??? so .... elliptic curve x with complex multiplication ... ??? getting galois representation from its p-torsion ... ??? but then .... ??trying to connect this with .... ?? points of x over finite fields ... ??? more specifically over finite k-fields where k is the imaginary quadratic number field associated to x .... ????....

??? "class field" .... ??? ??? how (??k-abelian) algebraic integer j transforms wrt absolute abelian galois group of k as equivalent to how it manifests in finite k-fields ... ?????? ......

??? counting solutions of y^2 = x^3-x (or something like that ...) over finite fields .... tying things in here somehow ... ????

?? points of x over finite k-field f as forming abelian group .... ??? how p-torsion of this abelian group varies as q varies, taking f = f_q .... ???? ... ??? ....

???? ......