John Cremona on Wed, 30 May 2012 13:04:47 +0200

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Fwd: ellgenerators

I meant my reply to go to the list, but it only went to Max.

---------- Forwarded message ----------
From: John Cremona <>
Date: 30 May 2012 11:57
Subject: Re: ellgenerators
To: Max Alekseyev <>

Sage incorprates my library eclib which includes  a 2-descent
implementation in C++) as used in my programme mwrank.  pari does not.

There is another implementation of 2-descent in gp by Denis Simon.  It
would be great if that was part of the pari library, but you can use
it as a script.  (It also works -- sometimes! -- over number fields.)

Also, somewhere I have a script by Karim which allows gp to call
mwrank (assuming that you have installed that on your system).

Of course, for conductors up to 230000 (and in a few days up to
240000)  both Sage and pari have access to the generators in my
database, as optional packages



                  GP/PARI CALCULATOR Version 2.6.0 (development git-154d5c9)
                 amd64 running linux (x86-64/GMP-4.3.2 kernel) 64-bit version
              compiled: Jan 19 2012, gcc version 4.4.3 (Ubuntu 4.4.3-4ubuntu5)
                        (readline v6.1 enabled, extended help enabled)

gp > ellheegner(ellinit([-35750837071872,63237970697887678464]))
%1 = [206471808, 2965585996800]

works because your curve has rank 1.

On 30 May 2012 11:35, Max Alekseyev <> wrote:
> Why pari cannot compute generators of an elliptic curve, while sage can?
> I thought they have roughly the same "power" w.r.t. elliptic curves.
> ? ellgenerators(ellinit([-35750837071872,63237970697887678464]))
>  ***   at top-level: ellgenerators(ellini
>  ***                 ^--------------------
>  *** ellgenerators: error opening elldata file:
> `/usr/local/share/pari/elldata/ell1816'.
>  ***   Break loop: type 'break' to go back to GP
> sage: EllipticCurve([-35750837071872,63237970697887678464]).gens()
> [(-2365632 : 11600547840 : 1)]
> Thanks,
> Max