{
  "id": 2702,
  "curve_key": "273:-9369",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-6",
    "12"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "naive_height": 18.290323291902375,
  "faltings_height": -0.4292963394276126,
  "conductor": "39023",
  "bad_primes": [
    "39023"
  ],
  "discriminant": "-39023",
  "regulator": "1.2676518356606668794268217392553456420832999",
  "points": [
    [
      "2",
      "1"
    ],
    [
      "0",
      "3"
    ],
    [
      "3",
      "2"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Cremona 39023a1 = LMFDB 39023.a1: https://www.lmfdb.org/EllipticCurve/Q/39023/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 39023, minimal discriminant -39023, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:18:25",
  "updated_at": "2026-09-26 20:18:25"
}