{
  "id": 2392,
  "curve_key": "3656872846081:-6537009653116859521",
  "ainvs": [
    "1",
    "0",
    "0",
    "-76184850960",
    "7565977046073600"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 86.78288845345011,
  "faltings_height": 5.184420165802928,
  "conductor": "58702530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "31",
    "47",
    "79"
  ],
  "discriminant": "3570508003350887533497286656000000",
  "regulator": "7.691755735683768983705320642413298964212",
  "points": [
    [
      "-316320",
      "3944880"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=16; A=(3q-p)(p+q)^3=-266625, B=-(p+3q)(p-q)^3=1764991. 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 19:58:43",
  "updated_at": "2026-09-26 19:58:43"
}