Determination of all imaginary cyclic quartic fields with class number 2

Determination of all imaginary cyclic quartic fields with class number $2$
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by Kenneth Hardy, Richard H. Hudson, David Richman and Kenneth S. Williams PDF

Trans. Amer. Math. Soc. 311 (1989), 1-55 Request permission

It is proved that there are exactly $8$ imaginary cyclic quartic fields with class number $2$.

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