On the class number divisibility of pairs of quadratic fields obtained from points on elliptic curves

抄録

Let l be the prime 3,5 or 7 and let m be a nonzero integer. We give a method for constructing an infinite family of pairs of quadratic fields ℚ(√D) and ℚ(√(mD)) with both class numbers divisible by l. Such quadratic fields are parametrized by rational points on a specified elliptic curve.