Citation
Dr. Qiu et Xk. Zhang, Selmer groups and Mordell-Weil groups of two types of elliptic curves, PROG NAT SC, 10(12), 2000, pp. 946-949
Citations number
9
Categorie Soggetti
Multidisciplinary
Journal title
PROGRESS IN NATURAL SCIENCE
ISSN journal
10020071
→ ACNP
Volume
10
Issue
12
Year of publication
2000
Pages
946 - 949
Database
ISI
SICI code
1002-0071(200012)10:12<946:SGAMGO>2.0.ZU;2-P
Abstract
Let E: gamma (2) = x(x +/- p)(x +/- q) he two types of elliptic curves, whe
re p and q are twin prime numbers. The Selmer groups, the sum of rank(E) an
d F-2-dimension of Shafarevich-Tate group (2-torsion subgroup) of E are det
ermined, and the Mordell-Weil group and Shafarevich-Tate group of E are exh
ibited explicitly in many cases. Besides, the Kodaira symbol and the torsio
n parts of E are also obtained.