ellorder

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

Dear PARI developers,

I have fixed a problem with ellorder found by John Cremona:
It was not possible to ask for the order of a point over a Fp when the curse was
defined over Z. i.e 
? ellisoncurve(ellinit([0,0,0,0,2],1),[-1,-1]*Mod(1,101))
%2 = 1
? ellorder(ellinit([0,0,0,0,2],1),[-1,-1]*Mod(1,101))
%1 = 0
did not work.

Also I did some archeology and actually ellorder already existed in version 2.0.17
and the code was:

GEN
orderell(GEN e, GEN p)
{
  ...
  p1=p; k=1;
  for (k=1; k<16; k++)
  {
    if (lg(p1)<3) { avma=av; return stoi(k); }
    p1 = addell(e,p1,p);
  }
  avma=av; return gzero;
}

so the ellorder slowness for large non-torsion point is not a new feature.

Cheers,
Bill.