{
  "id": 3781,
  "curve_key": "450320310607681:-1831093676204256797921",
  "ainvs": [
    "1",
    "1",
    "1",
    "-9381673137660",
    "2119317475465193565"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "naive_height": 101.22294074049866,
  "faltings_height": 6.501216458775252,
  "conductor": "13843123266030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "23",
    "41",
    "43",
    "67",
    "97",
    "103"
  ],
  "discriminant": "50906726379913066956705911155137538560000",
  "regulator": "7134.19322187735100811436981706351975168246267961",
  "points": [
    [
      "-2431947",
      "3249543473"
    ],
    [
      "-459107",
      "2516126873"
    ],
    [
      "-1000732611/361",
      "17926842209115/6859"
    ],
    [
      "301137925/49",
      "4556850839687/343"
    ],
    [
      "1077771373/81",
      "34443892363697/729"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (4945,3296) 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 19:48:50",
  "updated_at": "2026-10-01 19:48:50"
}