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Modular Curves of Composite Level

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 $X_0 (N)$.
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Contributor : Andreas Enge <>
Submitted on : Wednesday, May 20, 2009 - 6:56:46 PM
Last modification on : Thursday, March 5, 2020 - 6:26:41 PM


  • HAL Id : inria-00386309, version 1



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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