{
  "id": 2504,
  "curve_key": "325789239889:-185953814269399513",
  "ainvs": [
    "1",
    "0",
    "0",
    "-6787275831",
    "215223756464745"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 79.5285495174951,
  "faltings_height": 4.118580462794794,
  "conductor": "870870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29"
  ],
  "discriminant": "1254177133752707722958400",
  "regulator": "3.227101207846579633605741685948836266066",
  "points": [
    [
      "-87192",
      "12049821"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=14; A=(3q-p)(p+q)^3=55, B=-(p+3q)(p-q)^3=570807. 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 20:05:42",
  "updated_at": "2026-09-26 20:05:42"
}