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ON THE MERTENS CONJECTURE FOR ELLIPTIC CURVES OVER FINITE FIELDS
Published online by Cambridge University Press: 28 February 2013
Abstract
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.
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- ©2013 Australian Mathematical Publishing Association Inc.