高阶椭圆曲线与扭转ℤ/4ℤ。

Q4 Mathematics Integers Pub Date : 2016-01-01

Foad Khoshnam, Dustin Moody

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摘要

在ℚ(t)域上，木原构造了一条椭圆曲线，它具有扭转群ℤ/4ℤ和五个独立的有理点，表明秩至少为五。按照他的方法，我们给出了一个新的无穷椭圆曲线族，其扭转群为ℤ/4ℤ，秩至少为五。这与目前此类曲线的记录相吻合。此外，我们还给出了这些阶数高达 10 和 11 的曲线的具体例子。

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/4ℤ.

Working over the field ℚ(t), Kihara constructed an elliptic curve with torsion group ℤ/4ℤ and five independent rational points, showing the rank is at least five. Following his approach, we give a new infinite family of elliptic curves with torsion group ℤ/4ℤ and rank at least five. This matches the current record for such curves. In addition, we give specific examples of these curves with high ranks 10 and 11.

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