For real quadratic fields, there is the bound $$h\leq \lfloor\sqrt{\Delta}/2\rfloor$$
Is there anything similar for imaginary quadratic fields? More generally, I'm interested in a bound for $h$ involving the discriminant of the number field.
For real quadratic fields, there is the bound $$h\leq \lfloor\sqrt{\Delta}/2\rfloor$$
Is there anything similar for imaginary quadratic fields? More generally, I'm interested in a bound for $h$ involving the discriminant of the number field.
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