{
  "id": 3272,
  "curve_key": "45185296:-303735237056",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-941360",
    "351859200"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 52.87884684642977,
  "faltings_height": 1.979892184007034,
  "conductor": "68880",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "41"
  ],
  "discriminant": "127606845542400",
  "regulator": "9.00194907641696072474973149333779524640078",
  "points": [
    [
      "570",
      "390"
    ],
    [
      "562",
      "58"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 68880br4 = LMFDB 68880.q2: https://www.lmfdb.org/EllipticCurve/Q/68880/q/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 68880, minimal discriminant 127606845542400, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:49:29",
  "updated_at": "2026-09-26 20:49:29"
}