{
  "id": 3371,
  "curve_key": "4889836513:-326716446073681",
  "ainvs": [
    "1",
    "0",
    "0",
    "-101871594",
    "378135545508"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    8
  ],
  "naive_height": 66.93127412084989,
  "faltings_height": 3.511425873341418,
  "conductor": "6981702",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "673"
  ],
  "discriminant": "5888197514236558569414912",
  "regulator": "10.1813611658367064121620662777149449377111",
  "points": [
    [
      "-108",
      "623862"
    ],
    [
      "1602",
      "467226"
    ]
  ],
  "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 = -6/7; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 6981702, torsion ℤ/8ℤ.",
  "created_at": "2026-09-26 21:16:09",
  "updated_at": "2026-09-26 21:16:09"
}