{
  "id": 5565,
  "curve_key": "5272972923614789075605456:-7327873198060021649771543660818568896",
  "ainvs": [
    "0",
    "1",
    "0",
    "-109853602575308105741780",
    "8481334719940259041932702461070528"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 170.773909672444,
  "faltings_height": 12.272179728002163,
  "conductor": "4770181345220703583080",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "29",
    "37",
    "47",
    "83",
    "131",
    "1759",
    "26641"
  ],
  "discriminant": "53769269261190698752966654739111222809504775477945586236309564100000000",
  "regulator": "12479758.62387548633784279173883869448079875228006939",
  "points": [
    [
      "-249305245574",
      "142735135354493250"
    ],
    [
      "-56900627729",
      "120614458331819790"
    ],
    [
      "82179075696",
      "2942007455565360"
    ],
    [
      "-19395699128246/529",
      "1358123372695515283650/12167"
    ],
    [
      "200945007349/4",
      "444664853565614745/8"
    ],
    [
      "30583970984974/49",
      "146760522759232428150/343"
    ],
    [
      "20545875108391894/66049",
      "1127214739587418223684670/16974593"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (447525,804602) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 7.",
  "created_at": "2026-10-23 08:52:28",
  "updated_at": "2026-10-23 08:52:28"
}