丢番图三元组诱导的具有Z/2Z × Z/4Z扭转的高阶椭圆曲线

Q1 Mathematics Lms Journal of Computation and Mathematics Pub Date : 2014-01-01 DOI:10.1112/S1461157014000023

A. Dujella, J. C. Peral

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引用次数: 23

摘要

在有理函数域上构造了一条扭转群为Z/2Z × Z/4Z且秩为4的椭圆曲线，以及Q上具有相同扭转群且秩为9的椭圆曲线。这两个结果都改进了先前关于该扭转群曲线阶的记录。它们是通过考虑丢番图三元组诱导的椭圆曲线得到的。

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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High rank elliptic curves with torsion Z/2Z × Z/4Z induced by Diophantine triples

We construct an elliptic curve over the field of rational functions with torsion group Z/2Z × Z/4Z and rank equal to four, and an elliptic curve over Q with the same torsion group and rank nine. Both results improve previous records for ranks of curves of this torsion group. They are obtained by considering elliptic curves induced by Diophantine triples.

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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.