{
  "id": 2683,
  "curve_key": "376713:-190717605",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-7848",
    "222700"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "naive_height": 38.51771670991501,
  "faltings_height": 1.2118175445828376,
  "conductor": "349398",
  "bad_primes": [
    "2",
    "3",
    "7",
    "47",
    "59"
  ],
  "discriminant": "9888395954724",
  "regulator": "5.3161952407993944300987564764092639418228401",
  "points": [
    [
      "26",
      "176"
    ],
    [
      "89",
      "428"
    ],
    [
      "21",
      "248"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 349398c2 = LMFDB 349398.c3: https://www.lmfdb.org/EllipticCurve/Q/349398/c/3\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 349398, minimal discriminant 9888395954724, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:17:34",
  "updated_at": "2026-09-26 20:17:34"
}