{
  "id": 2993,
  "curve_key": "-11999:1508399",
  "ainvs": [
    "1",
    "0",
    "0",
    "250",
    "-1725"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 28.45311876282399,
  "faltings_height": 0.48273058963864374,
  "conductor": "22515",
  "bad_primes": [
    "3",
    "5",
    "19",
    "79"
  ],
  "discriminant": "-2316455775",
  "regulator": "7.22815580881490801666629265464477590214817",
  "points": [
    [
      "7",
      "16"
    ],
    [
      "70",
      "565"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 22515f1 = LMFDB 22515.e4: https://www.lmfdb.org/EllipticCurve/Q/22515/e/4\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 22515, minimal discriminant -2316455775, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:32:22",
  "updated_at": "2026-09-26 20:32:22"
}