Last major update: 02/03/2012 Last minor update: 20/04/2012 20/04/12* Remade allisog.* files for 0-12 to have the correct order and numbering of curves in a class, and filled matrices. 13/04/12 * Added optimal.* files giving data about optimality and the Manin constant, together with a new section in the INDEX page. * Added subsection on modular degrees for all curves in INDEX. 11/04/12 * Switched 190096b1/2 as old b2 was optimal. + 48 more such switches in range 130k-230k. 07/04/12 * Added alldegphi.* files giving the modular degrees for all curves 02/04/12 * Fixed spacing in allcurves.9* and allcurves.12* * Added alllabels.* files giving the map from Cremona labels to LMFDB labels 27/03/12 * Changed all allgens files for non-cyclic torsion groups so that the torsion generator orders match the group invariants. 02/03/12 * Added all data for 220000-229999 30/01/12 * Replaced corrupt paricurves.130000-139999 13/01/12 * Added all data for 210000-219999 01/12/11 * Corrected paricurves.180000-189999 (186120bk2 was wrong) 21/11/11 * Added all data for 200000-209999 26/10/11 * Added all data for 190000-199999 15/09/11 * Added all data for 180000-189999 * Corrected allbsd data for 130725bc and 135346c (thanks to R Andrew Ohana) 09/08/11 * Added all data for 170000-179999 26/07/11 * Added all data for 160000-169999 08/07/11 * Added all data for 150000-159999 28/06/11 * Added all data for 140000-149999 * corrected count.130000-139999 (N=135045 had 0 not 6) 21/04/11 * Updated intpts.130000-139999 (data for 130416 was garbled), thanks to Geoff bailey. 15/04/11 * Updated allgens.n0000-n9999 for n in 0..12 to include torsion generators and rank 0 curves. Updated INDEX to reflect this. 12/04/11 * Corrected paricurves.130000-139999 (deleted extraneous Pythonic Ls) * Corrected L''(1) and |Sha| for 135014r1 08/04/11 * Added all data for 130000-139999 * Changed allgens format to include torsion (so there is one line in allgens* for each line in allcurves*). NB I have not yet recreated the allgens files for N<130000. 05/01/07 * Corrected aplist file entries for bad primes over 100, for N divisible by more than one such prime (or by the square of such a prime). Files affected: aplist.* (except aplist.00000-09999) 15/12/06 * Corrected Sha(51522f3) from 4 to 9 (thanks to Tom Fisher) Files affected: allbigsha.[05]0000-*, allbsd.50000*, shas.html 24/09/06 * Conductors divisible by 216 between 90000 and 99999 were missing, now included. All files *.90000-99999 affected. 04/09/06 * Saturation of given generators now proved for all curves! 04/09/06 * Corrected generators for 26 curves (52266d1, 124132a1 and 24 of conductor 122010) which were unsaturated. Files affected are allgens.{5,12}*, paricurves.{5,12}* but NOT the allbsd or allbigsha files which are unchanged (they already had the correct regulators). 13/07/06 * Corrected 20 entries in allisog.[0-7]* (curves incorrectly shown as self-isogenous), thanks to Tom Boothby 17/02/06 * Corrected files degphi.1[012]0000-1[012]9999 (wrong codes) 16/02/06 * Corrected files count.40000-49999 and count.60000-69999. 20/11/05 * Updated optimality claims to cover all N<50000 07/11/05 * Minor corrections to {allbsd,allgens,paricurves}.120000-129999 05/11/05 * Added all data for 120000-129999 01/11/05 * Minor corrections to allbigsha* and shas.html 20/09/05 * Minor corrections to files degphi.1[01]0000-1[01]9999, allbsd.[69]*, allgens.9*, allbigsha.9*, shas.html 18/09/05 * Added all data for 100000-119999 * allgens files now use new letter codes 02/09/05 * Changed all isogeny class codes to new simplified base-26 scheme: a,b,...,z,ba,bb,...,bz,ca,... 31/08/05 * Added all data for 90000-99999 26/08/05 * Added all data for 80000-89999 14/07/05 * Added all data for 70000-79999 * Deleted trailing field " ***!!!***" from allbsd.* for curves where field 11 (=analytic Sha) >1 * Added allisog* files ("Table 6") giving isogeny matrix for each class * Removed curves.* and gens.*, as they are subsets of the allcurves.* and allgens.* files 20/06/05 * Added all data for 60000-69999. 09/06/05 * Added all data for 50000-59999. * renamed files e.g. curves.00000-09999 etc; no changes to content since no elliptic curves have conductor divisible by 1000. 27/05/05 * Added all data for 40001-50000. 