Sharedwww / oisin / Curves.htmlOpen in CoCalc
Author: William A. Stein
Index of Curve Files

# Index of Curve Files

### Armand Brumer and Oisin McGuinness

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.

File StartEnd r=0r=1r=2r=3r=4r=5 EvenOdd Delta > 0Delta < 0 Number
001_1377444027 213132151355288110 34973503258344177000
001_2744726718224243 217132121320281160 35073493252344777000
001_31822834730905821 221231811305280211 35383462253544657000
001_43090610744997859 218131931341268170 35393461258544157000
001_54499886760345739 214032171338287180 34963504255944417000
001_66034892376229821 219532481260275202 34753525251644847000
001_77623089993178693 217631611344292261 35463454256644347000
001_89318243799995059 820124452711270 1354135697017402710
011_1197317659 192932291505319180 34523548256844327000
011_2731779718231547 200731971467309200 34943506258044207000
011_31823234930960803 198432021461320330 34783522257944217000
011_43096193944916083 195031641523330330 35063494261143897000
011_54491662960205459 207131931411292330 35153485255144497000
011_66021424376182091 200832001456307281 34923508264743537000
011_77618225192873779 203331711421342330 34873513255844427000
011_89288306799998891 839128757711990 14251406102918022831
021_1117413851 223133501249160100 34903510254244587000
021_2741474118450701 221433221249204110 34743526249045107000
021_31845219731193363 223332711277208110 35213479257344277000
021_43119434145351877 222232611313182220 35573443255744437000
021_54535385160483811 220832821281212170 35063494254844527000
021_66048454776653539 221432761255239160 34853515259444067000
021_77665421993629563 218433431245216120 34413559258544157000
021_89363124399999323 77711914468180 1231127294915542503
100_16118255343 159929761930469260 35553445254244587000
100_21825694345060227 164930191827465400 35163484254244587000
100_34507128176139519 158230671810489520 34443556259344077000
100_47614034999997543 109921011253336330 23852437175830644822
101_123318476179 23043300127911610 35843416260343977000
101_21848040145727007 22463300130814510 35553445254744537000
101_34572933177503003 22183352123319430 34543546254744537000
101_47750303999996131 144921648349700 22832261161229324544
110_18918425983 2430344210359300 34653535254344577000
110_21842631345966709 24343393105811320 34943506256544357000
110_34596707377651317 23563438109111410 34483552258044207000
110_47765174199997571 147121496967500 21672224161727744391
111_17918471559 188932191578300140 34813519259444067000
111_21847545945617113 195831201578324200 35563444254744537000
111_34561828976680059 197831091577315210 35763424251544857000
111_47668799399991981 122221331032242190 22732375165129974648
120_17318249191 23893391110411510 34943506258044207000
120_21824929945241037 23943354114510700 35393461255344477000
120_34524334376655753 24023348111013910 35133487250244987000
120_47665712399994553 1600224678410230 23872348169430414735
121_11718195409 181530271710422260 35513449262343777000
121_21819564344840681 178430781684428260 34943506246945317000
121_34484471375796309 182631001616429290 34713529260943917000
121_47579836199999827 121921641158294350 24122458173831324870
big4121399880579 8965921591500 105560710476151662
Total1199999827 9333914319261515118618045 155658155058113969196747310716

Page created on a Macintosh Performa 6205CD, using MPW, MacPerl, and OzTeX, Sun Apr 18 23:51:24 1999.