{
  "id": 2632,
  "curve_key": "7140086008441:-13137662542159261261",
  "ainvs": [
    "1",
    "0",
    "1",
    "-148751791843",
    "15205615546331306"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 88.79023781462288,
  "faltings_height": 5.4293506377652445,
  "conductor": "863272410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "89"
  ],
  "discriminant": "110769283052405048651183136095062500",
  "regulator": "8.00740071367575713015450380841763243201902",
  "points": [
    [
      "-428120",
      "20721662"
    ],
    [
      "-413435",
      "77905052"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-38, q=17; A=(3q-p)(p+q)^3=-824229, B=-(p+3q)(p-q)^3=2162875. 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 20:14:06",
  "updated_at": "2026-09-26 20:14:06"
}