Re: ellgenerators

[Max Alekseyev <maxale@gmail.com>]

John, thank you for clarification!

While we are on this page, I'd like also to report a strange error
produced by ellgenerators:

? ellgenerators(ellinit([-11972883, 21178268436096]))
  ***   at top-level: ellgenerators(ellini
  ***                 ^--------------------
  *** ellgenerators: overflow in t_INT-->long assignment.
  ***   Break loop: type 'break' to go back to GP

Looks like a bug in pari.

Regards,
Max

On Wed, May 30, 2012 at 3:03 PM, John Cremona <john.cremona@gmail.com> wrote:
> I meant my reply to go to the list, but it only went to Max.
>
>
> ---------- Forwarded message ----------
> From: John Cremona <john.cremona@gmail.com>
> Date: 30 May 2012 11:57
> Subject: Re: ellgenerators
> To: Max Alekseyev <maxale@gmail.com>
>
>
> Sage incorprates my library eclib which includes Âa 2-descent
> implementation in C++) as used in my programme mwrank. Âpari does not.
>
> There is another implementation of 2-descent in gp by Denis Simon. ÂIt
> would be great if that was part of the pari library, but you can use
> it as a script. Â(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) Âboth Sage and pari have access to the generators in my
> database, as optional packages
>
> John
>
> PS
>
> Â Â Â Â Â Â Â Â ÂGP/PARI CALCULATOR Version 2.6.0 (development git-154d5c9)
> Â Â Â Â Â Â Â Â amd64 running linux (x86-64/GMP-4.3.2 kernel) 64-bit version
> Â Â Â Â Â Â Âcompiled: Jan 19 2012, gcc version 4.4.3 (Ubuntu 4.4.3-4ubuntu5)
> Â Â Â Â Â Â Â Â Â Â Â Â(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 <maxale@gmail.com> 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]))
>> Â*** Â at top-level: ellgenerators(ellini
>> Â*** Â Â Â Â Â Â Â Â ^--------------------
>> Â*** ellgenerators: error opening elldata file:
>> `/usr/local/share/pari/elldata/ell1816'.
>> Â*** Â Break loop: type 'break' to go back to GP
>>
>> sage: EllipticCurve([-35750837071872,63237970697887678464]).gens()
>> [(-2365632 : 11600547840 : 1)]
>>
>> Thanks,
>> Max
>>