{
  "id": 2812,
  "curve_key": "2938040833:-159247451973025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-61209184",
    "184309079759"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "naive_height": 65.40302643849482,
  "faltings_height": 3.112170563635374,
  "conductor": "61208589",
  "bad_primes": [
    "3",
    "13",
    "23",
    "29",
    "181"
  ],
  "discriminant": "963031859491327872129",
  "regulator": "59.96368580584818674549371459219365298144949254",
  "points": [
    [
      "195677",
      "-86588236"
    ],
    [
      "30902",
      "-5288251"
    ],
    [
      "358906/25",
      "-188999269/125"
    ],
    [
      "4655",
      "-18298"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#850 via the rational 2-torsion point x=-2248. 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 20:23:33",
  "updated_at": "2026-09-26 20:23:33"
}