{
  "id": 2800,
  "curve_key": "1393286193:-51715553161545",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-29026796",
    "59863221006"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "naive_height": 63.164792884402516,
  "faltings_height": 3.104275310917118,
  "conductor": "86935797",
  "bad_primes": [
    "3",
    "13",
    "61",
    "937"
  ],
  "discriminant": "17484600270723119534169",
  "regulator": "140.4511236362066789140343967981214125094816902",
  "points": [
    [
      "433911",
      "-286020292"
    ],
    [
      "4092",
      "-99982"
    ],
    [
      "9399",
      "-790380"
    ],
    [
      "5027",
      "-204906"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#849 via the rational 2-torsion point x=-1459. 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 20:23:00",
  "updated_at": "2026-09-26 20:23:00"
}