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Almost prime values of the order of elliptic curves over finite fields

โœ Scribed by David, Chantal; Wu, Jie

Book ID
124159662
Publisher
Walter de Gruyter GmbH & Co. KG
Year
2012
Tongue
English
Weight
303 KB
Volume
24
Category
Article
ISSN
0933-7741

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Almost prime values of the order of elli
Almost prime values of the order of elliptic curves over finite fields
โœ David, Chantal; Wu, Jie ๐Ÿ“‚ Article ๐Ÿ“… 2012 ๐Ÿ› Walter de Gruyter GmbH & Co. KG ๐ŸŒ English โš– 303 KB

## Abstract. Let E $E$ be an elliptic curve over ${\mathbb {Q}}$ without complex multiplication. For each prime p $p$ of good reduction, let | E ( p ) | $|E({\mathbb {F}}\_p)|$ be the order of the group of points of the reduced curve over p ${\mathbb {F}}\_p$ . According to a co

Group Structure of Elliptic Curves over
Group Structure of Elliptic Curves over Finite Fields
โœ Christian Wittmann ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 123 KB

Let A be a finite abelian group such that there is an elliptic curve defined over a finite field F q with E(F q )$A. We will determine the possible group structures E(F q k) as E varies over all elliptic curves defined over F q with E(F q )$A.