Visualizing elements of order in the Tate–Shafarevich group of an elliptic curve

Q1 Mathematics

Lms Journal of Computation and Mathematics Pub Date : 2016-01-01 DOI:10.1112/S1461157016000243

Tom Fisher

引用次数: 1

Abstract

We study the elliptic curves in Cremona’s tables that are predicted by the Birch–Swinnerton-Dyer conjecture to have elements of order $7$ in their Tate–Shafarevich group. We show that in many cases these elements are visible in an abelian surface or abelian 3-fold.

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椭圆曲线的Tate-Shafarevich群中有序元素的可视化

我们研究了由Birch-Swinnerton-Dyer猜想预测的克雷莫纳表中的椭圆曲线在其Tate-Shafarevich群中具有$7阶的元素。我们证明，在许多情况下，这些元素在阿贝尔曲面或阿贝尔三折中是可见的。

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

Lms Journal of Computation and Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.