{
  "id": 3378,
  "curve_key": "12490128:17334976320",
  "ainvs": [
    "0",
    "0",
    "0",
    "-260211",
    "-20063630"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "naive_height": 49.02134739074342,
  "faltings_height": 2.1432435556668836,
  "conductor": "27127152",
  "bad_primes": [
    "2",
    "3",
    "13",
    "43",
    "337"
  ],
  "discriminant": "953703558817910784",
  "regulator": "43.24318052489523385678178765307101708180803617",
  "points": [
    [
      "-430",
      "3510"
    ],
    [
      "-423",
      "3784"
    ],
    [
      "-391",
      "4680"
    ],
    [
      "-337",
      "5418"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = -387, b = -1011; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 27127152, torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-26 21:17:23",
  "updated_at": "2026-09-26 21:17:23"
}