{
  "id": 2414,
  "curve_key": "2086077981409:-1711493248785323473",
  "ainvs": [
    "1",
    "0",
    "0",
    "-43459957946",
    "1980891342208740"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 85.09892056510256,
  "faltings_height": 5.136506165396619,
  "conductor": "85278270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "29",
    "67"
  ],
  "discriminant": "3558345449879542067954509735526400",
  "regulator": "4.782240664780350872678140721593953835782",
  "points": [
    [
      "47806",
      "3511864"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-5, q=24; A=(3q-p)(p+q)^3=528143, B=-(p+3q)(p-q)^3=1634063. 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 20:00:07",
  "updated_at": "2026-09-26 20:00:07"
}