{
  "id": 2744,
  "curve_key": "4812751486589719239073:-333348757007355950912174699169265",
  "ainvs": [
    "1",
    "0",
    "0",
    "-100265655970619150814",
    "385820320602010212595243194804"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 149.77666772423166,
  "faltings_height": 10.272054433240724,
  "conductor": "1623822158052798",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17",
    "19",
    "29",
    "59",
    "197",
    "225983"
  ],
  "discriminant": "205053515067517098406389422928643576052914699364637006280464",
  "regulator": "12200.08189827003613306242933574836619462535808",
  "points": [
    [
      "22228787779103499/3648100",
      "231596382945021422268237/6967871000"
    ],
    [
      "160779253529796/26569",
      "112209181278111942618/4330747"
    ],
    [
      "2507777939074218/146689",
      "-107604422229095393412222/56181887"
    ],
    [
      "3584878775774519390/588208009",
      "-477409937013924395369040844/14265808842277"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1633 via the rational 2-torsion point x=-2795938596. 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 20:20:21",
  "updated_at": "2026-09-26 20:20:21"
}