Unit-generated quadratic orders have class numbers asymptotically equivalent to log(|Δ|/2), implying only finitely many with class number 1 or 2-torsion class groups, all of which are classified or listed.
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Unit-generated orders of real quadratic fields I. Class number bounds
Unit-generated quadratic orders have class numbers asymptotically equivalent to log(|Δ|/2), implying only finitely many with class number 1 or 2-torsion class groups, all of which are classified or listed.