{
  "id": 2471,
  "curve_key": "1548233928481:-1926423522770307121",
  "ainvs": [
    "1",
    "0",
    "0",
    "-32254873510",
    "2229654167152100"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 84.20440798880675,
  "faltings_height": 4.636184918801361,
  "conductor": "7752570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "29",
    "67"
  ],
  "discriminant": "30641392183312533159936000000",
  "regulator": "3.544234449999414526797926631828502525826",
  "points": [
    [
      "-176020",
      "49621130"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-19, q=16; A=(3q-p)(p+q)^3=-1809, B=-(p+3q)(p-q)^3=1243375. 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 20:03:40",
  "updated_at": "2026-09-26 20:03:40"
}