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Published online by Cambridge University Press: 24 October 2008
Let ψ be the Grossencharacter attached to an elliptic curve E defined over an imaginary quadratic field K ⊂ of discriminant −dK, and having complex multiplication by the maximal order
of K. We denote the conductor of ψ by
and fix a Weierstrass model for E with coefficients in
,
whose discriminant is divisible only by primes dividing 6
. Let Kab be the abelian closure of K in
and choose a fundamental period Ω ∈
for the above model of the curve.