{
  "id": 3258,
  "curve_key": "391225:-244703341",
  "ainvs": [
    "1",
    "0",
    "1",
    "-8151",
    "282542"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    3
  ],
  "naive_height": 38.6311143635458,
  "faltings_height": 0.617142951405071,
  "conductor": "7826",
  "bad_primes": [
    "2",
    "7",
    "13",
    "43"
  ],
  "discriminant": "-15652",
  "regulator": "6.33037617317133995821465976173349115765320",
  "points": [
    [
      "57",
      "34"
    ],
    [
      "38",
      "148"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 7826f1 = LMFDB 7826.b1: https://www.lmfdb.org/EllipticCurve/Q/7826/b/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 7826, minimal discriminant -15652, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:47:11",
  "updated_at": "2026-09-26 20:47:11"
}