The count of F(s,t) that are norms from such L has a specific order of magnitude derived via the fundamental lemma of sieve theory and geometry of numbers.
Lartaux, Sur le nombre d’idéaux dont la norme est la valeur d’une forme binaire de degré 3,The Quart
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Solubility for families of norm equations coming from abelian number fields
The count of F(s,t) that are norms from such L has a specific order of magnitude derived via the fundamental lemma of sieve theory and geometry of numbers.