{
  "id": 3483,
  "curve_key": "118781639511409717648:-1294556451604970805007913563840",
  "ainvs": [
    "0",
    "1",
    "0",
    "-2474617489821035784",
    "1498329225569769638818813956"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "naive_height": 138.67145555793027,
  "faltings_height": 9.174059835836358,
  "conductor": "62271688747599408",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "23",
    "31",
    "37",
    "47",
    "73",
    "97",
    "101"
  ],
  "discriminant": "13308324430688211366524792624427609457403470008075264",
  "regulator": "258595.49169646766155061057770627460179125788453536",
  "points": [
    [
      "674259543",
      "11676071296890"
    ],
    [
      "913558680",
      "259588068894"
    ],
    [
      "95325319890/121",
      "8177722022535984/1331"
    ],
    [
      "1457985521106/1225",
      "662879333844199296/42875"
    ],
    [
      "3199776381576/3481",
      "116170441649063802/205379"
    ],
    [
      "75801564176893344/42941809",
      "14432395998653961301607634/281397674377"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found by a conductor-oriented search in the standard Z/2Z x Z/4Z family\r\ny^2 = x(x+u^2)(x+v^2), with (u,v) = (1971,52217).\r\n\r\nPARI/GP 2.17.4 gives exact rank 6 and torsion Z/2Z x Z/4Z.\r\nConductor N = 62271688747599408.\r\n\r\n",
  "created_at": "2026-09-27 09:21:03",
  "updated_at": "2026-09-27 09:21:03"
}