  We consider some problems of analytic number theory for elliptic curves which
can be considered as analogues of classical questions around the distribution
of primes in arithmetic progressions to large moduli, and of the question of
twin primes. This leads to some local results on the distribution of the group
structures of elliptic curves defined over a prime finite field, exhibiting an
interesting dichotomy for the occurence of the possible groups. (Note : This
paper was initially written in 2000/01, but after a four year wait for a
referee report, it is now withdrawn and deposited in the arXiv).
