{
  "id": 1160,
  "curve_key": "90709008:-830467422144",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1889771",
    "961189146"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4
  ],
  "naive_height": 54.969501679744795,
  "faltings_height": 2.5079118699289746,
  "conductor": "217328",
  "bad_primes": [
    "2",
    "17",
    "47"
  ],
  "discriminant": "32806040800515080192",
  "regulator": "18.249249326808464621019381621512796836236098",
  "points": [
    [
      "629",
      "4624"
    ],
    [
      "965",
      "6016"
    ],
    [
      "-774",
      "44274"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 217328c3, rank exactly 3 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.210000-219999 . Found by screening the local allgens tables for missing torsion size records; torsion and independence independently verified by the site.",
  "created_at": "2026-09-23 21:37:57",
  "updated_at": "2026-09-23 21:37:57"
}