  This is an introduction to a probabilistic model for the arithmetic of
elliptic curves, a model developed in a series of articles of the author with
Bhargava, Kane, Lenstra, Park, Rains, Voight, and Wood. We discuss the
theoretical evidence for the model, and we make predictions about elliptic
curves based on corresponding theorems proved about the model. In particular,
the model suggests that all but finitely many elliptic curves over $\mathbb{Q}$
have rank $\le 21$, which would imply that the rank is uniformly bounded.
