Primality of the number of points on an elliptic curve over a finite field
نویسندگان
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...
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Article history: Received 14 July 2008 Revised 9 February 2009 Available online 10 March 2009 Communicated by Neal Koblitz
متن کاملSziklai's conjecture on the number of points of a plane curve over a finite field III
In the paper [11], Sziklai posed a conjecture on the number of points of a plane curve over a finite field. Let C be a plane curve of degree d over Fq without an Fq-linear component. Then he conjectured that the number of Fq-points Nq(C) of C would be at most (d− 1)q+1. But he had overlooked the known example of a curve of degree 4 over F4 with 14 points ([10], [1]). So we must modify this conj...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1988
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1988.131.157