{
  "id": 2627,
  "curve_key": "18331017330609:-78262421211982570473",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-381896194388",
    "90581601506435831"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 91.61884703127481,
  "faltings_height": 5.447673953031624,
  "conductor": "114504390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "31",
    "41"
  ],
  "discriminant": "20078388500331509364865963932417600",
  "regulator": "17.6407779770580377745836013179429869187130",
  "points": [
    [
      "-501549",
      "395163061"
    ],
    [
      "-441185/4",
      "2899947651/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-15, q=26; A=(3q-p)(p+q)^3=123783, B=-(p+3q)(p-q)^3=4342023. 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 20:13:37",
  "updated_at": "2026-09-26 20:13:37"
}