2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60223Let $p\ge 5$ be a prime. We show that the space of weight one Eisenstein series defines an embedding into $\PP^{(p-3)/2}$ of the modular curve $X_1(p)$ for the congruence group $Γ_1(p)$ that is scheme-theoretically cut out by explicit quadratic equations.AMS-LaTeX, 15 pagesAlgebraic GeometryNumber Theory11F11; 14G35; 14H52; 14H70text