Editing Quadratic field (section)

===Other cyclotomic fields===
If one takes the other cyclotomic fields, they have Galois groups with extra <math>2</math>-torsion, so contain at least three quadratic fields.  In general a quadratic field of field discriminant <math>D</math> can be obtained as a subfield of a cyclotomic field of <math>D</math>-th roots of unity.  This expresses the fact that the [[Conductor (class field theory)|conductor]] of a quadratic field is the absolute value of its discriminant, a special case of the [[conductor-discriminant formula]].