Index of Curve Files

The table contains links to the files containing the curves we found, and a summary of information about the curves in that file. We give the smallest and largest conductor in each file, the number of curves of each rank, the total number of even and odd rank curves, and the number of curves of each discriminant sign, and the total number of curves in each file. Each file (except for the last in each family) contains 7000 curves; this was a choice made for convenience, as it was a size which made the resulting files fit nicely on a Macintosh double-density floppy diskette, which was our simplest method of backup and transport during the computations. The total size of the curve files is about 29 Megabytes; each of the larger files is about 650 Kbytes.

The curve files are listed by "family", where, for example, "021" means a₁=0, a₂=-1, a₃=1; see Notations and conventions for more details. Within each file, the curves are listed by increasing size of conductor; there is no particular order among the curves of the same conductor, for example, no attempt was or has been made to correlate with the order used by John Cremona in his lists of curves of conductors up to 1000 and up to 5077.

There are 49 files listed; 8 each from the 001, 011, and 021 families; 4 each from the 100, 101, 110, 111, 120 and 121 families; and 1 other file, "curvesbig" with some assorted curves. (These extra curves were found by the same search program which generated all the other curves, but were found at a later date from the rest; they were not incorporated into the other files.) The total number of curves in these files is 310,716. Some other curves, which satisfy |a₆| > 2³¹-1, see curveshuge, were not included in the processing. Note that the first curve in this file is the curve of conductor 38593 described at the end of section 4 of "The Behavior of the Mordell-Weil Group of Elliptic Curves".

If you want to use these files in a program, parsing the format should be easy in most languages. The format was designed for ease of use in Maple: simply prepend the file with a line: CurveList := [, and postpend with a line: ]:, and then the file can be read into Maple, with CurveList becoming a Maple list of lists.