Since every reduced binary quadratic form with discriminant d corresponds to one class of ideals in the quadratic fields Q(d^(1/2))with d>0 , Is there an effective way to determine all reduced binary quadratic form with discriminant d or at least can we determine the number of reduced binary quadratic form with discriminant d ?
Lots of information about algorithms to compute all classes of forms is given in the book: "Binary Quadratic Forms - An Algorithmic Approach" by Johannes Buchmann and Ulrich Vollmer.
Look at
1]:Stark,H.M. A complete determination of the complex quadratic ...elds of
class number one.M ich:M ath:J:14(1967); 1 27:
[2]:Birch,J.B.Weber’s Class Invariants.M athematika 16(1969); 283 294:
[3]:Schertz,R."Complex Multiplication",2010.
[4]:Zagier,
also, Pilar Bayer work is very interesting
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