Bill Allombert on Wed, 11 May 2005 18:25:43 +0200

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Re: Proposed elldata database at the PARI workshop

On Mon, May 09, 2005 at 08:52:49PM +0200, Bill Allombert wrote:
> On Wed, May 04, 2005 at 11:03:34AM +0200, Jeroen Demeyer wrote:
> > It would be very cool to have a "reverse lookup" feature:
> > 
> > Given a curve E, there should be a command ellidentify(E) giving back 
> > the curve number and a matrix defining the isomorphism with the curve in 
> > Cremona's list.
> This is a good idea!
> I think it is easy to implement with ellglobalred() and a elllist()
> routine.

OK, so I have a tentative implementation.
It includes 3 functions:

ellbyname(name): retrieve a curve by its name.
ellcondlist(conductor): retrieve all curves of a given conductor.
ellidentify(curve): retrieve the name of the curve and the base change.

and an elldata package that include all curves from John Cremona database
upto conductor 39999 (based on a first version by William Stein).

Now, three questions:
1) A better name for ellcondlist and ellbyname?
2) Should ellbyname by available directly under GP or only through
ellinit() ?
3) Should we store more information in the tables than just the names
and the coefficients? if yes, how we will use them ?