{
  "id": 2346,
  "curve_key": "14539834776769:-32775704076510757153",
  "ainvs": [
    "1",
    "0",
    "0",
    "-302913224516",
    "37934817438378000"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 90.9237396738329,
  "faltings_height": 5.619531816043088,
  "conductor": "104747370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "37",
    "61"
  ],
  "discriminant": "1157160357150979734413607878672486400",
  "regulator": "7.645505043533549969247661953950982885838",
  "points": [
    [
      "-453756",
      "286509420"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=12; A=(3q-p)(p+q)^3=-4305505, B=-(p+3q)(p-q)^3=-2950753. 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 19:55:51",
  "updated_at": "2026-09-26 19:55:51"
}