{
  "id": 2711,
  "curve_key": "208:-8344",
  "ainvs": [
    "0",
    "1",
    "1",
    "-4",
    "8"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "naive_height": 18.058595993361216,
  "faltings_height": -0.44241060722867104,
  "conductor": "35083",
  "bad_primes": [
    "35083"
  ],
  "discriminant": "-35083",
  "regulator": "1.2364281089527077263843947167679416335068828",
  "points": [
    [
      "1",
      "2"
    ],
    [
      "-1",
      "3"
    ],
    [
      "2",
      "3"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Cremona 35083c1 = LMFDB 35083.a1: https://www.lmfdb.org/EllipticCurve/Q/35083/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 35083, minimal discriminant -35083, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:18:50",
  "updated_at": "2026-09-26 20:18:50"
}