{
  "id": 2780,
  "curve_key": "95262043294543824673:48151032608998305855417160655",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1984625901969663014",
    "-55730361981355753237538076"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 138.00948935608434,
  "faltings_height": 9.568868075384211,
  "conductor": "187511281391406",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "23",
    "31",
    "37",
    "61",
    "151",
    "967"
  ],
  "discriminant": "498941486260560083314659917811614550899210327031683883264",
  "regulator": "804.8904237123832154511529539720868094197828387",
  "points": [
    [
      "155013963856/25",
      "-59428771274844094/125"
    ],
    [
      "17874660386680/1681",
      "-74903697763298781682/68921"
    ],
    [
      "1700493580",
      "-38558684923142"
    ],
    [
      "66966191764/25",
      "-14709785802937222/125"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1634 via the rational 2-torsion point x=224737695/4. 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 20:22:05",
  "updated_at": "2026-09-26 20:22:05"
}