Is there a handy listing of the discriminants of imaginary quadratic fields having a given ideal class group? It would be nice to use such a resource as a source of examples.
For example, we're all set for class number $4$:
- A013658 Discriminants with class number $4$
If we want just the cyclic or the non-cyclic groups, we can intersect with these lists:
- A227735 Discriminants with cyclic class groups of composite order
- A227734 Discriminants with noncyclic class groups
The latter of which results in:
- A192322 Discriminants whose class group is the Klein $4$-group, $C_2\times C_2$
So that's really convenient! But are there also pre-computed lists to distinguish, say, $C_2\times C_2\times C_2$ from $C_4\times C_2$?
(The closest resource I've found is A225365 Discriminants with non-isomorphic class groups, which is still a great source of examples, if not exhaustive.)