{
  "id": 2713,
  "curve_key": "208:-7640",
  "ainvs": [
    "0",
    "-1",
    "1",
    "-4",
    "10"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "naive_height": 17.88230576432113,
  "faltings_height": -0.4584925257426595,
  "conductor": "28571",
  "bad_primes": [
    "28571"
  ],
  "discriminant": "-28571",
  "regulator": "1.2231261170461095956013967947315288068928580",
  "points": [
    [
      "1",
      "2"
    ],
    [
      "2",
      "2"
    ],
    [
      "-1",
      "3"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Cremona 28571a1 = LMFDB 28571.a1: https://www.lmfdb.org/EllipticCurve/Q/28571/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 28571, minimal discriminant -28571, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:18:54",
  "updated_at": "2026-09-26 20:18:54"
}