{
  "id": 2198,
  "curve_key": "4987664398237249:-351531083493754846692193",
  "ainvs": [
    "1",
    "0",
    "0",
    "-103909674963276",
    "406864671310484084880"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 108.43723241590804,
  "faltings_height": 6.83638315383027,
  "conductor": "1313542230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "31",
    "83"
  ],
  "discriminant": "291092496811796384029191730644196416000000",
  "regulator": "4.011023050457090261078550409177408995752",
  "points": [
    [
      "6102486",
      "123318000"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=52; A=(3q-p)(p+q)^3=1731807, B=-(p+3q)(p-q)^3=71473375. 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 19:46:32",
  "updated_at": "2026-09-26 19:46:32"
}