Karim Belabas on Fri, 28 Oct 2005 15:43:01 +0200


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Re: Supersingular Elliptic Curves 

* Ariel Pacetti [2005-10-22 06:08]:
> Is there a routine in GP to compute the Hasse invariant of an elliptic 
> curve in F_p? I tried to compute the number of points of order p, or the 
> j-invariant, but didn't succed. (y^2+y = x^3 should answer 0 for p=2).

What is your specific problem ? The following seems to work in 2.2.11

  ? ellHasse(e, p) =
      if (p < 5, e.j != Mod(0,p), ellap(e, p) != 0)

  ? e = ellinit([0,0,1,0,0] * Mod(1,2));
  ? ellHasse(e, 2)
  %2 = 0

Cheers,

    Karim.
-- 
Karim Belabas                  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-bordeaux.fr/~belabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]