{
  "id": 3327,
  "curve_key": "162971425:-2080497481777",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3395238",
    "2407700260"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6
  ],
  "naive_height": 56.727256309963636,
  "faltings_height": 2.066959450521112,
  "conductor": "90538",
  "bad_primes": [
    "2",
    "7",
    "29",
    "223"
  ],
  "discriminant": "31657879232",
  "regulator": "20.5622253989528665723472328121099234265994",
  "points": [
    [
      "-330",
      "59260"
    ],
    [
      "1304",
      "13422"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 90538d2 = LMFDB 90538.c2: https://www.lmfdb.org/EllipticCurve/Q/90538/c/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 90538, minimal discriminant 31657879232, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:58:23",
  "updated_at": "2026-09-26 20:58:23"
}