to other number fields is a fundamental open problem in number theory. In this paper, we study this question in the case that $K$ is a quadratic field, subject to the assumption that $E$ is semistable at the primes of $K$ above $p$. We prove results both for families of quadratic fields and for specific quadratic fields.
