Explicit isogenies of prime degree over number fields

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2025-05-14 DOI:10.2140/ant.2025.19.1147

Barinder S. Banwait, Maarten Derickx

引用次数: 0

Abstract

We provide an explicit and algorithmic version of a theorem of Momose classifying isogenies of prime degree of elliptic curves over number fields, which we implement in Sage and PARI/GP. Combining this algorithm with recent work of Box, Gajović and Goodman we obtain the first classifications of the possible prime degree isogenies of elliptic curves over cubic number fields, as well as for several quadratic fields not previously known. While the correctness of the general algorithm relies on the generalised Riemann hypothesis, the algorithm is unconditional for the restricted class of semistable elliptic curves.

查看原文本刊更多论文

数域上素数次的显式同基因

在Sage和PARI/GP中实现了数域上椭圆曲线素数次的Momose分类同基因定理的一个显式和算法版本。将该算法与Box、gajoviki和Goodman最近的工作相结合，我们获得了三次数域上椭圆曲线可能的素次同胚的第一个分类，以及一些以前不知道的二次域。一般算法的正确性依赖于广义黎曼假设，但对于半稳定椭圆曲线的限制类，该算法是无条件的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.