  We give a formula for the duality structure of the 3-manifold obtained by
doing zero-framed surgery along a knot in the 3-sphere, starting from a diagram
of the knot. We then use this to give a combinatorial algorithm for computing
the twisted Blanchfield pairing of such 3-manifolds. With the twisting defined
by Casson-Gordon style representations, we use our computation of the twisted
Blanchfield pairing to show that some subtle satellites of genus two ribbon
knots yield non-slice knots. The construction is subtle in the sense that, once
based, the infection curve lies in the second derived subgroup of the knot
group, and that we identify these infection curves explicitly.
