{
  "id": 2607,
  "curve_key": "399039217408561:-7940661356815772374441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-8313317029345",
    "9190579581315910025"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 100.86024245169857,
  "faltings_height": 6.230001107562624,
  "conductor": "10872959790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "43",
    "47",
    "137"
  ],
  "discriminant": "281150699887800040379071577560281000000",
  "regulator": "16.4872573350650799828234160001457672043782",
  "points": [
    [
      "1550810",
      "166320755"
    ],
    [
      "1919552",
      "551915261"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=30; A=(3q-p)(p+q)^3=-673081, B=-(p+3q)(p-q)^3=19630919. 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 20:12:23",
  "updated_at": "2026-09-26 20:12:23"
}