  Silverman and Stange define the notion of an aliquot cycle of length L for a
fixed elliptic curve E defined over the rational numbers, and conjecture an
order of magnitude for the function which counts such aliquot cycles. In the
present note, we combine heuristics of Lang-Trotter with those of Koblitz to
refine their conjecture to a precise asymptotic formula by specifying the
appropriate constant. We give a criterion for positivity of the conjectural
constant, as well as some numerical evidence for our conjecture.
