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Mathematics of Computation

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Class groups of the quadratic fields found by F. Diaz y Diaz

Author: Daniel Shanks
Journal: Math. Comp. 30 (1976), 173-178
MSC: Primary 12A25; Secondary 12A50
Corrigendum: Math. Comp. 30 (1976), 900.
Corrigendum: Math. Comp. 30 (1976), 900.
MathSciNet review: 0399039
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Abstract: 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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Article copyright: © Copyright 1976 American Mathematical Society