We give an effective bound to the number of torsion points of these families of certain groups. Key ingredient in our construction is
a suitable Eisenstein series (analytic object). The constant terms of these Eisenstein series encode information about the special values of LL-functions. The torsion points of these groups are studied by using an explicit description of the special fibers of the the certain curves due to Edixhoven and Manin-Drinfeld theorem.
The above mentioned bound is an effective version of Bogomolov's conjecture. This is a joint work with Chitrabhanu Chowdhuri and Diganta Borah.