# Can we find the 18 imaginary quadratic ffields with class number 2 algorithmically?

I am reading about the class number problem. There is a well known complete list of imaginary quadratic fields $\mathbb{Q}(\sqrt{-d})$ with class number $1$.

I found a paper by Stark that says there are exactly 18 such fields with class number $2$. I don't have access.

The comments indicate this was easy to find using Google? The paper he points to was written in 1998. Since I am totally clueless, is it possible to compute this result e.g. using continued fractions?

By Moore's law computing power, say in a smart phone, exceeds what was available to the authors of that paper.

Wikipedia has the Dirichlet Class number formula.

$$h(d) = \frac{w\sqrt{d}}{2\pi} L(1, \chi)$$

and there is even a formula for $L(1, \chi)$ which nobody seems to understand.

• The first version of your question read like you wanted only the list. If you want to find them algorithmically you can use Pari, and see Henri Cohen's book for reference on the algorithms. – Bill Dubuque May 27 '15 at 0:02
• The reference for the algorithms in Pari is Henri Cohen's A Course in Computational Algebraic Number Theory. There you will find everything you seek (and much more!) – Bill Dubuque May 27 '15 at 0:22
• @BillDubuque it is indeed; don't be surprised if I revise this question or post another one asking for more details – cactus314 May 27 '15 at 0:30
• Just for the sake of reference: oeis.org/A005847 – David R. May 28 '15 at 21:41