Re: How to use a named elliptic curve?

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Sat, Jan 09, 2021 at 06:45:18PM +0100, Ján Jančár wrote:
> I just had a look on the format of pari-elldata and also the original Cremona's database
> at https://github.com/JohnCremona/ecdata and the format does not seem to include a way
> to define the base field of the curve, all the curves are assumed to be over the rationals.

Indeed.

> So to support standard elliptic curves this functionality/format would have to be extended
> to allow for specification of the base field (usually a prime field or a binary extension
> field with polynomial basis with a chosen generator polynomial).

What matters is that the file be readable with readvec.
For example each lines could be
["name",[a1,a2,a3,a4,a6],e,card]
with g = p or ffgen(...)
so that
ellinit([a1,a2,a3,a4,a6],g);
gives back the curve, and card is the corresponding group order.
One might also add the standard generator and its order.

Cheers,
Bill.