{
  "id": 2388,
  "curve_key": "3974937797889:-6872672182271702913",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-82811204123",
    "7954502395245131"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 87.03309064674778,
  "faltings_height": 5.2408466439966945,
  "conductor": "117810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17"
  ],
  "discriminant": "9010945022845577916088355232153600",
  "regulator": "4.389108076187385496103875540777356441592",
  "points": [
    [
      "-284277",
      "92458810"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-33, q=16; A=(3q-p)(p+q)^3=-397953, B=-(p+3q)(p-q)^3=1764735. 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 19:58:27",
  "updated_at": "2026-09-26 19:58:27"
}