A remark on Honda's conjecture
by
Jung-Jo Lee
Queen's University
Coauthors: Ram Murty

Let the quadratic twist, denoted E_D, of an elliptic curve E : y²=x³+ax+b with a, b in Q be given by

Dy2=x3+ax+b.

In 1960, Honda conjectured that the Mordell-Weil ranks of any quadratic twists of a fixed elliptic curve over Q is universally bounded.

The purpose of this talk is to discuss some heuristic arguments in favor of Honda's conjecture. In particular, we will show that a hypothesis which is weaker than Honda's conjecture implies the conjecture itself, hence providing a reason supporting it.

Date received: January 21, 2004