{
  "id": 2779,
  "curve_key": "5529:-169533",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-115",
    "225"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 25.8532867390138,
  "faltings_height": 0.21144010731963356,
  "conductor": "9010",
  "bad_primes": [
    "2",
    "5",
    "17",
    "53"
  ],
  "discriminant": "81180100",
  "regulator": "2.36225407250349526690972460616404779585717",
  "points": [
    [
      "0",
      "15"
    ],
    [
      "20",
      "65"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 9010a2 = LMFDB 9010.b2: https://www.lmfdb.org/EllipticCurve/Q/9010/b/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 9010, minimal discriminant 81180100, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:22:05",
  "updated_at": "2026-09-26 20:22:05"
}