Bill Allombert on Sat, 09 Jun 2012 00:05:37 +0200


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Re: ell from j 

On Fri, Jun 08, 2012 at 09:04:57PM +0100, John Cremona wrote:
> I wrote a similar function for Sage,  called EllipticCurve_from_j, but
> it is not normally called directly, rather one does EllipticCurve
> (j=...).  Can gp use named parameters, so you could do ellinit(j=...)?
> 
> The Sage function has special cases for characteristics 2 and 3, and
> also over Q it gives a minimal quadratic twist.

The computation of the minimal quadratic twist requires the factorisation
of j/(1728-j) which can be large, so this would change the complexity of
the function.

Cheers,
Bill.