{
  "id": 3275,
  "curve_key": "-1184:-7136",
  "ainvs": [
    "0",
    "-1",
    "0",
    "25",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 21.229961446331853,
  "faltings_height": -0.16023376259501165,
  "conductor": "1320",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11"
  ],
  "discriminant": "-990000",
  "regulator": "1.349113723629621392171108121322455375132",
  "points": [
    [
      "1",
      "5"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1320i1 = LMFDB 1320.e4: https://www.lmfdb.org/EllipticCurve/Q/1320/e/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 1320, minimal discriminant -990000, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:49:59",
  "updated_at": "2026-09-26 20:49:59"
}