{
  "id": 4049,
  "curve_key": "163229178688:-54374507225192960",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-3400607889",
    "62934590972529"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "naive_height": 77.45526316342682,
  "faltings_height": 4.456708655599596,
  "conductor": "5829048278592",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "67",
    "79",
    "163",
    "457"
  ],
  "discriminant": "805817595730852196893536436224",
  "regulator": "894.96483351030331431544602313490956585132909559445",
  "points": [
    [
      "-1131",
      "8171856"
    ],
    [
      "8504",
      "5884789"
    ],
    [
      "5961325/9",
      "14500120096/27"
    ],
    [
      "90729491/289",
      "850069540628/4913"
    ],
    [
      "-24925329/529",
      "132478369968/12167"
    ],
    [
      "312219/25",
      "591778572/125"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/2+Z/2. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-07 22:24:24",
  "updated_at": "2026-10-07 22:24:24"
}