{
  "id": 4092,
  "curve_key": "682033:-648884809",
  "ainvs": [
    "1",
    "0",
    "0",
    "-14209",
    "749840"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4
  ],
  "naive_height": 40.581531537861125,
  "faltings_height": 1.3678965119158666,
  "conductor": "2131311",
  "bad_primes": [
    "3",
    "7",
    "13",
    "37",
    "211"
  ],
  "discriminant": "-60064165420623",
  "regulator": "78.999206700739668170976978872631178815146734",
  "points": [
    [
      "116",
      "758"
    ],
    [
      "-19",
      "1016"
    ],
    [
      "701",
      "17963"
    ]
  ],
  "submitter": "NDElkies",
  "history": [],
  "commentary": "Third-smallest Faltings height of all curves of naïve height at most 2^90 with this MW group",
  "created_at": "2026-10-09 14:21:31",
  "updated_at": "2026-10-09 14:21:31"
}