{
  "id": 3358,
  "curve_key": "53343068275201:-389593849454310728449",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1111313922400",
    "450918714629292032"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    10
  ],
  "naive_height": 94.82329546799305,
  "faltings_height": 5.533543510932255,
  "conductor": "168077130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "101",
    "251"
  ],
  "discriminant": "1980809600967795936308490000000000",
  "regulator": "14.3675842136920189358005985088525832565765",
  "points": [
    [
      "2390591/4",
      "114654409/8"
    ],
    [
      "821837426/1369",
      "541125523244/50653"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/10ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with d=t^2/(t-(t-1)^2), c=td-t, b=cd, at t = 15/17; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 168077130, torsion ℤ/10ℤ.",
  "created_at": "2026-09-26 21:11:35",
  "updated_at": "2026-09-26 21:11:35"
}