{
  "id": 2212,
  "curve_key": "33565161214438561:-6149401185912527682019441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-699274191967470",
    "7117362425422205856900"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 114.15679516602543,
  "faltings_height": 7.07139277434253,
  "conductor": "37216304790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "53",
    "113",
    "127",
    "233"
  ],
  "discriminant": "28108484220507539632736051979883584000000",
  "regulator": "5.526347195745572913100750670265846735447",
  "points": [
    [
      "61112835/4",
      "172116315/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=60; A=(3q-p)(p+q)^3=79919, B=-(p+3q)(p-q)^3=183247919. 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 19:47:26",
  "updated_at": "2026-09-26 19:47:26"
}