%0 Journal Article %@ 1755-1633 %A HUMPHRIES, PETER %D 2014 %F discovery:1569443 %J Bulletin of the Australian Mathematical Society %N 01 %P 19-32 %T On the Mertens Conjecture for Elliptic Curves Over Finite Fields %U https://discovery.ucl.ac.uk/id/eprint/1569443/ %V 89 %X 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 of the size of the finite field and the trace of the Frobenius endomorphism acting on the curve. %Z This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.