{
  "id": 3240,
  "curve_key": "20785:-2996425",
  "ainvs": [
    "1",
    "0",
    "0",
    "-433",
    "3432"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 29.825960555060213,
  "faltings_height": 0.15978202668477076,
  "conductor": "103525",
  "bad_primes": [
    "5",
    "41",
    "101"
  ],
  "discriminant": "517625",
  "regulator": "5.1502060304058257200075541878505665427029567",
  "points": [
    [
      "11",
      "0"
    ],
    [
      "13",
      "0"
    ],
    [
      "3",
      "45"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 103525c1 = LMFDB 103525.a2: https://www.lmfdb.org/EllipticCurve/Q/103525/a/2\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 103525, minimal discriminant 517625, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:44:15",
  "updated_at": "2026-09-26 20:44:15"
}