= Conductor-discriminant formula
{title2=$\mathfrak d_{L/K}=\prod_{\chi}\mathfrak f(\chi)$}
For a finite <abelian extension> of <number fields>, its <relative discriminant> <ideal> is the product of the finite conductor <ideals> of the characters of its <Galois group>, with the <trivial character> contributing one. In a multiquadratic extension of $\mathbb Q$, the nontrivial characters correspond to its quadratic subfields, and their conductors are the <absolute values> of the corresponding <fundamental discriminants>. This gives an efficient discriminant computation and can prove that a compositum is unramified over a quadratic subfield.
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