{
  "id": 2269,
  "curve_key": "1903651627220281:-83057490428774025347821",
  "ainvs": [
    "1",
    "0",
    "1",
    "-39659408900423",
    "96131351357982158006"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 105.5476510369263,
  "faltings_height": 6.408050719993616,
  "conductor": "12353367390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "71",
    "163"
  ],
  "discriminant": "44248342403321467621188119899092562500",
  "regulator": "4.050728159588305093568475764046947027430",
  "points": [
    [
      "3681720",
      "148023277"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-46, q=39; A=(3q-p)(p+q)^3=-55909, B=-(p+3q)(p-q)^3=43602875. 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 19:50:59",
  "updated_at": "2026-09-26 19:50:59"
}