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Mathematics of Computation

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



Class groups of quadratic fields. II

Author: Duncan A. Buell
Journal: Math. Comp. 48 (1987), 85-93
MSC: Primary 11R29; Secondary 11R11, 11Y40
MathSciNet review: 866100
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Abstract: A computation has been made of the noncyclic class groups of imaginary quadratic fields $ Q(\sqrt { - D} )$ for even and odd discriminants $ - D$ from 0 to $ - 25000000$. Among the results are that 95% of the class groups are cyclic, and that $ - 11203620$ and $ - 18397407$ are the first discriminants of imaginary quadratic fields for which the class group has rank three in the 5-Sylow subgroup. The latter was known to be of rank three; this computation demonstrates that it is the first odd discriminant of 5-rank three or more.

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Article copyright: © Copyright 1987 American Mathematical Society