Tables of ideal class groups of real quadratic fields
The authors gave a table of the ideal class groups of imaginary quadratic fields \({\mathbb{Q}}(\sqrt{-m})\), \(m<100,000\) [(*) the authors, Sophia Kokyuroku Math. 28 (Tokyo 1988; Zbl 0629.12003)], and H. Wada gave a table of the ideal class numbers (and the sign of the norm of the principal unit) of real quadratic fields \({\mathbb{Q}}(\sqrt{m})\), \(m<100,000\) [(**) \textit{H. Wada}, Sophia Kokyuroku Math. 10 (Tokyo 1981; Zbl 0536.12001)]. By the methods of (*) the authors now give a list of the class groups (in the narrow and in the wide sense) for all these real fields of (**). By genus theory the 2-rank of these groups is known. It is astonishing that there are few class groups which are not cyclic (for \(t\leq 2)\) or of the form (as abelian group) (2a,2,...,2) (for \(t>2)\) (where t is the number of ramified primes in \({\mathbb{Q}}(\sqrt{m}))\), and therefore these tables cover only two pages.
scientific article; zbMATH DE number 4097508