On the Mertens Conjecture for Elliptic Curves over Finite Fields
  We introduce an analogue of the Mertens conjecture for elliptic curves over finite fields. Using a result of Waterhouse, we classify the isogeny classes of elliptic curves for which this conjecture holds in terms the size of the finite field and the trace of the Frobenius endomorphism acting on the curve. 
Peter Humphries
math.NT