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ON THE j-INVARIANTS OF THE QUADRATIC Q-CURVES

Published online by Cambridge University Press:  19 March 2001

JOSEP GONZÁLEZ
JOSEP GONZÁLEZ
Affiliation:
Departament de Matemàtica Aplicada i Telemàtica, Escola Universitària Politècnica de Vilanova i la Geltrú, Avenida Victor Balaguer s/n, Vilanova i la Geltrú 08800, Spain; josepg@mat.upc.es
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Abstract

The j-invariants of the quadratic Q-curves without complex multiplication are studied. Some properties of the norms of these invariants are shown and a relationship between the field Q(j) and the degree of an isogeny of the Q-curve to its Galois conjugate is found. In the case when the degree of the isogeny is a prime p, some properties of the primes of potentially multiplicative reduction for the Q-curve and of the reduction of j modulo a prime [Pfr ] in Q(j) over p when the Q-curve has potentially good reduction at [Pfr ] are found.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 52 - 68
Copyright
The London Mathematical Society 2001

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Footnotes

This research has been partially supported by DGICYT, grant PB96-0970-C02-02.