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Journal Articles Acta Arithmetica Year : 2005

Modular Curves of Composite Level

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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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Dates and versions

inria-00386309 , version 1 (20-05-2009)

Identifiers

  • HAL Id : inria-00386309 , version 1

Cite

Andreas Enge, Reinhard Schertz. Modular Curves of Composite Level. Acta Arithmetica, 2005, 118 (2), pp.129-141. ⟨inria-00386309⟩
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