{
  "id": 4041,
  "curve_key": "21553:987319",
  "ainvs": [
    "1",
    "1",
    "1",
    "-449",
    "-1330"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "naive_height": 29.934810890939442,
  "faltings_height": 0.5566101302302718,
  "conductor": "12190893",
  "bad_primes": [
    "3",
    "11",
    "13",
    "157",
    "181"
  ],
  "discriminant": "5229893097",
  "regulator": "15.83026170824213054991534954472248706822836545",
  "points": [
    [
      "-16",
      "53"
    ],
    [
      "36",
      "157"
    ],
    [
      "49",
      "287"
    ],
    [
      "140",
      "1574"
    ]
  ],
  "submitter": "NDElkies",
  "history": [],
  "commentary": "2nd-smallest naïve height for this MW group, by exhaustive search",
  "created_at": "2026-10-06 19:18:01",
  "updated_at": "2026-10-06 19:18:01"
}