Re: elltors() bug

[Michael Stoll <stoll@math.uni-duesseldorf.de>]

[Karim:]
> P.S: From a cursory glance at the code, elltors follows Nagell-Lutz approach,
> which is a disaster when the discriminant gets big. Computing modulo small
> primes of good reduction should be infinitely more efficient. [Anybody
> implemented that already ?]

You might want to have a look at
  ftp://math.uni-duesseldorf.de/home/stoll/papers/genus2/height-const.dvi.gz
where I'm describing an algorithm to compute the rational torsion subgroup of
a genus two Jacobian. A simplified version of this should work for elliptic
curves. (The idea is to lift the group E(F_p) to a torsion subgroup of E(Q_p)
(where p is a good prime not dividing the group order) and then use a bound
on the difference between naive and canonical height to find out which of the
elements are really in E(Q).)

Michael