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

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 |

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 |