  We give an extension of Fox's formula of the Alexander polynomial for double
branched covers over the three-sphere. Our formula provides the Reidemeister
torsion of a double branched cover along a knot for a non-trivial one
dimensional representation by the product of two factors derived from the knot
group. One of the factors is determined by the twisted Alexander polynomial and
the other is determined by a rational function on the character variety. As an
application, we show that these products distinguish isotopy classes of
two-bridge knots up to mirror images.
