{
  "id": 5523,
  "curve_key": "159864258769629577873:-2020978632415213156803591136985",
  "ainvs": [
    "1",
    "1",
    "1",
    "-3330505391033949539",
    "2339095637981749092628899656"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 139.56257023906971,
  "faltings_height": 9.338804860445462,
  "conductor": "112418315816996811",
  "bad_primes": [
    "3",
    "23",
    "29",
    "41",
    "43",
    "59",
    "83",
    "2297",
    "2833"
  ],
  "discriminant": "711390425196999918854670326027990472857843904654716289",
  "regulator": "2465758.4720631302023779850496382524067472374779026",
  "points": [
    [
      "-13228834772/9",
      "1720160072542309/27"
    ],
    [
      "1585134316297/1521",
      "14864025416957725/59319"
    ],
    [
      "73540546555761/105625",
      "649292088000796966159/34328125"
    ],
    [
      "1427868142805662/4076361",
      "286931220801526829786510/8230172859"
    ],
    [
      "5628384467604642/5396329",
      "867211428010627955077/12535672267"
    ],
    [
      "7706511318330588/4507129",
      "387884308898568510592364/9568634867"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (9188,112631) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 6.",
  "created_at": "2026-10-22 21:26:33",
  "updated_at": "2026-10-22 21:26:33"
}