  Let E be an elliptic curve having complex multiplication by a given quadratic
order of an imaginary quadratic field K. The field of definition of E is the
ring class field Omega of the order. If the prime p splits completely in Omega,
then we can reduce E modulo one the factors of p and get a curve Ep defined
over GF(p). The trace of the Frobenius of Ep is known up to sign and we need a
fast way to find this sign. For this, we propose to use the action of the
Frobenius on torsion points of small order built with class invariants a la
Weber, in a manner reminiscent of the Schoof-Elkies-Atkin algorithm for
computing the cardinality of a given elliptic curve modulo p. We apply our
results to the Elliptic Curve Primality Proving algorithm (ECPP).
