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Primality of the
number of points on an elliptic curve over a finite field
Neal I. Koblitz |
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Vol. 131 (1988), No. 1, 157–165
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Abstract |
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Given a fixed elliptic curve E defined over Q having no rational torsion points, we discuss the probability that the number of points on E mod p is prime as the prime p varies. We give conjectural asymptotic formulas for the number of p ≤ n for which this number is prime, both in the case of a complex multiplication and a non-CM curve E. Numerical evidence is given supporting these formulas. |
Mathematical Subject Classification 2000
Primary: 11G05
Secondary: 11Y40, 14G15
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Milestones
Received: 21 August 1986
Revised: 9 April 1987
Published: 1 January 1988
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Authors |
| Neal I. Koblitz | |
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