The density of elliptic curves having a global minimal Weierstrass equation

[摘要] We show that a positive density of elliptic curves over a number field counted using their short Weierstrass equations belong to a given Weierstrass class and in particular, a positive density of elliptic curves have a global minimal Weierstrass equation. The density is given by a ratio of partial zeta functions of the number field K evaluated at 10 with some extra factors for the bad primes. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-11-01

[关键词] elliptic curve;Weierstrass equation;zeta function