{
  "id": 3183,
  "curve_key": "9804025:-19567530125",
  "ainvs": [
    "1",
    "1",
    "0",
    "-204250",
    "22562500"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "naive_height": 48.294910720819466,
  "faltings_height": 2.0617804842957144,
  "conductor": "344850",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19"
  ],
  "discriminant": "323763845006250000",
  "regulator": "5.7628604225632419419723762837766849809436765",
  "points": [
    [
      "0",
      "4750"
    ],
    [
      "400",
      "2050"
    ],
    [
      "391",
      "1438"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 344850c2 = LMFDB 344850.c3: https://www.lmfdb.org/EllipticCurve/Q/344850/c/3\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 344850, minimal discriminant 323763845006250000, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:41:18",
  "updated_at": "2026-09-26 20:41:18"
}