Imaginary quadratic fields with a prescribed class number

Give an algorithm that, for h between 2^90 and 2^100, quickly finds an imaginary quadratic field with class number exactly h.

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "number-theory",
	5	+ "algorithms-complexity"
	6	+ ],
	7	+ "type": "algorithm",
	8	+ "also": [
	9	+ "proof"
	10	+ ],
	11	+ "source": {
	12	+ "key": "frontiermath-open",
	13	+ "name": "FrontierMath: Open Problems",
	14	+ "url": "https://epoch.ai/frontiermath/open-problems/quadratic-field-class-number",
	15	+ "id": "quadratic-field-class-number",
	16	+ "curator": "Epoch AI",
	17	+ "status": "unsolved",
	18	+ "as_of": "2026-10-20",
	19	+ "catalog": "0521c19bbd38"
	20	+ }
	21	+}