{
  "id": 1040,
  "curve_key": "850273:-784017809",
  "ainvs": [
    "1",
    "1",
    "1",
    "-17714",
    "900047"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    8
  ],
  "naive_height": 40.9599382601129,
  "faltings_height": 1.069400962759865,
  "conductor": "966",
  "bad_primes": [
    "2",
    "3",
    "7",
    "23"
  ],
  "discriminant": "19093020912",
  "regulator": "2.429046614030699609497398526925843435269",
  "points": [
    [
      "79",
      "-1"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 966g4 = LMFDB 966.g2: https://www.lmfdb.org/EllipticCurve/Q/966/g/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 966, minimal discriminant 19093020912, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:19:42",
  "updated_at": "2026-09-23 15:19:42"
}