{
  "id": 3082,
  "curve_key": "-416:-5464",
  "ainvs": [
    "0",
    "1",
    "1",
    "9",
    "9"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "naive_height": 18.09205578078379,
  "faltings_height": -0.3968568041250874,
  "conductor": "58939",
  "bad_primes": [
    "17",
    "3467"
  ],
  "discriminant": "-58939",
  "regulator": "3.1813721975881424995385102317190892337351693",
  "points": [
    [
      "-1",
      "0"
    ],
    [
      "1",
      "4"
    ],
    [
      "-3/4",
      "9/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 58939a1 = LMFDB 58939.a1: https://www.lmfdb.org/EllipticCurve/Q/58939/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 58939, minimal discriminant -58939, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:36:25",
  "updated_at": "2026-09-26 20:36:25"
}