{
  "id": 2719,
  "curve_key": "564673:-83694241",
  "ainvs": [
    "1",
    "0",
    "0",
    "-11764",
    "95888"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    8
  ],
  "naive_height": 39.73200624455939,
  "faltings_height": 1.376834167417425,
  "conductor": "4074",
  "bad_primes": [
    "2",
    "3",
    "7",
    "97"
  ],
  "discriminant": "100141447053312",
  "regulator": "1.334530946710411858526666866257105810724",
  "points": [
    [
      "8",
      "44"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 4074l1 = LMFDB 4074.k6: https://www.lmfdb.org/EllipticCurve/Q/4074/k/6\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 4074, minimal discriminant 100141447053312, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:19:11",
  "updated_at": "2026-09-26 20:19:11"
}