{
  "id": 2222,
  "curve_key": "1219279767437169:-42134413044937002505353",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-25401661821608",
    "48766688115388837931"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 104.21111017430486,
  "faltings_height": 6.550932531263791,
  "conductor": "3224706030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "23",
    "53"
  ],
  "discriminant": "21600204349176429668675888390614753934400",
  "regulator": "3.339036684360689327208539158167504488053",
  "points": [
    [
      "2633625",
      "366111157"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-57, q=34; A=(3q-p)(p+q)^3=-1934553, B=-(p+3q)(p-q)^3=33910695. 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 19:48:03",
  "updated_at": "2026-09-26 19:48:03"
}