{
  "id": 1167,
  "curve_key": "8656:-725696",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-180",
    "900"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4,
    2
  ],
  "naive_height": 27.198024003258787,
  "faltings_height": 0.23976789321873074,
  "conductor": "840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7"
  ],
  "discriminant": "70560000",
  "regulator": "1.098298981876534643228948977213290779042",
  "points": [
    [
      "5",
      "10"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 840f2, rank exactly 1 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.00000-09999 . 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 21:38:10",
  "updated_at": "2026-09-23 21:38:10"
}