{
  "id": 2193,
  "curve_key": "6288860961933361:-497245940783943476777641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-131017936706945",
    "575516124248439854025"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 109.1326690862753,
  "faltings_height": 6.9090480486649195,
  "conductor": "9193657290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "23",
    "31",
    "131",
    "193"
  ],
  "discriminant": "850400929733720458422857990186618721000000",
  "regulator": "4.403498015035708341992324406165870989522",
  "points": [
    [
      "6299992",
      "384443221"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=54; A=(3q-p)(p+q)^3=2348231, B=-(p+3q)(p-q)^3=80450375. 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 19:46:13",
  "updated_at": "2026-09-26 19:46:13"
}