Open in CoCalc 310716 Elliptic Curves of Prime Conductor

310716 Elliptic Curves of Prime Conductor

Armand Brumer and Oisin McGuinness


This Web site presents the 310,716 elliptic curves of prime conductor less than 108 found during computations performed at Fordham University during 1989 and 1990. Some additional materials are also given.

The aim of the calculations was to explore the rank distribution of elliptic curves; those of prime conductor were chosen both because of their own interest, and because various computations are simpler for such curves.

The most interesting results of these calculations were published in our paper "The Behavior of the Mordell-Weil Group of Elliptic Curves", and were described in talks given during 1990 and 1991 at MSRI by Brumer, and at Brown University, Columbia University, CUNY Graduate Center, and Rutgers University by McGuinness. (See Slides for the slides used for some of these talks.)

See here for a summary of the results.

The page Curves contains an overview of the curves found, including links to files available for downloading.

The notations and conventions we use are explained here.

Links to related published and unpublished material are here.

Comments and questions may be addressed to either Armand Brumer, or Oisin McGuinness.

The significant delay in making the curves readily available is the responsibility of the second author alone!

The Behavior of the Mordell-Weil Group of Elliptic Curves

This paper was published in the Bulletin (New Series) of the American Mathematical Society, Volume 23, Number 2, October 1990, pages 375--382. (Math Reviews: MR 91b:11076; Zentralblatt: ZBL741.14010.)

An AMSTeX version is available here, with a DVI version here.

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We expect that this will be an evolving Web site, as we make more material available. Any significant changes will be described here. Bookmark this page!

Page created on a Macintosh Performa 6205CD, using MPW, MacPerl, and OzTeX, Sun Apr 18 23:51:16 1999.