{
  "id": 5524,
  "curve_key": "78778996258009260001:-658696738555135529468363250001",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1641229088708526250",
    "762380484302045179492302500"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 137.43953427083434,
  "faltings_height": 9.399999055063763,
  "conductor": "852132368352046470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "71",
    "101",
    "107",
    "587",
    "131111"
  ],
  "discriminant": "31846827818354933709094631265287454678763859660021760000",
  "regulator": "47034.498281984064643505618883156482918896390782366",
  "points": [
    [
      "13966257140",
      "1643783615865350"
    ],
    [
      "-88685740031560/218089",
      "3759479194914841112470/101847563"
    ],
    [
      "109349230292/121",
      "5525854184408626/1331"
    ],
    [
      "6726331674410/11449",
      "1184424839814105550/1225043"
    ],
    [
      "22704701159780/7921",
      "98716961409563516230/704969"
    ],
    [
      "286818482903540/508369",
      "1449791780673454843030/362467097"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (34151,96960) 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 21:27:28",
  "updated_at": "2026-10-22 21:27:28"
}