{
  "id": 2569,
  "curve_key": "584648689:-14136467639113",
  "ainvs": [
    "1",
    "0",
    "0",
    "-12180181",
    "16360637345"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 60.55956507954258,
  "faltings_height": 2.6477959421127863,
  "conductor": "30030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13"
  ],
  "discriminant": "834505270358760000",
  "regulator": "3.270112321583608897548806044893333846473",
  "points": [
    [
      "-2314",
      "180479"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-25, q=1; A=(3q-p)(p+q)^3=-387072, B=-(p+3q)(p-q)^3=-386672. 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 20:09:53",
  "updated_at": "2026-09-26 20:09:53"
}