  Silverman and Stange defined the notion of an aliquot cycle of length $L$ for
a fixed elliptic curve $E/\mathbb{Q}$, and conjectured an order of magnitude
for the function that counts such aliquot cycles. We show that the conjectured
upper bound holds for the number of aliquot cycles on average over the family
of all elliptic curves with short bounds on the size of the parameters in the
family.
