{
  "id": 2401,
  "curve_key": "3024949070529:-4668303650562393633",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-63019772303",
    "5403144980131031"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 86.21374611324259,
  "faltings_height": 5.1643040965241855,
  "conductor": "11932830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "31",
    "47"
  ],
  "discriminant": "3406356229868532261113144338022400",
  "regulator": "9.947111350267433677982760968189526509419",
  "points": [
    [
      "-283829",
      "20756742"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-39, q=8; A=(3q-p)(p+q)^3=-1876833, B=-(p+3q)(p-q)^3=-1557345. 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 19:59:18",
  "updated_at": "2026-09-26 19:59:18"
}