The density of elliptic curves having a global minimal Weierstrass equation

Bekyel, Ebru (2004) The density of elliptic curves having a global minimal Weierstrass equation. Journal of number theory, 109 (1). pp. 41-58. ISSN 0022-314X

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Official URL: http://dx.doi.org/10.1016/j.jnt.2004.06.003

Abstract

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.

Item Type:	Article
Uncontrolled Keywords:	elliptic curve; Weierstrass equation; zeta function
Subjects:	UNSPECIFIED
ID Code:	471
Deposited By:	Ebru Bekyel
Deposited On:	30 Dec 2004 02:00
Last Modified:	25 May 2011 14:23

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