Primality of the number of points on an elliptic curve over a finite field (Q1086273)
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scientific article; zbMATH DE number 3983257
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Primality of the number of points on an elliptic curve over a finite field |
scientific article; zbMATH DE number 3983257 |
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Primality of the number of points on an elliptic curve over a finite field (English)
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1988
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Given a fixed elliptic curve \(E\) defined over \(\mathbb Q\) and 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 \(p\leq n\) 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.
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primality
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finite field
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computational number theory
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elliptic curve
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asymptotic formulas
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complex multiplication
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non-CM curve
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