{
  "id": 2223,
  "curve_key": "1117839596244361:-33539428409516929039141",
  "ainvs": [
    "1",
    "0",
    "1",
    "-23288324921758",
    "38818780940691591056"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 103.95052285652395,
  "faltings_height": 6.637659210856534,
  "conductor": "641230590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "131",
    "163"
  ],
  "discriminant": "157361332606169725304029078170606756000000",
  "regulator": "3.240175721120154869198050188258297218308",
  "points": [
    [
      "3810565",
      "2323617917"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-16, q=49; A=(3q-p)(p+q)^3=5857731, B=-(p+3q)(p-q)^3=35975875. 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 19:48:06",
  "updated_at": "2026-09-26 19:48:06"
}