{
  "id": 3361,
  "curve_key": "3656128:-4855178240",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-76169",
    "5644809"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "naive_height": 45.33574566565268,
  "faltings_height": 1.807239472662125,
  "conductor": "121000128",
  "bad_primes": [
    "2",
    "3",
    "73",
    "89",
    "97"
  ],
  "discriminant": "14641030976016384",
  "regulator": "63.30217928691081122069388058741387885043208495",
  "points": [
    [
      "-211",
      "3504"
    ],
    [
      "-65",
      "3212"
    ],
    [
      "419",
      "6864"
    ],
    [
      "665",
      "15768"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = 146, b = 534; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 121000128, torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-26 21:12:04",
  "updated_at": "2026-09-26 21:12:04"
}