{
  "id": 3137,
  "curve_key": "10768:769600",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-224",
    "-816"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 27.853002155653527,
  "faltings_height": 0.3512237922106519,
  "conductor": "9744",
  "bad_primes": [
    "2",
    "3",
    "7",
    "29"
  ],
  "discriminant": "379782144",
  "regulator": "1.88643100546349253788780218449459888751273",
  "points": [
    [
      "24",
      "84"
    ],
    [
      "-8",
      "20"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 9744c2 = LMFDB 9744.c2: https://www.lmfdb.org/EllipticCurve/Q/9744/c/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 9744, minimal discriminant 379782144, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:39:00",
  "updated_at": "2026-09-26 20:39:00"
}