{
  "id": 2207,
  "curve_key": "3036930002366481:-166498016129138656544121",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-63269375049302",
    "192706053003846837029"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 106.94887059727897,
  "faltings_height": 6.749484246855232,
  "conductor": "385564410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "41",
    "59"
  ],
  "discriminant": "166577245771067595151708808283890625000000",
  "regulator": "6.036298056353334215725661474809771854676",
  "points": [
    [
      "19944523/4",
      "8741230973/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-27, q=50; A=(3q-p)(p+q)^3=2153559, B=-(p+3q)(p-q)^3=56153559. 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 19:47:06",
  "updated_at": "2026-09-26 19:47:06"
}