John Cremona on Thu, 18 Feb 2016 11:12:30 +0100

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Re: New elldata package update (conductor up to 380000)

Thanks, Bill for including this.  I am not sure how far this will go,
very likely not past 400000 without some new techniques.

One thing I should stress is that though the curves themselves are
found by independent C++ programs, the generators for many of the rank
1 curves (including all the large generators) are found using pari's
ellheegner function written by Bill, which is very impressive indeed.
There are now 36 rank1 curves whose generator has (logarithmic!)
height over 1000, the record being 3313.96 for 287560p1.


On 15 February 2016 at 10:17, Bill Allombert
<> wrote:
> Dear PARI users,
> John Cremona has extended his Elliptic Curve Data to all conductors < 380000
> <>
> I have updated the PARI package elldata to match.
> This package contains elliptic curves defined over the rationals representing
> all isogeny classes for all conductor at most 380000. Theses data are needed by
> ellsearch, ellidentify and ellgenerators and require PARI/GP 2.2.11 and up.
> The package can be downloaded from
> <>
> Thanks to John for providing this very useful database.
> At this point the package is a bit large, we might want to provide a smaller
> version for conductors <=100000 (or <=200000).
> If diskspace is an issue, you can compress all the elldata/ell*
> files using gzip, GP is able to read gziped files.
> Cheers,
> Bill.