The density of elliptic curves having a global minimal Weierstrass equation

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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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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
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Ebru Bekyel
Date Deposited: 30 Dec 2004 02:00
Last Modified: 22 Oct 2019 15:12
URI: https://research.sabanciuniv.edu/id/eprint/471

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