{
  "id": 3782,
  "curve_key": "5453303897491216:-401239342447467691507136",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-113610497864400",
    "464397424962142449600"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "naive_height": 108.70499411889615,
  "faltings_height": 6.881736119384484,
  "conductor": "15309447130320",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "37",
    "41",
    "61",
    "71",
    "73"
  ],
  "discriminant": "682983580100349285542160077663970002534400",
  "regulator": "37916.0491187461911938987879136195729147294469670",
  "points": [
    [
      "199800",
      "21016803360"
    ],
    [
      "9187210",
      "14002810950"
    ],
    [
      "856061165/121",
      "5110497494450/1331"
    ],
    [
      "15207522040/3249",
      "1098290433140000/185193"
    ],
    [
      "38166800821240/4255969",
      "113384641286347648800/8780064047"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (4331,779) 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 19:49:13",
  "updated_at": "2026-10-01 19:49:13"
}