Exact arithmetic for the two curves requested in Post81 comment eBObyNnTh9UdsqKC.
Run the rank probe and rank replay with arguments 273 305 and 1425 2993 using Sage Python; then run 131_named_cosets.py. Run 132_fraction_replay.py with ordinary Python.
PARI ellrank bounds and a separate eclib proof agree on rank one. The standard-library replay checks the reported points, R=-G-S and every mixed edge. The calculation is about 1-xy=+/-square and does not give a rational septuple. The scope contains only the two named inputs. No external data or keys are needed.
