{
  "id": 2389,
  "curve_key": "3959221472809:-1333572960858569173",
  "ainvs": [
    "1",
    "0",
    "1",
    "-82483780684",
    "1543480349567546"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 87.02120557227467,
  "faltings_height": 5.31824343780574,
  "conductor": "27999510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "23",
    "31"
  ],
  "discriminant": "34886632350765265330922544382592400",
  "regulator": "3.570057421099434632127832332576234965564",
  "points": [
    [
      "-92744",
      "91674017"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-4, q=27; A=(3q-p)(p+q)^3=1034195, B=-(p+3q)(p-q)^3=2293907. 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 19:58:31",
  "updated_at": "2026-09-26 19:58:31"
}