{
  "id": 2756,
  "curve_key": "2387279910345429655201:-116640229756307905844360827282801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-49734998132196451150",
    "135000265917508085623660512500"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 147.67332467354993,
  "faltings_height": 9.94620683438398,
  "conductor": "566645048606910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "37",
    "97",
    "101",
    "30137"
  ],
  "discriminant": "241064784414476125389168415624251443098654812149076810000",
  "regulator": "2897.894518848233385033795135185355965011404574",
  "points": [
    [
      "10391691380",
      "-860435138847130"
    ],
    [
      "36130041541675/2916",
      "187699248584411129225/157464"
    ],
    [
      "68567231810338/15129",
      "-96449500419254153408/1860867"
    ],
    [
      "264421044093786050/33051001",
      "-94849240430500600630295050/190010204749"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1640 via the rational 2-torsion point x=-2029317700. 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 20:21:00",
  "updated_at": "2026-09-26 20:21:00"
}