{
  "id": 3740,
  "curve_key": "771764160183990961:-677747395989483556087596041",
  "ainvs": [
    "1",
    "1",
    "1",
    "-16078420003833145",
    "784429849769968003133870"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "naive_height": 123.56236621882088,
  "faltings_height": 8.034865740352842,
  "conductor": "357067097216445",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "23",
    "29",
    "31",
    "41",
    "1129"
  ],
  "discriminant": "194776482947709644937899434183038474938094140625",
  "regulator": "5970.49571594971053748300544465918846965747434845",
  "points": [
    [
      "-80916827",
      "1247293039713"
    ],
    [
      "304343207/4",
      "315146523399/8"
    ],
    [
      "618189218",
      "15069223861368"
    ],
    [
      "57051036923/676",
      "2971446453024213/17576"
    ],
    [
      "228693897122/4489",
      "93921800084956344/300763"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u, v)=(29716, 3025) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5.",
  "created_at": "2026-10-01 04:20:54",
  "updated_at": "2026-10-01 04:20:54"
}