  Let p be a prime number and M a quadratic number field, M not equal to
Q(\sqrt{p}) if p is congruent to 1 modulo 4. We will prove that for any
positive integer d there exists a Galois extension F/Q with Galois group D_{2p}
and an elliptic curve E/Q such that F contains M and the p-Selmer group of E/F
has size at least p^d.
