{
  "id": 70,
  "curve_key": "273:999",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-6",
    "0"
  ],
  "rank_lower_bound": 3,
  "naive_height": 16.82841538555488,
  "faltings_height": -0.5324408450204543,
  "conductor": "11197",
  "bad_primes": [
    "11197"
  ],
  "discriminant": "11197",
  "regulator": "0.86842195369372664900484860186367158964425101",
  "points": [
    [
      "0",
      "0"
    ],
    [
      "-1",
      "2"
    ],
    [
      "-2",
      "1"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: found by a local bounded-height search over reduced integral Weierstrass models. Invariants are c4=273, c6=999, Delta=11197. The submitted points (0,0), (-1,2), (-2,1) were checked exactly on the curve, with an additional finite-field independence sanity check; the site Neron-Tate verifier gives the definitive certificate.",
  "created_at": "2026-05-29 13:46:04",
  "updated_at": "2026-07-01 23:04:07"
}