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The Probability that the Number of Points on an Elliptic Curve over a Finite Field is Prime
- Source :
- Journal of the London Mathematical Society. 62:671-684
- Publication Year :
- 2000
- Publisher :
- Wiley, 2000.
-
Abstract
- The paper gives a formula for the probability that a randomly chosen elliptic curve over a finite field 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 finite field has kq points where k is a small number and q is a prime.
Details
- ISSN :
- 00246107
- Volume :
- 62
- Database :
- OpenAIRE
- Journal :
- Journal of the London Mathematical Society
- Accession number :
- edsair.doi...........1ecc3c18747e69558c0359026bf58b08