{
  "id": 2822,
  "curve_key": "-66567104:-137054620160",
  "ainvs": [
    "0",
    "-1",
    "0",
    "1386815",
    "158165761"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "naive_height": 54.041163238653404,
  "faltings_height": 2.5764988935066273,
  "conductor": "1147880256",
  "bad_primes": [
    "2",
    "3",
    "17",
    "137",
    "151"
  ],
  "discriminant": "-181571032719477669888",
  "regulator": "116.612655249416327038751471179870241825890192215",
  "points": [
    [
      "2488",
      "137853"
    ],
    [
      "193",
      "-20808"
    ],
    [
      "31",
      "14184"
    ],
    [
      "-163/4",
      "80631/8"
    ],
    [
      "-96",
      "-4913"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1269 via the rational 2-torsion point x=57. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:23:59",
  "updated_at": "2026-09-26 20:23:59"
}