{
  "id": 5744,
  "curve_key": "0:2272235161097230164864",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-2629901806825497876"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 98.35010190476352,
  "faltings_height": 6.253497734521922,
  "conductor": "35563286457515224348725967345296",
  "bad_primes": [
    "2",
    "3",
    "7",
    "1861",
    "38148308389"
  ],
  "discriminant": "-2987877677851015925715896337481180914432",
  "regulator": "553162501337.348589067583014214348955340203309870781284555674",
  "points": [
    [
      "1417773",
      "468973071"
    ],
    [
      "1518958",
      "935248006"
    ],
    [
      "7255605",
      "19476466443"
    ],
    [
      "9174333",
      "27740924631"
    ],
    [
      "13833022/9",
      "27014531138/27"
    ],
    [
      "268074030/169",
      "2563348218354/2197"
    ],
    [
      "1315315750/121",
      "47654068506758/1331"
    ],
    [
      "2247282622/729",
      "101639199133522/19683"
    ],
    [
      "12950819518/5041",
      "1354720834196506/357911"
    ],
    [
      "1912048659318/52441",
      "2643848884897489206/12008989"
    ],
    [
      "58529238351150/32041",
      "447774449708559213198/5735339"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed from the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(9/6,-9/6,-1/6) and specialization t=-1133/838. The specialization was selected through a three-stage Mestre–Nagao sieve over 328 primes. \r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [11,11] on this model and its rationally 3-isogenous partner.",
  "created_at": "2026-10-24 18:13:15",
  "updated_at": "2026-10-24 18:13:15"
}