{
  "id": 3387,
  "curve_key": "59239882017:-14418579182058801",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1234164209",
    "16688478890657"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    9
  ],
  "naive_height": 74.4145879816982,
  "faltings_height": 3.795288659189138,
  "conductor": "524286",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "73"
  ],
  "discriminant": "-658995091276965605277696",
  "regulator": "4.916870444873368745290116405034967251162",
  "points": [
    [
      "71679/25",
      "453512132/125"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/9ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=t^2(t-1), b=c(t^2-t+1), at t = 1/8; converted to the global minimal model. The 1 witness points were found with PARI/GP ellrank. Conductor 524286, torsion ℤ/9ℤ.",
  "created_at": "2026-09-26 21:18:55",
  "updated_at": "2026-09-26 21:18:55"
}