{
  "id": 3241,
  "curve_key": "92881:-28306745",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1935",
    "31956"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 34.31722314868304,
  "faltings_height": 0.4262116519638698,
  "conductor": "278499",
  "bad_primes": [
    "3",
    "13",
    "37",
    "193"
  ],
  "discriminant": "835497",
  "regulator": "7.3351883682610550005877424535280515111017028",
  "points": [
    [
      "24",
      "-4"
    ],
    [
      "29",
      "21"
    ],
    [
      "13",
      "89"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 278499a1 = LMFDB 278499.a2: https://www.lmfdb.org/EllipticCurve/Q/278499/a/2\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 278499, minimal discriminant 835497, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:44:25",
  "updated_at": "2026-09-26 20:44:25"
}