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
SK1 of Affine Curves over Finite Fields
β Scribed by Andrew Nestler
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 62 KB
- Volume
- 225
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
β¦ Synopsis
We show that SK 1 X = 0 for every affine curve X over a finite field.
π SIMILAR VOLUMES
In this paper we introduce a definition for L-functions associated to an Abelian covering of algebraic curves with singularities. The main result is a proof that this definition is compatible with the definition of the zeta function of a singular curve.
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.
In [11], a new bound for the number of points on an algebraic curve over a "nite "eld of odd order was obtained, and applied to improve previous bounds on the size of a complete arc not contained in a conic. Here, a similar approach is used to show that a complete arc in a plane of even order q has