  We generalize a construction of families of moderate rank elliptic curves
over $\mathbb{Q}$ to number fields $K/\mathbb{Q}$. The construction, originally
due to Steven J. Miller, \'Alvaro Lozano-Robledo and Scott Arms, invokes a
theorem of Rosen and Silverman to show that computing the rank of these curves
can be done by controlling the average of the traces of Frobenius, the
construction for number fields proceeds in essentially the same way. One
novelty of this method is that we can construct families of moderate rank
without having to explicitly determine points and calculating determinants of
height matrices.
