关于Lecacheux的五次多项式族

Pub Date : 2020-03-30 DOI:10.3792/pjaa.97.001
A. Hoshi, Masakazu Koshiba
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引用次数: 0

摘要

Kida、Rikuna和Sato [KRS10]通过由相关椭圆曲线产生的Kummer理论,发展了Brumer五次多项式的分类理论。我们将其结果推广到与Lecacheux的五次$F_{20}$-多项式相关的椭圆曲线上,而不是与Brumer的五次$D_5$-多项式相关的椭圆曲线上。
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On Lecacheux’s family of quintic polynomials
Kida, Rikuna and Sato [KRS10] developed a classification theory for Brumer's quintic polynomials via Kummer theory arising from associated elliptic curves. We generalize their results to elliptic curves associated to Lecacheux's quintic $F_{20}$-polynomials instead of Brumer's quintic $D_5$-polynomials.
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