Models of CM elliptic curves with a prescribed ℓ-adic Galois image

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-05-05 DOI:10.1016/j.jnt.2025.03.001

Enrique González–Jiménez , Álvaro Lozano-Robledo , Benjamin York

引用次数: 0

Abstract

For each prime number ℓ and for each imaginary quadratic order of class number one or two, we determine all the possible ℓ-adic Galois representations that occur for any elliptic curve with complex multiplication by such an order over its minimal field of definition, and then we determine all the isomorphism classes of elliptic curves that have a prescribed ℓ-adic Galois representation.

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具有给定的矢量伽罗瓦像的CM椭圆曲线模型

对于每一个素数，对于第1类或第2类的每一个虚二次阶，我们确定了在其最小定义域上复乘这样一个阶的任何椭圆曲线的所有可能的l -进伽罗瓦表示，然后我们确定了具有规定的l -进伽罗瓦表示的椭圆曲线的所有同构类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.