{
  "id": 3367,
  "curve_key": "60127517526658561:-14743723906629775718749441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1252656615138720",
    "17064495157914929894400"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 115.90573198201584,
  "faltings_height": 7.274484738188986,
  "conductor": "83973799470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "71",
    "109",
    "131",
    "251"
  ],
  "discriminant": "1576189838975742673577701543174718016000000",
  "regulator": "265.29989440217662032409007268670884005413221",
  "points": [
    [
      "-22294560",
      "184159104480"
    ],
    [
      "19160427660/529",
      "1686132546866460/12167"
    ],
    [
      "34638558240/1681",
      "89367027636480/68921"
    ]
  ],
  "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 = 19/30; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 83973799470, torsion ℤ/2ℤ × ℤ/6ℤ.",
  "created_at": "2026-09-26 21:13:32",
  "updated_at": "2026-09-26 21:13:32"
}