Re: Pari Bug?

[Ariel Pacetti <apacetti@math.utexas.edu>]

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.

Ariel

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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