{
  "id": 5789,
  "curve_key": "0:234374692793256",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-271267005548"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 66.17588440380717,
  "faltings_height": 3.5723129427755604,
  "conductor": "31789060545100188647892987",
  "bad_primes": [
    "3",
    "28087",
    "38632393"
  ],
  "discriminant": "-31789060545100188647892987",
  "regulator": "112030215.72941524867156287578594122280378943237778105254",
  "points": [
    [
      "6530",
      "84723"
    ],
    [
      "7040",
      "278651"
    ],
    [
      "9572",
      "778299"
    ],
    [
      "38825/4",
      "6415833/8"
    ],
    [
      "11030",
      "1034723"
    ],
    [
      "77642",
      "21628140"
    ],
    [
      "187334",
      "81080412"
    ],
    [
      "408998/49",
      "191056452/343"
    ],
    [
      "2097560/289",
      "1637382724/4913"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization at t=-219/541 of a generic rank-four Mordell family arising from the Burkhardt parametrization, with construction parameters (4,6,-4).\r\n\r\nThe specialization was identified using the coordinated Mestre–Nagao sieve and subsequently examined by a PARI/GP rank calculation.\r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [9,9].",
  "created_at": "2026-10-25 08:39:43",
  "updated_at": "2026-10-25 08:39:43"
}