{
  "id": 2362,
  "curve_key": "9411557447961:-16193966942769596541",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-196074113499",
    "18743066313400593"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 89.61887869712864,
  "faltings_height": 5.5138698142556155,
  "conductor": "13026510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "29",
    "31"
  ],
  "discriminant": "330675261174527779289636788392562500",
  "regulator": "5.306914798037420272856372045031311186720",
  "points": [
    [
      "-477471",
      "59479341"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-6, q=29; A=(3q-p)(p+q)^3=1131531, B=-(p+3q)(p-q)^3=3472875. 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 19:56:51",
  "updated_at": "2026-09-26 19:56:51"
}