{
  "id": 3354,
  "curve_key": "42013648:-121356267200",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-875284",
    "140750404"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "naive_height": 52.66051522752901,
  "faltings_height": 2.443283452157681,
  "conductor": "5245656",
  "bad_primes": [
    "2",
    "3",
    "13",
    "17",
    "23",
    "43"
  ],
  "discriminant": "34394042302997854464",
  "regulator": "22.460458169304061878432358751804900994264210",
  "points": [
    [
      "-731",
      "19734"
    ],
    [
      "868",
      "5850"
    ],
    [
      "1492",
      "46410"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/2ℤ × ℤ/4ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with b=t^2-1/16, c=0, at t = -17/276; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 5245656, torsion ℤ/2ℤ × ℤ/4ℤ.",
  "created_at": "2026-09-26 21:10:55",
  "updated_at": "2026-09-26 21:10:55"
}