{
  "id": 2363,
  "curve_key": "21781216817089:-101617220393220484513",
  "ainvs": [
    "1",
    "0",
    "0",
    "-453775350356",
    "117612485788651920"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 92.13620730127796,
  "faltings_height": 5.415337209150716,
  "conductor": "425683230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "43",
    "47",
    "59"
  ],
  "discriminant": "4291682308755232215502500692889600",
  "regulator": "4.743445650267770211793794524738085880593",
  "points": [
    [
      "366364",
      "23052316"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=4; A=(3q-p)(p+q)^3=-4690913, B=-(p+3q)(p-q)^3=-4642785. 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 19:56:55",
  "updated_at": "2026-09-26 19:56:55"
}