{
  "id": 1689,
  "curve_key": "21149569600:-55894980286016000",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-440616033",
    "64693411091937"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4
  ],
  "naive_height": 77.12450194587235,
  "faltings_height": 4.484870012157674,
  "conductor": "18648177600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "41",
    "197"
  ],
  "discriminant": "-1802539657332277557258240000000",
  "regulator": "376.235235282628468090527488609719108214270729612",
  "points": [
    [
      "7053/4",
      "63960975/8"
    ],
    [
      "726009/49",
      "2688066576/343"
    ],
    [
      "2828073",
      "4755810096"
    ],
    [
      "5552163/529",
      "95202357900/12167"
    ],
    [
      "3881",
      "7939888"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/4. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 06:10:28",
  "updated_at": "2026-09-25 06:10:28"
}