We show that every elliptic curve over a finite field of odd characteristic whose number of rational points is divisible by 4 is isogenous to an elliptic curve in Legendre form, with the sole exception of a minimal respectively maximal elliptic curve. We also collect some results concerning the supe
Group Structure of Elliptic Curves over Finite Fields
โ Scribed by Christian Wittmann
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 123 KB
- Volume
- 88
- Category
- Article
- ISSN
- 0022-314X
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โฆ Synopsis
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.
๐ SIMILAR VOLUMES
We show that SK 1 X = 0 for every affine curve X over a finite field.
Using Drinfeld modular curves we determine the places of supersingular reduction of elliptic curves over F 2 r( T) with certain conductors. This enables us to classify and describe explicitly all elliptic curves over F 2 r( T ) having a conductor of degree 4. Our results also imply that extremal ell