{
  "id": 5582,
  "curve_key": "87069573988769347370649808:-809299072832360768786615660763328964800",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1813949458099361403555204",
    "936688741703516610350327598008223456"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 179.1862491958246,
  "faltings_height": 12.75774194769178,
  "conductor": "8224704040914907186872",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "23",
    "29",
    "41",
    "61",
    "71",
    "73",
    "101",
    "409",
    "733"
  ],
  "discriminant": "2962436917453602713282171144417593825485680559381630768222592295957915904",
  "regulator": "9793538.888146978564732718527697132134261874164444370",
  "points": [
    [
      "1594526884956",
      "1448588160684053928"
    ],
    [
      "41802139063116",
      "270131365570434670512"
    ],
    [
      "-92004433010639046/143641",
      "73761077402996214674222010/54439939"
    ],
    [
      "13709797205625/16",
      "6864216365024910549/64"
    ],
    [
      "99532310090184/25",
      "942246766872206378352/125"
    ],
    [
      "138966918817340/169",
      "72747794041461774312/2197"
    ],
    [
      "217291533444581832/5331481",
      "11434930952640744257936987760/12310389629"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (281358,1539919) 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 19:34:59",
  "updated_at": "2026-10-23 19:34:59"
}