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Elliptic functions and equations of modular curves

Lev Borisov·Paul Gunnells·Sorin Popescu
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Abstract

Let $p\ge 5$ 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.

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Lev Borisov, Paul Gunnells, Sorin Popescu. 2000-11-07. Elliptic functions and equations of modular curves. https://arxiv.org/abs/math/0010272

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