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Mathematics of Computation

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



Class groups of complex quadratic fields

Author: R. J. Schoof
Journal: Math. Comp. 41 (1983), 295-302
MSC: Primary 12A25; Secondary 12-04, 12A50, 14K07
MathSciNet review: 701640
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Abstract: We present 75 new examples of complex quadratic fields that have 5-rank of their class groups $\geqslant 3$. Only one of these fields has 5-rank of its class group $> 3$: The field ${\mathbf {Q}}(\sqrt { - 258559351511807} )$ has a class group isomorphic to \[ C(5) \times C(5) \times C(5) \times C(5) \times C(2) \times C(11828).\] The fields were obtained by applying ideas of J. F. Mestre to the 5-isogeny ${X_1}(11) \to {X_0}(11)$.

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Article copyright: © Copyright 1983 American Mathematical Society