{
  "id": 5847,
  "curve_key": "0:-164111366812248",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "189943711588"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 65.4631327584403,
  "faltings_height": 3.51291697232832,
  "conductor": "5195320354356522816605481",
  "bad_primes": [
    "3",
    "983",
    "12473",
    "61967"
  ],
  "discriminant": "-15585961063069568449816443",
  "regulator": "19253765.641875476226867841026164315310708758826659255291",
  "points": [
    [
      "-5372",
      "186859"
    ],
    [
      "-4582",
      "306179"
    ],
    [
      "-3716",
      "372331"
    ],
    [
      "-3518",
      "382627"
    ],
    [
      "-2362",
      "420435"
    ],
    [
      "3944",
      "501291"
    ],
    [
      "11134",
      "1253068"
    ],
    [
      "148937/4",
      "57583945/8"
    ],
    [
      "-586631/196",
      "1108288847/2744"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization at t = 22/827 of a generic rank-four Mordell family constructed through the Burkhardt parametrization with parameters (-6, 8, -10).\r\n\r\nThe specialization was identified using a 328-prime Mestre–Nagao sieve with an improved multistage candidate-retention algorithm. Its score was approximately 47.039518.\r\n\r\nPARI/GP 2.17.4 returned matching computational rank bounds [9,9].",
  "created_at": "2026-10-25 11:09:13",
  "updated_at": "2026-10-25 11:09:13"
}