Elliptic functions and equations of modular curves

Lev Borisov; Paul Gunnells; Sorin Popescu

Elliptic functions and equations of modular curves

Algebraic Geometry 2007-05-23 v2 Number Theory

Authors: Lev Borisov , Paul Gunnells , Sorin Popescu

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 $\Gamma_1(p)$ that is scheme-theoretically cut out by explicit quadratic equations.

Keywords

eisenstein series elliptic curves moduli spaces

Cite

@article{arxiv.math/0010272,
  title  = {Elliptic functions and equations of modular curves},
  author = {Lev Borisov and Paul Gunnells and Sorin Popescu},
  journal= {arXiv preprint arXiv:math/0010272},
  year   = {2007}
}

Comments

AMS-LaTeX, 15 pages

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