{
  "id": 5543,
  "curve_key": "439173760314311074805008:-239887842913394006815762363242054080",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-9149453339881480725104",
    "277647966337996584927833599179264"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 163.31754629103082,
  "faltings_height": 11.611977368838266,
  "conductor": "11916990873131684484144",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "19",
    "29",
    "41",
    "43",
    "71",
    "97",
    "181",
    "239",
    "857"
  ],
  "discriminant": "15716923249956014444108874161424395167554281791460109030164644859904",
  "regulator": "329462.5619993971892941719394493427417294605281950661",
  "points": [
    [
      "-26346336600",
      "22369952515441608"
    ],
    [
      "20166365185",
      "10066680312370132"
    ],
    [
      "30577867594",
      "5144675189982394"
    ],
    [
      "73512792770",
      "1522773559105722"
    ],
    [
      "100057245320",
      "19076090056695672"
    ],
    [
      "-1576914257019/49",
      "7961479406162135358/343"
    ],
    [
      "8860022543289352/96721",
      "434027729305799395541320/30080231"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (195263,425929) 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 00:09:49",
  "updated_at": "2026-10-23 00:09:49"
}