additional information to 'the fine Tate-Shafarevich group'
as explained in the article, the fine Tate-Shafarevich group is a certain canonically defined subgroup of the usual Tate-Shafarevich group of an elliptic curve over an number field.
the section 4 contains numerical computations. we include here further information on these computations
there is a very badly written pari-script that performs a complete 2-descent on an elliptic curve of rank 0 with rational 2-torsion
fsha.gp.
it extracts the information on the fine subgroup.
using the following script
fsha.script.gp
and the list of curves with non-trivial 2-torsion in sha obtained from cremona's tables, one obtains the
tables.
(!! there are still a few minor bugs !!)
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