{
  "id": 2469,
  "curve_key": "395897367321:-248992311080256381",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-8247861819",
    "288187607197233"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 80.1132625235335,
  "faltings_height": 4.419829521333051,
  "conductor": "4823910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "31"
  ],
  "discriminant": "31073030682941202153215062500",
  "regulator": "5.341180344797384660000792675053895790776",
  "points": [
    [
      "59913",
      "2985426"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-18, q=13; A=(3q-p)(p+q)^3=-7125, B=-(p+3q)(p-q)^3=625611. 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 20:03:30",
  "updated_at": "2026-09-26 20:03:30"
}