ENGE, Andreas; SCHERTZ, Reinhard

doi:10.1112/S146115701300020X

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ENGE, Andreas
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]

SCHERTZ, Reinhard
Institut für Mathematik [Augsburg]

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Article de revue

Ce document a été publié dans

LMS Journal of Computation and Mathematics. 2013, vol. 16, p. 407-418

London Mathematical Society

Résumé en anglais

We determine the conditions under which singular values of multiple $\eta$-quotients of square-free level, not necessarily prime to~$6$, yield class invariants, that is, algebraic numbers in ring class fields of imaginary-quadratic number fields. We show that the singular values lie in subfields of the ring class fields of index $2^{k' - 1}$ when $k' \geq 2$ primes dividing the level are ramified in the imaginary-quadratic field, which leads to faster computations of elliptic curves with prescribed complex multiplication. The result is generalised to singular values of modular functions on $X_0^+ (p)$ for $p$ prime and ramified.< Réduire

Mots clés en anglais

complex multiplication

class invariants

eta quotients

ring class fields

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189602

DOI

http://dx.doi.org/10.1112/S146115701300020X

Projet Européen

Algorithmic Number Theory in Computer Science

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251