{
  "id": 3319,
  "curve_key": "25129:-3982933",
  "ainvs": [
    "1",
    "0",
    "1",
    "-524",
    "4566"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6
  ],
  "naive_height": 30.395333510009603,
  "faltings_height": 0.2386995680376552,
  "conductor": "2090",
  "bad_primes": [
    "2",
    "5",
    "11",
    "19"
  ],
  "discriminant": "2528900",
  "regulator": "1.580049917079489213763931396547031660057",
  "points": [
    [
      "11",
      "7"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 2090e1 = LMFDB 2090.b2: https://www.lmfdb.org/EllipticCurve/Q/2090/b/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 2090, minimal discriminant 2528900, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:57:06",
  "updated_at": "2026-09-26 20:57:06"
}