{
  "id": 3329,
  "curve_key": "25287289:-127160844877",
  "ainvs": [
    "1",
    "0",
    "1",
    "-526819",
    "147133002"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6
  ],
  "naive_height": 51.13743724913948,
  "faltings_height": 1.7234981648964023,
  "conductor": "351130",
  "bad_primes": [
    "2",
    "5",
    "13",
    "37",
    "73"
  ],
  "discriminant": "138466710980",
  "regulator": "23.1354015500200555098541939168503888796475",
  "points": [
    [
      "123",
      "9114"
    ],
    [
      "-542",
      "16809"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 351130a1 = LMFDB 351130.a4: https://www.lmfdb.org/EllipticCurve/Q/351130/a/4\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 351130, minimal discriminant 138466710980, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:58:42",
  "updated_at": "2026-09-26 20:58:42"
}