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 Poincare 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 prime knots of at most 15 crossings. Moreover, we determine for many friends in our census if their traces are equivalent or not. For that, we develop a new obstruction for two traces being homeomorphic coming from symmetry-exceptional slopes of hyperbolic knots. This is enough to also determine the minimum value of c(K)+c(K') among all friends K and K' whose traces are not homeomorphic.

T.A. is supported by the Research Promotion Program for Acquiring Grants in-Aid for Scientific Research (KAKENHI) in Ritsumeikan University. MK is supported by the DFG, the German Research Foundation, (Project: 561898308) and by the SFB/TRR 191 "Symplectic Structures in Geometry, Algebra and Dynamics"; by a Ramon y Cajal grant (RYC2023-043251-I) and the project PID2024-157173NB-I00 funded by MCIN/AEI/10.13039/50110001-1033, by ESF+, and by FEDER, EU; and by a VII Plan Propio de Investigacian y Transferencia (SOL2025-36103) of the University of Sevilla.