algorithms
this page contains a few files with algorithms either written in
parigp or in magma. most of these are obsolete now.
my new and favourite package for doing computational number theory is sage. everything I have and will contribute to it is included in the latest version.
selfpoints
here you can find more details on the computations of selfpoints.
shark : computing tateshafarevich groups via iwasawa theory
shark was originally a package of algorithms written in magma that computes upper bounds on the rank and on the pprimary part of the TateShafarevich group of an elliptic curve over Q. it has now been transferred to sage and is part of the latest version.
on request i can provide you with the obsolete magma package.
elliptic curves over function fields
the file ecff.m contains certain functions to work with elliptic curves over function fields in magma.
note that the current version of magma has all of this function implemented. this was written for an earlier version.
the following functions, already defined in magma for number fields, are exended to curves E over FldFunG; here v stands for a place PlcFunElt :
LocalInformation(E, v)
LocalInformation(E)
Conductor(E)
TamagawaNumber(E,v)
TamagawaNumbers(E)
BadPlaces(E)
Reduction(E,v)
EllNp(E,v), added, the number of elements in the reduction
TorsionSubgroup(E)
see the file readme.ecff.m for more information are some examples how to use the functions. see also on the help page of magma on the corresponding functions for number fields.
heights on the fine selmer group
the file hell.gp, containing functions defined in parigp
can be used to compute the canonical padic height on an elliptic curve over Q.
note that mazur, tate, and stein have found a much faster algorithm for computing these heights. it has been improved even further by david harvey. His algorithm is implemented in sage.
then the file,
fine.gp
contains most of the algorithms used in my thesis to do computations on the fine selmer group,
such as the padic regulator and the upper bound on the eulercharacteristic.
the fine tateshafarevich group
for the computation of the fine tateshafarevich group, see
here.
