{
  "id": 3391,
  "curve_key": "4280957718891361:-280098902908032263806609",
  "ainvs": [
    "1",
    "0",
    "0",
    "-89186619143570",
    "324188537600226487812"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    10
  ],
  "naive_height": 107.97885943670582,
  "faltings_height": 6.337883405657676,
  "conductor": "42283410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "181",
    "599"
  ],
  "discriminant": "572209808730197167968750000000000",
  "regulator": "99.5152849901246057609435579758155703645584",
  "points": [
    [
      "13560664",
      "40098719518"
    ],
    [
      "7580855050756/1270129",
      "3030673010666398994/1431435383"
    ]
  ],
  "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 = 1/26; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 42283410, torsion ℤ/10ℤ.",
  "created_at": "2026-09-26 21:19:36",
  "updated_at": "2026-09-26 21:19:36"
}