  Let p be a prime and K be a number field. Let rho_{E,p}:G_K \longrightarrow
Aut(T_p E)\cong GL_2(Z_p) be the Galois representation given by the Galois
action on the p-adic Tate module of an elliptic curve E over K. Serre showed
that the image of rho_{E,p} is open if E has no complex multiplication. For an
elliptic curve E over K whose j-invariant does not appear in an exceptional
finite set, we give an explicit uniform lower bound of the size of the image of
rho_{E,p}.
