On Lecacheux's family of quintic polynomials.

Kida, Rikuna and Sato [KRS10] developed a classification theory for Brumer's dihedral 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.