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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 !!)