{
  "id": 2266,
  "curve_key": "273002207993641:-1767065295841066335061",
  "ainvs": [
    "1",
    "0",
    "1",
    "-5687545999868",
    "2045213988816845306"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 99.72150299690878,
  "faltings_height": 6.3683102223224,
  "conductor": "1068411630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "37",
    "53",
    "127"
  ],
  "discriminant": "9967818821123358773285084760475521000000",
  "regulator": "8.248083947624020720490962207777232765785",
  "points": [
    [
      "-2518455",
      "630109207"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-8, q=45; A=(3q-p)(p+q)^3=7243379, B=-(p+3q)(p-q)^3=18907379. 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 19:50:47",
  "updated_at": "2026-09-26 19:50:47"
}