Singerman, D.; Syddall, R. I. Belyĭ uniformization of elliptic curves. (English) Zbl 0868.14019 Bull. Lond. Math. Soc. 29, No. 4, 443-451 (1997). Belyĭ’s theorem implies that a Riemann surface \(X\) represents a curve defined over a number field if and only if it can be expressed as \(U/ \Gamma\) where \(U\) is simply-connected and \(\Gamma\) is a subgroup of finite index in a triangle group. We consider the case when \(X\) has genus 1 and ask for which curves and number fields can \(\Gamma\) be chosen to be a lattice. As an application we give examples of Galois actions on Grothendieck dessins. Reviewer: D.Singerman (Southampton) Cited in 7 Documents MSC: 14H55 Riemann surfaces; Weierstrass points; gap sequences 14L30 Group actions on varieties or schemes (quotients) 11G05 Elliptic curves over global fields 14H52 Elliptic curves 30F10 Compact Riemann surfaces and uniformization Keywords:Belyj uniformization; elliptic curve; Riemann surface; Galois actions on Grothendieck dessins PDFBibTeX XML Full Text: DOI