{
  "id": 3356,
  "curve_key": "202305754913089:-2723220074000749190113",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4214703227356",
    "3151874734423746320"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 98.82240392135323,
  "faltings_height": 6.1780802912941155,
  "conductor": "4661767110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "53",
    "101"
  ],
  "discriminant": "499979849606919636436410282650206310400",
  "regulator": "37.045958336204883939881531575268773036738518",
  "points": [
    [
      "7603808",
      "20262926396"
    ],
    [
      "-18928808/9",
      "44499213452/27"
    ],
    [
      "2438513828/1681",
      "20684439274696/68921"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/2ℤ × ℤ/6ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=(10-2t)/(t^2-9), b=c+c^2, at t = -47/6; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 4661767110, torsion ℤ/2ℤ × ℤ/6ℤ.",
  "created_at": "2026-09-26 21:11:16",
  "updated_at": "2026-09-26 21:11:16"
}