{
  "id": 3176,
  "curve_key": "2376976:-3584844224",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-49520",
    "4165632"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "naive_height": 44.04401894859221,
  "faltings_height": 1.57038939521908,
  "conductor": "305040",
  "bad_primes": [
    "2",
    "3",
    "5",
    "31",
    "41"
  ],
  "discriminant": "334977845760000",
  "regulator": "3.9296421030520191182456382134416567036404786",
  "points": [
    [
      "154",
      "410"
    ],
    [
      "72",
      "984"
    ],
    [
      "149",
      "270"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 305040s2 = LMFDB 305040.s3: https://www.lmfdb.org/EllipticCurve/Q/305040/s/3\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 305040, minimal discriminant 334977845760000, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:40:59",
  "updated_at": "2026-09-26 20:40:59"
}