{
  "id": 2763,
  "curve_key": "66352671646181370391873:17089261750387500000878223083882015",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1382347325962111883164",
    "-19779238137137765055957749004016"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 157.6478129363956,
  "faltings_height": 10.845400268986914,
  "conductor": "469844835723354",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "23",
    "29",
    "31",
    "41",
    "1015057"
  ],
  "discriminant": "50067399773461753067331094073953280187273881291103817331441664",
  "regulator": "5728.686979714444768124772903659081243860046478",
  "points": [
    [
      "118707447194",
      "38586037214605622"
    ],
    [
      "-3537014736635464/165649",
      "3092613327236321714812/67419143"
    ],
    [
      "-107701733042428/5041",
      "17085040151071940824/357911"
    ],
    [
      "1590229798882424",
      "-63414684531373768759516"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1638 via the rational 2-torsion point x=10839389624. 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 20:21:19",
  "updated_at": "2026-09-26 20:21:19"
}