{
  "id": 5740,
  "curve_key": "0:-47773632000219964632",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "55293555555810144"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 90.62601105878176,
  "faltings_height": 5.609823497356775,
  "conductor": "1320786987553495959933110666920909083",
  "bad_primes": [
    "3",
    "223",
    "859109",
    "1154466611"
  ],
  "discriminant": "-1320786987553495959933110666920909083",
  "regulator": "1739284378473.1743703606061408926855837318382241137317550534114",
  "points": [
    [
      "-352548",
      "107122976"
    ],
    [
      "-46167/4",
      "1881140383/8"
    ],
    [
      "8316",
      "235147040"
    ],
    [
      "68508",
      "235828512"
    ],
    [
      "294273/4",
      "1887927589/8"
    ],
    [
      "364233/4",
      "1893966409/8"
    ],
    [
      "5835096",
      "14097186144"
    ],
    [
      "-44249871072/143641",
      "8788082077042208/54439939"
    ],
    [
      "-341478359/900",
      "700053278561/27000"
    ],
    [
      "1376272/9",
      "6551017669/27"
    ],
    [
      "8473084/225",
      "794000291552/3375"
    ],
    [
      "232906612/81",
      "3558583781767/729"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Constructed from the rational Bruin–Nasserden parametrization of the Burkhardt quartic using parameters (u,v,w)=(7/6,-5/6,3/6) and specialization t=-11/336. The curve was selected by a three-stage Mestre–Nagao sieve over 328 primes. PARI/GP 2.17.4 returned matching computational rank bounds [12,12] for this model and its 3-isogenous partner.",
  "created_at": "2026-10-24 18:10:29",
  "updated_at": "2026-10-24 18:10:29"
}