๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Elliptic curves and their torsion subgroups over number fields of type (2, 2, ..., 2)

โœ Scribed by Derong Qiu; Xianke Zhang

Publisher
SP Science China Press
Year
2001
Tongue
English
Weight
492 KB
Volume
44
Category
Article
ISSN
1674-7283

No coin nor oath required. For personal study only.

๐Ÿ“œ SIMILAR VOLUMES

Torsion subgroups of elliptic curves in
Torsion subgroups of elliptic curves in elementary abelian 2-extensions of
โœ Yasutsugu Fujita ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 217 KB

Let E be an elliptic curve over Q and let F := Q({ โˆš m ; m โˆˆ Z}). Laska and Lorenz showed that there exist at most 31 possibilities for the type of the torsion subgroup E(F ) tors of E over F. In this paper, we showed that there exist exactly 20 possibilities for E(F ) tors .

Number of Points on the Projective Curve
Number of Points on the Projective Curves aYl=bXl+cZl and aY2l=bX2l+cZ2l Defined over Finite Fields, l an Odd Prime
โœ N. Anuradha; S.A. Katre ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 201 KB

The number of points on the curve aY e =bX e +c (abc{0) defined over a finite field F q , q#1 (mod e), is known to be obtainable in terms of Jacobi sums and cyclotomic numbers of order e with respect to this field. In this paper, we obtain explicitly the Jacobi sums and cyclotomic numbers of order e