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
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.
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