  In a recent paper, Rosen and Silverman showed that Tate's conjecture on the
order of vanishing of L(E,s) implies Nagao's formula, which gives the rank of
an elliptic surface in terms of a weighted average of fibral Frobenius trace
values. The aim of this article is to extend their result to the case of
elliptic threefolds, and deduce, from Tate's conjecture, a Nagao-type formula
for the rank of an elliptic threefold E. This will require a two-pronged
approach: on the one hand, we need some cohomological results in order to
derive a Shioda-Tate-like formula for elliptic threefolds; on the other, we
compute an "average" number of rational points on the singular fibers and
relate this to the action of Galois on those fibers.
