椭圆曲线的最小复盖模型

Q1 Mathematics

Lms Journal of Computation and Mathematics Pub Date : 2014-01-01 DOI:10.1112/S1461157014000217

T. Fisher

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引用次数: 0

摘要

本文给出了椭圆曲线的$2$覆盖和$3$覆盖相加的新公式，避免了任何域扩展的需要。我们证明了所得到的$6$ -覆盖可以用对三次形式表示。在此基础上，证明了雅可比椭圆曲线的整数系数模型与最小模型具有相同判别式的存在性定理。这项工作对求椭圆曲线上大高度的有理点有一定的应用价值。

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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Minimal models for -coverings of elliptic curves

In this paper we give a new formula for adding $2$ -coverings and $3$ -coverings of elliptic curves that avoids the need for any field extensions. We show that the $6$ -coverings obtained can be represented by pairs of cubic forms. We then prove a theorem on the existence of such models with integer coefficients and the same discriminant as a minimal model for the Jacobian elliptic curve. This work has applications to finding rational points of large height on elliptic curves.

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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.