{
  "id": 3046,
  "curve_key": "80547451456:-33943878577123840",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1678071905",
    "39286337143999"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "naive_height": 76.12696985130293,
  "faltings_height": 4.372477750887452,
  "conductor": "29231074244902976",
  "bad_primes": [
    "2",
    "17",
    "73",
    "89",
    "137",
    "257",
    "457"
  ],
  "discriminant": "-364354011624553099954124259328",
  "regulator": "27173.9561341275043301670401132706842751403452358509094",
  "points": [
    [
      "9849",
      "4869752"
    ],
    [
      "21069",
      "3644732"
    ],
    [
      "-55107/4",
      "61859243/8"
    ],
    [
      "-365837/9",
      "-171477368/27"
    ],
    [
      "952057",
      "-928115816"
    ],
    [
      "662649",
      "-538423048"
    ],
    [
      "27095209/144",
      "-138081689117/1728"
    ],
    [
      "-16280397/3481",
      "-1408490977480/205379"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1347 via the rational 2-torsion point x=24843. 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 20:34:47",
  "updated_at": "2026-09-26 20:34:47"
}