{
  "id": 3393,
  "curve_key": "79729168:-392270091200",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-1661024",
    "454569984"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "naive_height": 54.5824381476161,
  "faltings_height": 2.595102717473079,
  "conductor": "85068816",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "53",
    "281"
  ],
  "discriminant": "204248718332035743744",
  "regulator": "36.34652530478295612169338456330656251202086406",
  "points": [
    [
      "-846",
      "35406"
    ],
    [
      "3088",
      "157360"
    ],
    [
      "34560",
      "6420288"
    ],
    [
      "-3680/9",
      "881216/27"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = 833, b = 2529; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 85068816, torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-26 21:19:55",
  "updated_at": "2026-09-26 21:19:55"
}