{
  "id": 3308,
  "curve_key": "589681:-951410825",
  "ainvs": [
    "1",
    "1",
    "1",
    "-12285",
    "1096051"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    5
  ],
  "naive_height": 41.34691303973407,
  "faltings_height": 1.4924344366860285,
  "conductor": "369278",
  "bad_primes": [
    "2",
    "7",
    "13",
    "2029"
  ],
  "discriminant": "-405171591170528",
  "regulator": "5.87324294708823381569041058299318265095927",
  "points": [
    [
      "37",
      "814"
    ],
    [
      "331",
      "5616"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 369278a1 = LMFDB 369278.a2: https://www.lmfdb.org/EllipticCurve/Q/369278/a/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 369278, minimal discriminant -405171591170528, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:55:19",
  "updated_at": "2026-09-26 20:55:19"
}