{
  "id": 2484,
  "curve_key": "52531890049:-11612559179817793",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1094414376",
    "13440370812480"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 74.05405875491437,
  "faltings_height": 4.094155957198456,
  "conductor": "1009470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23"
  ],
  "discriminant": "5853845685143298051662745600",
  "regulator": "2.946692958386621495491459920258819406922",
  "points": [
    [
      "-28572",
      "4638696"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=4; A=(3q-p)(p+q)^3=-240065, B=-(p+3q)(p-q)^3=-216513. 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 20:04:28",
  "updated_at": "2026-09-26 20:04:28"
}