{
  "id": 2405,
  "curve_key": "2630847974769:-4119057152427049353",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-54809332808",
    "4767440962086731"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 85.79498200205207,
  "faltings_height": 5.071478046617846,
  "conductor": "7580430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "31"
  ],
  "discriminant": "718991272616515905668595321960000",
  "regulator": "6.438694510700982008184660144246878452549",
  "points": [
    [
      "-178455",
      "94244977"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-9, q=22; A=(3q-p)(p+q)^3=164775, B=-(p+3q)(p-q)^3=1698087. 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 19:59:35",
  "updated_at": "2026-09-26 19:59:35"
}