{
  "id": 2319,
  "curve_key": "172344402460609:-2262461118149008762273",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3590508384596",
    "2618588957907876240"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 98.34154779185633,
  "faltings_height": 5.857859628498756,
  "conductor": "3116190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "71"
  ],
  "discriminant": "199850251649122942309906608291840000",
  "regulator": "6.117010915949899256417809386516737805451",
  "points": [
    [
      "-2167544",
      "467471980"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-25, q=32; A=(3q-p)(p+q)^3=41503, B=-(p+3q)(p-q)^3=13148703. 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 19:54:09",
  "updated_at": "2026-09-26 19:54:09"
}