Relative imaginary quadratic fields of class number 1 or 2

Goldstein, Larry Joel

doi:10.1090/S0002-9947-1972-0291124-8

Relative imaginary quadratic fields of class number $1$ or $2$
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Trans. Amer. Math. Soc. 165 (1972), 353-364 Request permission

Abstract:

Let K be a normal totally real algebraic number field. It is shown how to effectively classify all totally imaginary quadratic extensions of class number 1. Let K be a real quadratic field of class number 1, whose fundamental unit has norm $- 1$. Then it is shown how to effectively classify all totally imaginary quadratic extensions of class number 2.

References

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On the imaginary quadratic corpora of class number one

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