{
  "id": 3386,
  "curve_key": "23776479073:-3663717956130961",
  "ainvs": [
    "1",
    "0",
    "0",
    "-495343314",
    "4240373022468"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    8
  ],
  "naive_height": 71.6758879641455,
  "faltings_height": 3.732986298649085,
  "conductor": "6618066",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "23",
    "31"
  ],
  "discriminant": "10713335734636867166994432",
  "regulator": "9.57032739987868529027103429038567741219073",
  "points": [
    [
      "-4284",
      "2508894"
    ],
    [
      "4896",
      "1387710"
    ]
  ],
  "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 = -4/13; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 6618066, torsion ℤ/8ℤ.",
  "created_at": "2026-09-26 21:18:45",
  "updated_at": "2026-09-26 21:18:45"
}