Article contents
Descent Calculations for the Elliptic Curves of Conductor 11
Published online by Cambridge University Press: 09 June 2003
Abstract
Let $A$ be any one of the three elliptic curves over $\mathbb{Q}$ with conductor 11. We show that $A$ has Mordell–Weil rank zero over its field of 5-division points. In each case we also compute the 5-primary part of the Tate–Shafarevich group. Our calculations make use of the Galois equivariance of the Cassels–Tate pairing.
Keywords
- Type
- Research Article
- Information
- Copyright
- 2003 London Mathematical Society
- 3
- Cited by