I came across the following line and was wondering what it meant exactly and how you go about showing it. Let d be a fundamental discriminant. Let P(d) = the divisors of d except for the largest.

The cardinality of P(d) is at most the 2-adic valuation of the h (the class number).

I only have a vague notation of what is meant by the 2-adic valuation, so any clarification on that as well as how to prove the statement would be helpful. Thank you.

genus theoryand the point is that it predictably tells you information about the quotient group C/C^2, where C is the class group of a quadratic field. – KConrad Jul 15 '10 at 9:13