Bill Allombert on Wed, 01 Jun 2005 15:04:45 +0200

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Re: Proposed elldata database at the PARI workshop

On Wed, Jun 01, 2005 at 10:38:08AM +0200, Jeroen Demeyer wrote:
> Thanks for coding this up, it works very well.
> Since you asked for extensions:
> Maybe you could implement ellinit("40A3") and forell() as prososed
> earlier?  I like the idea of these functions, especially forell(), which
> could be used to search for a curve with certain properties.

ellinit("40A3") is trivial to implement, but I did not want my
patch to touch too many files. 

forell() is more tricky to implement, especially if we want it to be
supported by gp2c. Also what should excatly do this function ?

> If I'm allowed to add one more wishlist item: a function ellgens(E),
> returning the generators of the rational elliptic curve E.  This
> shouldn't be too hard to implement using ellidentify() and then looking
> up the generators of the curbe.
> Hypothetical example:
> gp> E = ellinit("9744C2");
> gp> ellgens(E)
> %40 = [[-11, 14], [-10, 18]]

Yes, this is planned, but I need to rewrite the elldata files to include
the generators. If you could provide a script that build the new elldata
files from John Cremona database, that would help a lot!