{
  "id": 3244,
  "curve_key": "24928:-3934720",
  "ainvs": [
    "0",
    "1",
    "0",
    "-519",
    "4381"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 30.371240846011425,
  "faltings_height": 0.25868243715983547,
  "conductor": "345856",
  "bad_primes": [
    "2",
    "7",
    "193"
  ],
  "discriminant": "4841984",
  "regulator": "5.6801193798719366044970201315169729320769389",
  "points": [
    [
      "12",
      "5"
    ],
    [
      "15",
      "14"
    ],
    [
      "5",
      "44"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 345856c1 = LMFDB 345856.c2: https://www.lmfdb.org/EllipticCurve/Q/345856/c/2\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 345856, minimal discriminant 4841984, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:44:54",
  "updated_at": "2026-09-26 20:44:54"
}