  For an elliptic curve E over Q, the Galois action on the l-power torsion
points defines representations whose images are subgroups of GL_2(Z/l^n Z).
There are three exceptional prime powers l^n=2,3,4 when surjectivity of the mod
l^n representation does not imply that for l^(n+1). Elliptic curves with
surjective mod 3 but not mod 9 representation have been classified by Elkies.
The purpose of this note is to do this in the other two cases.

Number Theory