{
  "id": 2270,
  "curve_key": "253661524914889:1800020071993670718587",
  "ainvs": [
    "1",
    "0",
    "1",
    "-5284615102394",
    "-2083357005192081124"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 99.50106574559634,
  "faltings_height": 6.346668191558304,
  "conductor": "4095010830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "29",
    "43",
    "47",
    "137"
  ],
  "discriminant": "7570351750400080079130007456205705763600",
  "regulator": "5.118865964194567396452970609733797698239",
  "points": [
    [
      "2475758",
      "88607673"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-4, q=47; A=(3q-p)(p+q)^3=11528515, B=-(p+3q)(p-q)^3=18173187. 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 19:51:02",
  "updated_at": "2026-09-26 19:51:02"
}