{
  "id": 2191,
  "curve_key": "9317792573926281:-898815352782826534966821",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-194120678623464",
    "1040295595732515182448"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 110.31210644179208,
  "faltings_height": 6.952646710996916,
  "conductor": "4931436510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "43",
    "67"
  ],
  "discriminant": "644351188018896289853475274062542450250000",
  "regulator": "4.277297760151124856246391460962681351932",
  "points": [
    [
      "8253012",
      "584190444"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-36, q=55; A=(3q-p)(p+q)^3=1378659, B=-(p+3q)(p-q)^3=97210659. 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 19:46:05",
  "updated_at": "2026-09-26 19:46:05"
}