Heuristics on Tate-Shafarevitch groups of elliptic curves defined over Q

In a well-known paper, Cohen and Lenstra gave conjectures on class groups o f number fields. We give here similar conjectures for Tate-Shafarevitch gro ups of elliptic curves defined over Q. For such groups (ii they are finite) , there exists a nondegenerate, alternating, bilinear pairing. We give some properties of such groups and then formulate heuristics which allow us to give precise conjectures.