  In this note, we prove a finiteness result for fibers that are canonical
lifts in a given elliptic fibration. The question was motivated by the authors'
construction of an arithmetic Euler top, and it highlights an interesting
discrepancy between the arithmetic and the classical case: in the former, it is
impossible to extend the flows to a compactification of the phase space, viewed
as an elliptic fibration over the space of action variables.
