On determining the quadratic subfields of Z 2 -extensions of complex quadratic fields
Compositio Mathematica, Tome 30 (1975) no. 3, pp. 259-271. 
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     author = {Carroll, Joseph E.},
     title = {On determining the quadratic subfields of $Z_2$-extensions of complex quadratic fields},
     journal = {Compositio Mathematica},
     pages = {259--271},
     publisher = {Noordhoff International Publishing},
     volume = {30},
     number = {3},
     year = {1975},
     mrnumber = {374082},
     zbl = {0314.12005},
     language = {en},
     url = {http://www.numdam.org/item/CM_1975__30_3_259_0/}
}
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Carroll, Joseph E. On determining the quadratic subfields of $Z_2$-extensions of complex quadratic fields. Compositio Mathematica, Tome 30 (1975) no. 3, pp. 259-271. http://www.numdam.org/item/CM_1975__30_3_259_0/

[1] Edward A. Bender: A Lifting Formula for the Hilbert Symbol. Proc. Am. Math. Soc., Vol. 40. No. 1, Sept. 1973. | MR | Zbl

[2] J.W.S. Cassels and A. Fröhlich: Algebraic Number Theory, Thompson Book Company, 1967.

[3] Helmut Hasse: Zahlentheorie, Akademie-Verlag, 1949. | MR | Zbl

[4] Jean-Pierre Serre: Classes Des Corps Cyclotomic, Seminairé Bourbaki, Dec. 1958. | Numdam | Zbl

[5] Jean-Pierre Serre: Corps Locaux, Hermann, 1962. | MR | Zbl