  We say that two knots are friends if they share the same 0-surgery. Two
friends with different sliceness status would provide a counterexample to the
4-dimensional smooth Poincar\'e conjecture. Here we create a census of all
friends with small crossing numbers c and tetrahedral complexities t, and
compute their smooth 4-genera. In particular, we compute the minimum of
c(K)+c(K') and of t(K)+t(K') among all friends K and K'. Along the way, we
classify all 0-surgeries of knots of at most 15 crossings.
