Re: ellgenerators

[Kevin Acres <research@research-systems.com>]

Hi Max,

If you just want generators, and a lower bound on 
rank, and in a reasonable time, then ratpoints 
and a few lines of gp script will do that for 
you.  My experience was that sage would run for 
many days on one curve without giving an answer.

John's mwrank program works pretty well, but can 
(in my experience) bog down at heights of 25 or 
more.  Even so it doesn't take long to make it 
into a command line version, which, once again, you can call from gp.

My particular problem was that I was looking for 
generators of MW curves of somewhat large 
conductor and there just wasn't really much out 
there that I could use 'off the shelf'.

Best Regards,

Kevin.


At 10:11 PM 30/05/2012, Max Alekseyev wrote:
> Kevin, thanks for the idea.
> I'm currently making system calls to sage in order to get generators
> when pari fails.
> Is there any advantage in calling ratpoints instead?
> Regards,
> Max
>
> On Wed, May 30, 2012 at 3:32 PM, Kevin Acres
> <research@research-systems.com> wrote:
> > Hi Max,
> >
> > I've recently extracted many 10's of millions of MW curves with conductors
> > in the region of 10^32. Â It's fairly easy to issue a system call to
> > ratpoints from gp in order to get an list of rational points. Â From there,
> > it's just a few more lines of gp script to extract the generators and
> > determine a lower bound for rank. Â The whole process usually takes just a
> > few milliseconds per curve.
> >
> > Currently I'm processing about 300,000 curves per day in this fashion but
> > discarding anything less than rank 8.
> >
> > If you want some code samples please let me know.
> >
> >
> > Best Regards,
> >
> > Kevin.
> >
> >
> >
> > At 08:35 PM 30/05/2012, 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]))
> >> 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
> >
> >