22.1 the Hilbert Class Polynomial
نویسنده
چکیده
The appellation “Hilbert” is sometimes reserved for cases where D is a fundamental discriminant (in which case HD(X) is more generally called a ring class polynomial), but we shall use the term Hilbert class polynomial to refer to HD(X) in general. Our first objective is to use the fact that ΦN ∈ Z[X,Y ] to prove that HD ∈ Z[X]. We require the following lemma. Lemma 22.2. If N is prime then the leading coefficient of ΦN (X,X) is −1. Proof. We have
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