{
  "id": 2925,
  "curve_key": "3529:-67717",
  "ainvs": [
    "1",
    "0",
    "1",
    "-74",
    "72"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 24.50630947102581,
  "faltings_height": 0.10376764325435564,
  "conductor": "325430",
  "bad_primes": [
    "2",
    "5",
    "7",
    "4649"
  ],
  "discriminant": "22780100",
  "regulator": "2.8610559810006646002878997685082151371473513",
  "points": [
    [
      "-9",
      "9"
    ],
    [
      "-6",
      "20"
    ],
    [
      "15",
      "41"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 325430a1 = LMFDB 325430.a1: https://www.lmfdb.org/EllipticCurve/Q/325430/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 325430, minimal discriminant 22780100, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:28:39",
  "updated_at": "2026-09-26 20:28:39"
}