In 2016, Balakrishnan, Ho, Kaplan, Spicer, Stein and Weigandt produced a database of elliptic
curves over
$\mathbb{Q}$
ordered by height in which they computed the rank, the size of the
$2$Selmer group,
and other arithmetic invariants. They observed that after a certain point, the average rank
seemed to decrease as the height increased. Here we consider the family of elliptic curves over
$\mathbb{Q}$ whose rational torsion
subgroup is isomorphic to
$\mathbb{Z}\u22152\mathbb{Z}\times \mathbb{Z}\u22158\mathbb{Z}$.
Conditional on GRH and BSD, we compute the rank of
$92\%$ of the
$202,\phantom{\rule{0.3em}{0ex}}461$ curves with parameter height
less than
$1{0}^{3}$. We also compute
the size of the
$2$Selmer
group and the Tamagawa product, and prove that their averages tend to infinity for
this family.
