On Lecacheux's family of quintic polynomials

2020/03/30 by Akinari Hoshi, Hoshi, Akinari, Masakazu Koshiba +1
Computer Science · Mathematics · #11G05 #11R20 #12F20 #12G05 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2003.13458

openalex publication_date 2020/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 F₂₀-polynomials instead of Brumer's quintic D₅-polynomials.

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