{
  "id": 2218,
  "curve_key": "7229313975738409:-614656177847646596124373",
  "ainvs": [
    "1",
    "0",
    "1",
    "-150610707827884",
    "711407600698698648746"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 109.5507616223683,
  "faltings_height": 6.7893096852690284,
  "conductor": "11133712590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "113",
    "193"
  ],
  "discriminant": "13471532683715201824250721096608560449600",
  "regulator": "3.622230526055361416812335953414398278163",
  "points": [
    [
      "7183993",
      "427063943"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-40, q=51; A=(3q-p)(p+q)^3=256883, B=-(p+3q)(p-q)^3=85153523. 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 19:47:48",
  "updated_at": "2026-09-26 19:47:48"
}