Elliptic curves with everywhere good reduction

We consider the question of which quadratic fields have elliptic curves with everywhere good reduction. By revisiting work of Setzer, we expand on congruence conditions that determine the real and imaginary quadratic fields with elliptic curves of everywhere good reduction and rational j  -invariant. Using this, we determine the density of such real and imaginary quadratic fields. If R(X)R(X) denotes the number of real quadratic fields K=Q[m] such that |ΔK|