{
  "id": 5506,
  "curve_key": "829782745958608:4340646166120359790400",
  "ainvs": [
    "0",
    "1",
    "0",
    "-17287140540804",
    "-5023901787982448544"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 103.05655509179729,
  "faltings_height": 6.654252323627321,
  "conductor": "30542816147592",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "43",
    "67",
    "739",
    "5023"
  ],
  "discriminant": "319732007783129977259105958306837886159104",
  "regulator": "1928.37764178659258692362425865925129053680332034",
  "points": [
    [
      "-1506570",
      "4195336194"
    ],
    [
      "4456758",
      "2540615490"
    ],
    [
      "-514349250/169",
      "9676294107102/2197"
    ],
    [
      "78582105/16",
      "341924746341/64"
    ],
    [
      "297075774/49",
      "3646439921286/343"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (2881,2142) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.",
  "created_at": "2026-10-22 20:04:12",
  "updated_at": "2026-10-22 20:04:12"
}