05/05/05 * corrected generators for 14 curves in range 30001-40000 which were not saturated, with consequent corrections to allgens.30001-40000, allbsd.30001-40000, allbigsha.30001-40000 and shas table. (None of these were optimal curves so gens.* unchanged) 03/5/05 * corrections to files allgens.30001-40000 gens.20001-30000 allgens.20001-30000 gens.30001-40000 allbsd.00001-10000 allgens.00001-10000 thanks to Geoff Bailey. (Some duplications, and some wrong numbering of curves in an isogeny class). 26/4/05 * added curve 25350III2 which had been missed 22/4/05: * added data for range 30001-40000 (thanks to Nottingham's multiprocessor GRID) * resorted files into uniform ranges of 10000 * only include gzip-ed files 1/3/05: added data for N=15299 (one curve) previously omitted 9/2/05: added data for range 25001-30000 + certification of optimal curves extended from 8000 to 11000 (extended to 12000 on 13/02/05). Swapped the two curves in classes 15180,15624,15744 as the conditionally optimal one was second not first. 21/6/04: added data for range 20001-25000 + certification of generators for all curves so far 9/3/04: corrections for 15810U3 -- previous generator was 3*generator; so |Sha|=9 not 1. 4/4/03: added data for range 17001-20000. 12/2/03: added data for range 16001-17000. 17/1/03: added data for range 15001-16000. 25/10/02: corrected torsion order for 4830N4 in allcurves.1-8000 mention 2 new curves of rank 3 in INDEX file 8/10/02: Added data for the range 12001-15000, with the same status as for the range 8001-12000 detailed below (except that Mark Watkins has not -- yet -- covered this range). [He has now: 25/10/02.] 14/1/02: Curves in classes 8160R, 8585C, 11024B reordered. For these levels the first curve in each class is guaranteed Gamma_0(N)-optimal. For other levels up to 12000 where there is no guarantee, our first curve is the one which has been /conditionally/ proved optimal by Mark Watkins. It is now the case that for all levels in the range 8001-12000 the first curve in each class is either proved optimal, or at least agrees with Mark Watkins's conditional list of optimal curves. The former holds whenever the degree of the modular parametrization is given in the curves file. 12/12/01: for around 10% of classes in the range 8201-9000 the ordering has been changed. In the new order the first curve in each class is more likely (though not guaranteed) to be optimal. This change makes this range compatible with the range 9001-12000 in that the same strategy is used throughout for finding a curve from each newform. November 2001: The tables are extended to level (conductor) 12000. For levels up to 8000 fuller data exists, including determination of the optimal curve in each isogeny class and the degree of the modular parametrization. The numbering of the curves in each class (with the optimal curve #1, except for class 990H) may be taken as canonical and standard in this range. For levels 8001-12000 we give all curves in each isogeny class, but the first curve is not known to be optimal (unless the class only contains one curve, of course). The numbering of the curves in each class containing more than one curve should NOT be taken as canonical and standard: it will change if the optimal curve turns out to be not the currently labelled first curve. It is likely (based on past observation) that, where the first curve in a class is not optimal, it is related to the optimal curve by a 2-isogeny. In the range 8001-12000 we also do not have the modular degree (in most cases). For any individual level in the range 8001-12000, it is possible to carry out the extra computations needed to fill these gaps (determining the optimal curve and modular degree), but doing so for all curves in the range would probably take a few months with the current algorithms and programs. An independent computation by Mark Watkins has determined, conditionally on the Stevens conjecture, which curve in each class is optimal, and has determined its modular degree. Our results agree for all levels up to 8000 and we expect them to agree in the higher range also. 17/9/01: Error corrected: added 5104B1 to files, omitted due to an error discovered while working on 2*5104=10208. Further checking has shown that no further omissions were made at around the same time. (for previous update messages see the files sept2001 etc.)