{
  "id": 5535,
  "curve_key": "1219672089116595518829328:-1346982824671323047190492390377639360",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-25409835189929073308944",
    "1559007898933612360793046254040064"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 166.38187282518592,
  "faltings_height": 11.479314183330477,
  "conductor": "132050268153089129424",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "19",
    "149",
    "457",
    "631",
    "1481",
    "19121"
  ],
  "discriminant": "12428166742473855400885255511833027945828799599831642104245981184",
  "regulator": "2787849.929897868795495056387597841785569068446777929",
  "points": [
    [
      "91823718570",
      "52694647430422"
    ],
    [
      "1111748822384/25",
      "2842139566308867552/125"
    ],
    [
      "1475772472225/16",
      "3010567713438537/64"
    ],
    [
      "83713289736960/961",
      "76299218907610336288/29791"
    ],
    [
      "491256170095576/5625",
      "1031702722893543821176/421875"
    ],
    [
      "1977470955885888/9409",
      "67697458214541095227840/912673"
    ],
    [
      "20864813157936280/1555009",
      "67743022542727148426068056/1939096223"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (19121,525623) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 7.",
  "created_at": "2026-10-22 23:26:03",
  "updated_at": "2026-10-22 23:26:03"
}