{
  "id": 2294,
  "curve_key": "101811574663969:-1025122901594187784753",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2121074472166",
    "1186484663051881700"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 96.76243474086179,
  "faltings_height": 5.865093661276581,
  "conductor": "223092870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23"
  ],
  "discriminant": "2581459841354944250740513188505190400",
  "regulator": "3.338974512695796624969556865144302581067",
  "points": [
    [
      "-1678612",
      "131442506"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-19, q=32; A=(3q-p)(p+q)^3=252655, B=-(p+3q)(p-q)^3=10214127. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 19:52:37",
  "updated_at": "2026-09-26 19:52:37"
}