{
  "id": 2474,
  "curve_key": "140540803929:-52300113656144733",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-2927933415",
    "60533270937225"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 77.00629110894043,
  "faltings_height": 4.269108573511534,
  "conductor": "3416490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "29"
  ],
  "discriminant": "23507163010132522151879240100",
  "regulator": "2.885057393778513937692049962828471889818",
  "points": [
    [
      "-49065",
      "9302070"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-18, q=11; A=(3q-p)(p+q)^3=-17493, B=-(p+3q)(p-q)^3=365835. 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 20:03:52",
  "updated_at": "2026-09-26 20:03:52"
}