{
  "id": 3076,
  "curve_key": "256:3880",
  "ainvs": [
    "0",
    "-1",
    "1",
    "-5",
    "-3"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "naive_height": 16.635532333438686,
  "faltings_height": -0.6716305131204295,
  "conductor": "997",
  "bad_primes": [
    "997"
  ],
  "discriminant": "997",
  "regulator": "0.571019259287366988341108843169484267450998",
  "points": [
    [
      "-1",
      "0"
    ],
    [
      "-3/4",
      "-3/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 997b1 = LMFDB 997.c1: https://www.lmfdb.org/EllipticCurve/Q/997/c/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 997, minimal discriminant 997, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:36:06",
  "updated_at": "2026-09-26 20:36:06"
}