{
  "id": 1131,
  "curve_key": "40096:-8028800",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-835",
    "9571"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 31.797095573087386,
  "faltings_height": 0.23770137615526676,
  "conductor": "80256",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19"
  ],
  "discriminant": "160512",
  "regulator": "6.6551076105186147677124242039055541907973747",
  "points": [
    [
      "18",
      "7"
    ],
    [
      "9",
      "52"
    ],
    [
      "26",
      "69"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 80256a1, rank exactly 3 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.80000-89999 . 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 21:37:01",
  "updated_at": "2026-09-23 21:37:01"
}