{
  "id": 3253,
  "curve_key": "2745:-332397",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-57",
    "399"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    3
  ],
  "naive_height": 25.42817063330389,
  "faltings_height": 0.16837028590242945,
  "conductor": "37962",
  "bad_primes": [
    "2",
    "3",
    "19",
    "37"
  ],
  "discriminant": "-51969978",
  "regulator": "11.4793442785780093742759105522523611603272",
  "points": [
    [
      "7",
      "14"
    ],
    [
      "-35/9",
      "686/27"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 37962m1 = LMFDB 37962.h1: https://www.lmfdb.org/EllipticCurve/Q/37962/h/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 37962, minimal discriminant -51969978, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:46:23",
  "updated_at": "2026-09-26 20:46:23"
}