... Conference talks: titles and abstracts . ... Now consider an elliptic curve E defined over a global field, assuming its Tate-Shafarevich group is finite, one can form the product of the order of this group and of the NИron-Tate regulator of E. Heuristically, this product measures the complexity of computing the Mordell-Weil group of E. This prompts the question of giving upper and lower bounds of this quantity in terms of simpler invariants of E, e.g. its height. ... automorphism group of powers . ...