{
  "id": 2334,
  "curve_key": "21965537330881:-63519640725411954721",
  "ainvs": [
    "1",
    "0",
    "0",
    "-457615361060",
    "73518064556835600"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 92.16148756831956,
  "faltings_height": 5.719794336601214,
  "conductor": "25025910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "89",
    "103"
  ],
  "discriminant": "3798202426047728168730624000000000000",
  "regulator": "7.939729016426670158511778492965385923626",
  "points": [
    [
      "714610",
      "333453640"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-7, q=32; A=(3q-p)(p+q)^3=1609375, B=-(p+3q)(p-q)^3=5279391. 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 19:55:06",
  "updated_at": "2026-09-26 19:55:06"
}