Article contents
Arithmetic on certain families of elliptic curves
Published online by Cambridge University Press: 17 April 2009
Abstract
Consider a family of elliptic curves (A, A0, d0 fixed integers). We prove that, under certain conditions on A0 and d0, the rational torsion subgroup of E(B) is either cyclic of order ≤ 3 or non-cyclic of order 4. Also, assuming standard conjectures, we establish estimates for the order of the Tate-Shafarevich groups as B varies.
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 2000
References
REFERENCES
- 1
- Cited by