Akinari Hoshi, Masakazu Koshiba
Proc. Japan Acad. Ser. A Math. Sci. 97 (1), 1-6, (January 2021) DOI: 10.3792/pjaa.97.001
KEYWORDS: Lecacheux’s quintic polynomial, Kummer theory, Elliptic curves, 11G05, 11R20, 12F20, 12G05
Kida, Rikuna and Sato [6] 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.
