{
  "id": 3089,
  "curve_key": "2113:-97345",
  "ainvs": [
    "1",
    "0",
    "0",
    "-44",
    "109"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "naive_height": 22.972033296826023,
  "faltings_height": -0.2823156221321254,
  "conductor": "24301",
  "bad_primes": [
    "19",
    "1279"
  ],
  "discriminant": "-24301",
  "regulator": "1.0885646024251077131442859489002163266618169",
  "points": [
    [
      "4",
      "-3"
    ],
    [
      "3",
      "1"
    ],
    [
      "7",
      "9"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 24301a1 = LMFDB 24301.a1: https://www.lmfdb.org/EllipticCurve/Q/24301/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 24301, minimal discriminant -24301, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:36:45",
  "updated_at": "2026-09-26 20:36:45"
}