{
  "id": 5747,
  "curve_key": "0:-940934412036691975527289056",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "1089044458375800897601029"
  ],
  "rank_lower_bound": 13,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 124.21783133746696,
  "faltings_height": 8.409141853913875,
  "conductor": "24393495144904469512782813122768868609422244",
  "bad_primes": [
    "2",
    "3",
    "7",
    "140983",
    "1714441",
    "486517463"
  ],
  "discriminant": "-512359703561825942614075542124354932291137123019312",
  "regulator": "15024928066151.89551090038826074910934845742144064426394172417120",
  "points": [
    [
      "-102854465",
      "30706011602"
    ],
    [
      "-2419809",
      "1043566140330"
    ],
    [
      "26063935",
      "1052022070898"
    ],
    [
      "87607891",
      "1327195355500"
    ],
    [
      "125282623",
      "1747983806414"
    ],
    [
      "146143263",
      "2051913943926"
    ],
    [
      "211731555",
      "3252848489352"
    ],
    [
      "227789023",
      "3592843527014"
    ],
    [
      "-4488843975/64",
      "441630524574099/512"
    ],
    [
      "-685502489/25",
      "129206008671866/125"
    ],
    [
      "-326530743/4",
      "5906215198107/8"
    ],
    [
      "-204680175/4",
      "7818182614809/8"
    ],
    [
      "16011650487/169",
      "3059667250520958/2197"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed using the rational Bruin–Nasserden parametrization of the Burkhardt quartic with parameters (u,v,w)=(13/9,4/9,16/9) and specialization t=119/4. The specialization was identified by a three-stage Mestre–Nagao sieve using 328 primes. \r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [13,13].",
  "created_at": "2026-10-24 18:40:56",
  "updated_at": "2026-10-24 18:40:56"
}