Physical Sciences and Mathematics Commons^™

Elliptic Functions And Equations Of Modular Curves, Lev A. Borisov, Paul E. Gunnells, Sorin Popescu

Paul Gunnells

Let P≥5 be a prime. We show that the space of weight one Eisenstein series defines an embedding into P(p−3)/2 of the modular curve X1(p) for the congruence group Γ1(p) that is scheme-theoretically cut out by explicit quadratic equations.