The imaginary quadratic fields of class number 4

We point out that although Baker [2, 3] and Stark [18, 19] succeeded in solving the class number 1 and 2 problems, their methods did not extend to the higher cases. It was not until the work of Goldfeld, Gross, and Zagier [12, 13] that a general method was developed. This new method, however, does not allow one to solve the even class number problems without a good deal of further work. In this regard, we note that Oesterlé [17] finished the class number 3 problem, while the class number 8 problem still appears to be intractable.

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