{
  "id": 3388,
  "curve_key": "1417957103233441:-64258548648382667723761",
  "ainvs": [
    "1",
    "0",
    "0",
    "-29540772984030",
    "74373317733156264900"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    9
  ],
  "naive_height": 105.03440344138531,
  "faltings_height": 6.751007594301276,
  "conductor": "8327367510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "331",
    "10891"
  ],
  "discriminant": "-739706710209979539570592866413751000000000",
  "regulator": "21.2087435722351243116767456669401933184984",
  "points": [
    [
      "-43558515/16",
      "742647676155/64"
    ],
    [
      "45376485/16",
      "234232961655/64"
    ]
  ],
  "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 = -11/10; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 8327367510, torsion ℤ/9ℤ.",
  "created_at": "2026-09-26 21:19:04",
  "updated_at": "2026-09-26 21:19:04"
}