In this paper we will prove some cases of the Fontaine-Mazur conjecture. Let
p
p
be an odd prime and let
G
Q
,
{
p
}
G_{\mathbb {Q},\{p\}}
be the Galois group over
Q
\mathbb {Q}
of the maximal unramified-outside-
p
p
extension of
Q
\mathbb {Q}
. We show that under certain hypotheses, the universal deformation of the action of
G
Q
,
{
p
}
G_{\mathbb {Q},\{p\}}
on the
2
2
-torsion of an elliptic curve defined over
Q
\mathbb {Q}
has finite image. We compute the associated universal deformation ring, and we show in the process that
S
^
4
\hat {S}_4
caps
Q
\mathbb {Q}
for the prime
2
2
, where
S
^
4
\hat {S}_4
is the double cover of
S
4
S_4
whose Sylow
2
2
-subgroups are generalized quaternion groups.