{
  "id": 3372,
  "curve_key": "7280065521:-622745389834569",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-151668032",
    "720808044131"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    9
  ],
  "naive_height": 68.13031773425651,
  "faltings_height": 3.4862511722068126,
  "conductor": "1302210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "53"
  ],
  "discriminant": "-1141811887702941000000000",
  "regulator": "3.161279463738307638216521849959339076915",
  "points": [
    [
      "-15681/4",
      "8978267/8"
    ]
  ],
  "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 = -5/2; converted to the global minimal model. The 1 witness points were found with PARI/GP ellrank. Conductor 1302210, torsion ℤ/9ℤ.",
  "created_at": "2026-09-26 21:16:20",
  "updated_at": "2026-09-26 21:16:20"
}