{
  "id": 2330,
  "curve_key": "24058323070609:-34946447724031734073",
  "ainvs": [
    "1",
    "0",
    "0",
    "-501215063971",
    "40447235690448065"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 92.43450637869795,
  "faltings_height": 5.765559924613126,
  "conductor": "2026094070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "53",
    "67"
  ],
  "discriminant": "7351720584302772926129722517299022400",
  "regulator": "9.167934663419349631959643723994229442238",
  "points": [
    [
      "-428944",
      "420354689"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=14; A=(3q-p)(p+q)^3=-5635305, B=-(p+3q)(p-q)^3=-3308393. 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 19:54:51",
  "updated_at": "2026-09-26 19:54:51"
}