{
  "id": 3328,
  "curve_key": "14687056:-56286224704",
  "ainvs": [
    "0",
    "1",
    "0",
    "-305980",
    "65044100"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6
  ],
  "naive_height": 49.50743135887347,
  "faltings_height": 1.600255590457306,
  "conductor": "60180",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "59"
  ],
  "discriminant": "51128928000",
  "regulator": "8.97731484596299317156647887423317064156581",
  "points": [
    [
      "400",
      "2610"
    ],
    [
      "680",
      "13110"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 60180k2 = LMFDB 60180.k2: https://www.lmfdb.org/EllipticCurve/Q/60180/k/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 60180, minimal discriminant 51128928000, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:58:33",
  "updated_at": "2026-09-26 20:58:33"
}