{
  "id": 3783,
  "curve_key": "1571662738468561:-20382154147508092624441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-32742973718095",
    "23590453460664334400"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "naive_height": 104.9727315688234,
  "faltings_height": 6.809122891426027,
  "conductor": "65357874569085",
  "bad_primes": [
    "3",
    "5",
    "7",
    "17",
    "19",
    "23",
    "41",
    "71",
    "107",
    "269"
  ],
  "discriminant": "2006232216892916831399589790985080550150625",
  "regulator": "610.343264038022997190505431331881850135098168847",
  "points": [
    [
      "-5794765",
      "4332347630"
    ],
    [
      "86297615/4",
      "773852917105/8"
    ],
    [
      "41643605",
      "266208350165"
    ],
    [
      "134500880",
      "1558395459980"
    ],
    [
      "32783033/64",
      "1349915153617/512"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (6745,4284) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.",
  "created_at": "2026-10-01 19:50:47",
  "updated_at": "2026-10-01 19:50:47"
}