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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Class groups of the quadratic fields found by F. Diaz y Diaz
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by Daniel Shanks PDF
Math. Comp. 30 (1976), 173-178 Request permission


F. Diaz y Diaz has discovered 99 discriminants d between $- 3321607$ and $- 60638515$ inclusive for which $Q(\sqrt d )$ have a 3-rank ${r_3} = 3$. These 99 imaginary quadratic fields are analyzed here and the class groups are given and discussed for all those of special interest. In 98 cases, the associated real quadratic fields have ${r_3} = 2$, but for $d = 44806173 = 3 \cdot 14935391,Q(\sqrt d )$ has a class group $C(3) \times C(3) \times C(3)$; and this is now the smallest known d for which a real quadratic field has ${r_3} = 3$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 173-178
  • MSC: Primary 12A25; Secondary 12A50
  • DOI:
  • MathSciNet review: 0399039