{
  "id": 2759,
  "curve_key": "227353330772703392094721:96787574770556755536312219566411519",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4736527724431320668640",
    "-112022655984835399921841753072400"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 161.34237685037223,
  "faltings_height": 11.422504829569611,
  "conductor": "503432816707590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "41",
    "181",
    "809",
    "1171"
  ],
  "discriminant": "1379602879710024845473007630677446045448693180547445131448473610000",
  "regulator": "76960.23911401689165461460292854485719922639549",
  "points": [
    [
      "8203405437959679/6724",
      "741797766799220460490101/551368"
    ],
    [
      "229023867166948050/508369",
      "-108248303259850912565476620/362467097"
    ],
    [
      "46609619854678922740470/139519431529",
      "9831356966986072083777434461736220/52113716623006667"
    ],
    [
      "601119286570511895/7431076",
      "-118392522405643314481951365/20257113176"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1639 via the rational 2-torsion point x=14289410880. 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 20:21:08",
  "updated_at": "2026-09-26 20:21:08"
}