{
  "id": 3271,
  "curve_key": "5158096:9324046144",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-107460",
    "-10755900"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 46.36823423134588,
  "faltings_height": 1.8736526875667878,
  "conductor": "62040",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "47"
  ],
  "discriminant": "29107772100000000",
  "regulator": "4.36782012405061090810557903857322414456116",
  "points": [
    [
      "450",
      "5640"
    ],
    [
      "-120",
      "630"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 62040s2 = LMFDB 62040.i4: https://www.lmfdb.org/EllipticCurve/Q/62040/i/4\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 62040, minimal discriminant 29107772100000000, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:49:19",
  "updated_at": "2026-09-26 20:49:19"
}