{
  "id": 3263,
  "curve_key": "22665465:-107906336973",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-472197",
    "125009643"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    3
  ],
  "naive_height": 50.80905887508318,
  "faltings_height": 1.4949530516238052,
  "conductor": "328482",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "79"
  ],
  "discriminant": "328482",
  "regulator": "93.2803951522359627041126609975247237397707",
  "points": [
    [
      "-2573/4",
      "104485/8"
    ],
    [
      "650623/1764",
      "57436063/74088"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 328482o1 = LMFDB 328482.o3: https://www.lmfdb.org/EllipticCurve/Q/328482/o/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 328482, minimal discriminant 328482, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:48:02",
  "updated_at": "2026-09-26 20:48:02"
}