{
  "id": 2248,
  "curve_key": "2511464421110401:-125858249347368954225601",
  "ainvs": [
    "1",
    "0",
    "0",
    "-52322175439800",
    "145669265717792040000"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 106.37892723788357,
  "faltings_height": 6.513111324995515,
  "conductor": "17250870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "71",
    "89"
  ],
  "discriminant": "373970470890111146078995673911296000000",
  "regulator": "4.802674271271233051092287292269284136064",
  "points": [
    [
      "4194720",
      "34342680"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=40; A=(3q-p)(p+q)^3=-123201, B=-(p+3q)(p-q)^3=50052799. 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 19:49:39",
  "updated_at": "2026-09-26 19:49:39"
}