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

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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.