{
  "id": 3180,
  "curve_key": "923025:819102375",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-19230",
    "-943228"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "naive_height": 41.20623479612594,
  "faltings_height": 1.3941736996842702,
  "conductor": "326975",
  "bad_primes": [
    "5",
    "11",
    "29",
    "41"
  ],
  "discriminant": "66820406640625",
  "regulator": "16.497949560267671766261881743318011837858891",
  "points": [
    [
      "-66",
      "220"
    ],
    [
      "-86",
      "305"
    ],
    [
      "184",
      "1220"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 326975c2 = LMFDB 326975.c2: https://www.lmfdb.org/EllipticCurve/Q/326975/c/2\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 326975, minimal discriminant 66820406640625, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:41:08",
  "updated_at": "2026-09-26 20:41:08"
}