{
  "id": 3385,
  "curve_key": "13355170273:-1543312412323921",
  "ainvs": [
    "1",
    "0",
    "0",
    "-278232714",
    "1786218031908"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    8
  ],
  "naive_height": 69.94550829955111,
  "faltings_height": 3.5011688355126704,
  "conductor": "3542322",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "23",
    "193"
  ],
  "discriminant": "128831394594552830836992",
  "regulator": "6.37106246009307405102742021086654808275427",
  "points": [
    [
      "-2916",
      "1605438"
    ],
    [
      "13716",
      "735030"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/8ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with b=(2t-1)(t-1), c=b/t, at t = 2/23; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 3542322, torsion ℤ/8ℤ.",
  "created_at": "2026-09-26 21:18:36",
  "updated_at": "2026-09-26 21:18:36"
}