The probability that the number of points on an elliptic curve over a finite field is prime

Authors
Galbraith, SD McKee, J
Citation
Sd. Galbraith et J. Mckee, The probability that the number of points on an elliptic curve over a finite field is prime, J LOND MATH, 62, 2000, pp. 671-684
Citations number
9
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
ISSN journal
00246107 → ACNP
Volume
62
Year of publication
2000
Part
3
Pages
671 - 684
Database
ISI
SICI code
0024-6107(200012)62:<671:TPTTNO>2.0.ZU;2-T
Abstract
The paper gives a formula for the probability that a randomly chosen ellipt ic curve over a finite field has a prime number of points. Two heuristic ar guments in support of the formula are given as well as experimental evidenc e. The paper also gives a formula for the probability thar a randomly chose n elliptic curve over a finite field has kq points where k is a small numbe r and q is a prime.