Defining equations of modular curves

• Autores: Yifan Yang
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 204, Nº 2, 2006, págs. 481-508
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.05.019
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• Resumen

  • We obtain defining equations of modular curves X0(N), X1(N), and X(N) by explicitly constructing modular functions using generalized Dedekind eta functions. As applications, we describe a method of obtaining a basis for the space of cusp forms of weight 2 on a congruence subgroup. We also use our model of X0(37) to find explicit modular parameterization of rational elliptic curves of conductor 37.