{
  "id": 5521,
  "curve_key": "908499411144999747856:-27320161865361946166307167746496",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-18927071065520828080",
    "31620557720848313232843942400"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 144.7749777407011,
  "faltings_height": 9.869514772143335,
  "conductor": "140285463605723280",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "61",
    "101",
    "139",
    "199",
    "439",
    "601"
  ],
  "discriminant": "2001149712175050916552953979254975806440075855253629440000",
  "regulator": "62648.250233125627849034918561854345450992043304650",
  "points": [
    [
      "643732360",
      "140368610159400"
    ],
    [
      "2205709480",
      "24577522692840"
    ],
    [
      "2363607025",
      "9434871680520"
    ],
    [
      "10441510885/4",
      "8214788813205/8"
    ],
    [
      "994014612218290/380689",
      "343855631395088726550/234885113"
    ],
    [
      "27151495700314570/13300609",
      "1872512715028414603515930/48507321023"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (14039,87361) 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 21:24:20",
  "updated_at": "2026-10-22 21:24:20"
}