{
  "id": 3383,
  "curve_key": "576335744007123961:-437535537094177975617030541",
  "ainvs": [
    "1",
    "0",
    "1",
    "-12006994666815083",
    "506406870636197175470306"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 122.68640032408224,
  "faltings_height": 7.593261361625927,
  "conductor": "9692581470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "83",
    "163",
    "167"
  ],
  "discriminant": "9153080591662607617971811845581585062500",
  "regulator": "235.97059532833888803600363768958787067572706",
  "points": [
    [
      "62632515",
      "8653617142"
    ],
    [
      "63263325",
      "-23805218"
    ],
    [
      "198398184105/3136",
      "-3944085519193/175616"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/2ℤ × ℤ/6ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=(10-2t)/(t^2-9), b=c+c^2, at t = 157/165; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 9692581470, torsion ℤ/2ℤ × ℤ/6ℤ.",
  "created_at": "2026-09-26 21:18:16",
  "updated_at": "2026-09-26 21:18:16"
}