{
  "id": 5706,
  "curve_key": "0:-2405335355376335039448",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "2783952957611498888"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 98.46395257523325,
  "faltings_height": 6.2629852903944,
  "conductor": "31243715072587803983534516506247361",
  "bad_primes": [
    "3",
    "7",
    "8417091330647011"
  ],
  "discriminant": "-3348170238323726838287509392358985946843",
  "regulator": "555441473551185.47602791862879655450619649414070857068033669834",
  "points": [
    [
      "462448",
      "1697896119"
    ],
    [
      "6087232",
      "15111010632"
    ],
    [
      "-53591927896152527/202656630276",
      "151713729615309471179166131/91230745877868024"
    ],
    [
      "-187576741352/564001",
      "702040616773780280/423564751"
    ],
    [
      "-71110277166/52441",
      "6473695730880019/12008989"
    ],
    [
      "-81834455087/553536",
      "686748263377897241/411830784"
    ],
    [
      "-1065143807/1156",
      "55607767453011/39304"
    ],
    [
      "56289048/289",
      "8208301041671/4913"
    ],
    [
      "161977794657/5776",
      "65194450960699057/438976"
    ],
    [
      "740016814818138/185204881",
      "20565436991614478947120/2520453225529"
    ],
    [
      "8702121860447316/505665169",
      "812000545371516986511233/11370892655303"
    ],
    [
      "390629260512520078/795951249921",
      "1209734893312833487383609920/710116663080769281"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed from the Burkhardt quartic using the rational Bruin–Nasserden parametrization, with parameters (u,v,w)=(2/3,-4/3,2/3) and specialization t=419/164. \r\n\r\nCandidates were selected by a three-stage Mestre–Nagao sieve over 328 primes, followed by PARI/GP 2.17.4 rank computations. Twelve rational points were obtained, and PARI returned matching rank bounds [12,12].",
  "created_at": "2026-10-24 14:07:20",
  "updated_at": "2026-10-24 14:07:20"
}