{
  "id": 5550,
  "curve_key": "4275516998284968742153168:-8839300693143109149556278625910537920",
  "ainvs": [
    "0",
    "1",
    "0",
    "-89073270797603515461524",
    "10230672098515574129127973163724096"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 170.14484178661525,
  "faltings_height": 11.887180965189064,
  "conductor": "3225632506223974541448",
  "bad_primes": [
    "2",
    "3",
    "13",
    "17",
    "29",
    "37",
    "61",
    "107",
    "251",
    "523",
    "653",
    "1013"
  ],
  "discriminant": "13546851644568695869150611429288493133873528281266975657073851250944",
  "regulator": "3269121.730040409372141789643825226753514111825348165",
  "points": [
    [
      "4033142590414",
      "8078059630277331750"
    ],
    [
      "2712855426526/25",
      "5365903855660634574/125"
    ],
    [
      "8701925927986/49",
      "1237755572110737030/343"
    ],
    [
      "14078105873035/49",
      "31352803105669845192/343"
    ],
    [
      "36961928115889/400",
      "422479160137398403887/8000"
    ],
    [
      "1009127094040528/1849",
      "28017861125221547798400/79507"
    ],
    [
      "425081513333177335/1907161",
      "100295830957289604476051394/2633789341"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (58682,720171) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 7.",
  "created_at": "2026-10-23 01:31:52",
  "updated_at": "2026-10-23 01:31:52"
}