The Elliptic Curve Database for Conductors to 130000

Abstract. Tabulating elliptic curves has been carried out since the earliest days of machine computation in number theory. After some historical remarks, we report on significant recent progress in enlarging the database of elliptic curves defined over Q to include all those of conductor N 130000. We also give various statistics, summarize the data, describe how it may be obtained and used, and mention some recent work regarding the verification of Manin's "c = 1" conjecture. 1 Background and history Tabulating elliptic curves has been carried out since the earliest days of machine computation in number theory. In this article we concentrate on tables which claim to contain complete lists of elliptic curves with conductors in certain ranges. Other tables exist, notably tables of curves with prime conductor by Brumer and McGuinness [4] and, more recently, by Stein and Watkins [21]. We first review the tables existing before 1990, and then describe the tables we have comp...

• Type: Conference
• Year: 2006
• Where: ANTS
• Authors: John Cremona
• Keywords: Algorithms, ANTS 2006, Elliptic Curves, Machine Computation, Number Theory