The Number of Points on an Elliptic Cubic Curve over a Finite Field
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چکیده
منابع مشابه
On the Exponent of the Group of Points of an Elliptic Curve over a Finite Field
We present a lower bound for the exponent of the group of rational points of an elliptic curve over a finite field. Earlier results considered finite fields Fqm where either q is fixed or m = 1 and q is prime. Here, we let both q and m vary; our estimate is explicit and does not depend on the elliptic curve.
متن کاملOn the Exponents of the Group of Points of an Elliptic Curve over a Finite Field
We present a lower bound for the exponent of the group of rational points of an elliptic curve over a finite field. Earlier results considered finite fields Fqm where either q is fixed or m = 1 and q is prime. Here we let both q and m vary and our estimate is explicit and does not depend on the elliptic curve.
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The paper gives a formula for the probability that a randomly chosen elliptic curve over a nite eld has a prime number of points. Two heuristic arguments in support of the formula are given as well as experimental evidence. The paper also gives a formula for the probability that a randomly chosen elliptic curve over a nite eld has kq points where k is a small number and where q is a prime. 1. I...
متن کاملThe fluctuations in the number of points on a hyperelliptic curve over a finite field
Article history: Received 4 May 2008 Revised 26 August 2008 Available online 21 October 2008 Communicated by J. Brian Conrey The number of points on a hyperelliptic curve over a field of q elements may be expressed as q + 1 + S where S is a certain character sum. We study fluctuations of S as the curve varies over a large family of hyperelliptic curves of genus g. For fixed genus and growing q,...
متن کاملAround Sziklai's conjecture on the number of points of a plane curve over a finite field
Article history: Received 14 July 2008 Revised 9 February 2009 Available online 10 March 2009 Communicated by Neal Koblitz
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1980
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(80)80033-3