Ariel Pacetti on Mon, 28 Jun 2004 18:30:06 +0200

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Re: Pari Bug?

In my case the curve was obtained as a quadratic twist of the curve E121D
by -55 (I misprint the name, it is E275B) hence it is not reduced. What I
did was the obvious routine:

reducecurve(E) = ellchangecurve(E,ellglobalred(E)[2])

and then run the elllseries routine to the reduced curve. Probably it is
not a bad idea (as Prof. Cremona suggested) to have a flag in ellseries so
as to reduce the curve first (default option) or not if flag is set to 1.


On Mon, 28 Jun 2004, Prof. J. E. Cremona wrote:

> It is very likely that elllseries only gives correct answers with a
> global minimal model.  This is true, though not always documented, with
> several of Pari's elliptic curve functions.  In your case your curve [0,
> 55, 3025, -121000, 34439625] is nonminimal at 11, as I am sure you know.
> So you will ask -- why does elllsseries not switch to a minimal model
> itself?  I suppose the answer is that this would only waste time when
> the curve was minimal already.  A solution would be to do this unless
> the user has set a switch/flag to say "don't bother minimising this
> model as I already know that it is minimal".
> John Cremona
> --
>   Prof. J. E. Cremona             |
>   University of Nottingham        | Tel.:  +44-115-9514920
>   School of Mathematical Sciences | Fax:   +44-115-9514951
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