Michael Stoll on Wed, 26 May 1999 13:52:08 +0200 |
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Re: elltors() bug |
[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