Re: elliptic curves with prescribed periods

[John Cremona <john.cremona@gmail.com>]

On 16 May 2012 12:54, Karim Belabas <Karim.Belabas@math.u-bordeaux1.fr> wrote:

>
> Funny. The whole point of elleisnum(..., flag = 1) is to activate
> the following code snippet:
>
>    else if (k==4 && flag) y = gdivgs(y,  12);
>    else if (k==6 && flag) y = gdivgs(y,-216);
>
> which your code then gets rid of. Final shortcut:
>
> x  = 0.0017237131288014931634375894696418139876;
> y  = 0.0088075252675047227730811538038700492673;
> om = [2*x,x+y*I];
> ellminimalmodel(ellinit([-27*round(elleisnum(om,4)),54*round(elleisnum(om,6))]))
>
> :-)
>

Funny indeed!  And I was looking at the code for elleisnum() to see
why (in this example) my own C++ code was not getting enough precision
to find c4c6 while libpari was doing so easily.

John

> Cheers,
>
>    K.B.
> --
> Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
> Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
> 351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~belabas/
> F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
> `