Re: elliptic curves with prescribed periods

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Sat, May 12, 2012 at 02:14:04PM +0200, Bill Allombert wrote:
> Dear PARI users,
> 
> Is there a convenient way to build an elliptic curve with prescribed period in
> ellinit Weierstrass form ?
> g2=elleisnum(om,4,1);
> g3=elleisnum(om,6,1); will give you the curve in the form
> y^2 = 4*x^3 - g2*x - g3
> and then you will have to do a coordinate change before being able to use ellinit,
> which is not very convenient.

Well it seems the correct formula is

f(om)=ellinit(-1/4*[elleisnum(om,4,1),elleisnum(om,6,1)])

so that f(om).omega==om

Cheers,
Bill.