Towards a classification of isolated 𝑗-invariants

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS

ACS Applied Bio Materials Pub Date : 2024-04-25 DOI:10.1090/mcom/3956

Abbey Bourdon, Sachi Hashimoto, Timo Keller, Z. Klagsbrun, David Lowry-Duda, Travis Morrison, Filip Najman, Himanshu Shukla

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引用次数: 0

Abstract

We develop an algorithm to test whether a non-complex multiplication elliptic curve E / Q E/\mathbf {Q} gives rise to an isolated point of any degree on any modular curve of the form X 1 ( N ) X_1(N) . This builds on prior work of Zywina which gives a method for computing the image of the adelic Galois representation associated to E E . Running this algorithm on all elliptic curves presently in the L L -functions and Modular Forms Database and the Stein–Watkins Database gives strong evidence for the conjecture that E E gives rise to an isolated point on X 1 ( N ) X_1(N) if and only if j ( E ) = − 140625 / 8 , − 9317 j(E)=-140625/8, -9317 , 351 / 4 351/4 , or − 162677523113838677 -162677523113838677 .

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对孤立𝑗变量进行分类

我们开发了一种算法来检验非复数乘法椭圆曲线 E / Q E/\mathbf {Q} 是否会在任何形式为 X 1 ( N ) X_1(N)的模态曲线上产生一个任意度的孤立点。这建立在 Zywina 之前的工作基础上，Zywina 给出了一种计算与 E E 相关联的adelic伽罗瓦表示的映像的方法。在 L L 函数和模块形式数据库以及 Stein-Watkins 数据库中的所有椭圆曲线上运行这一算法，有力地证明了以下猜想：当且仅当 j ( E ) = - 140625 / 8 , - 9317 j(E)=-140625/8, -9317 , 351 / 4 351/4 , 或 - 162677523113838677 -162677523113838677 时，E E 在 X 1 ( N ) X_1(N)上产生孤立点。

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464