Modular Curves of Composite Level

Andreas Enge 1, 2 Reinhard Schertz 3
2 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7161
Abstract : We examine a class of functions on $X_0 (N)$ where $N$ is the product of two arbitrary primes. The functions are built as products of Dedekind's $\eta$-function and play a role in the construction of elliptic curves with complex multiplication. We show how to determine the modular polynomials relating them to the absolute modular invariant $j$ and prove different properties of these polynomials. In particular, we show that they provide models for the modular curves $X_0 (N)$.
Type de document :
Article dans une revue
Acta Arithmetica, Instytut Matematyczny PAN, 2005, 118 (2), pp.129-141
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https://hal.inria.fr/inria-00386309
Contributeur : Andreas Enge <>
Soumis le : mercredi 20 mai 2009 - 18:56:46
Dernière modification le : jeudi 11 janvier 2018 - 06:22:14

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Andreas Enge, Reinhard Schertz. Modular Curves of Composite Level. Acta Arithmetica, Instytut Matematyczny PAN, 2005, 118 (2), pp.129-141. 〈inria-00386309〉

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