On the Cyclicity of Elliptic Curves over Finite Field Extensions
✍ Scribed by S.G. Vlăduţ
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 124 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1071-5797
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
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.
On average, there are qP#o (qP) F qP -rational points on curves of genus g de"ned over F O P . This is also true if we restrict our average to genus g curves de"ned over F O , provided r is odd or r'2g. However, if r"2, 4, 6, 2 or 2g then the average is qP#qP#o(qP). We give a number of proofs of the
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
## Abstract In this paper we study the Newton polygon of the __L__ ‐polynomial __L__ (__t__) associate to the Picard curves __y__^3^ = __x__^4^ – 1, __y__^3^ = __x__^4^ – __x__ defined over a finite field 𝔽~__p__~ . In the former case we get a complete classification. In the latter case we obtai