We explicitly describe the moduli space
M
s
(
X
,
3
)
M^s(X,3)
of stable rank 2 parabolic bundles over an elliptic curve
X
X
with trivial determinant bundle and 3 marked points. Specifically, we exhibit
M
s
(
X
,
3
)
M^s(X,3)
as a blow-up of an embedded elliptic curve in
(
C
P
1
)
3
(\mathbb {CP}^1)^3
. The moduli space
M
s
(
X
,
3
)
M^s(X,3)
can also be interpreted as the
S
U
(
2
)
SU(2)
character variety of the 3-punctured torus. Our description of
M
s
(
X
,
3
)
M^s(X,3)
reproduces the known Poincaré polynomial for this space.