{
  "id": 2281,
  "curve_key": "142752072067081:-1457086051945010626021",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2974001501398",
    "1686441941917711256"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 97.77639143914621,
  "faltings_height": 6.1407956923069404,
  "conductor": "87717630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "127"
  ],
  "discriminant": "454817104728198841795673573472656250000",
  "regulator": "5.762305545586032285147944813002522381733",
  "points": [
    [
      "-1953350",
      "207260252"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-52, q=25; A=(3q-p)(p+q)^3=-2499741, B=-(p+3q)(p-q)^3=10500259. 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 19:51:46",
  "updated_at": "2026-09-26 19:51:46"
}