{
  "id": 2240,
  "curve_key": "864090548260681:-25293922014119202372421",
  "ainvs": [
    "1",
    "0",
    "1",
    "-18001886422098",
    "29275371201369652756"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 103.17809604140693,
  "faltings_height": 6.426771903255814,
  "conductor": "9834099990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "47",
    "151"
  ],
  "discriminant": "3120865821406250109489855778281740250000",
  "regulator": "5.389067853517745636418739778542079982483",
  "points": [
    [
      "-4891510",
      "543980952"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-52, q=33; A=(3q-p)(p+q)^3=-1035709, B=-(p+3q)(p-q)^3=28863875. 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 19:49:09",
  "updated_at": "2026-09-26 19:49:09"
}