{
  "id": 2325,
  "curve_key": "131328441649161:-1504943555259254842341",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-2736009201024",
    "1741833502589400768"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 97.52616746861558,
  "faltings_height": 5.79594283132172,
  "conductor": "64234170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "31"
  ],
  "discriminant": "108499298044104642740159343249000000",
  "regulator": "3.017110715002690897593826278415168216080",
  "points": [
    [
      "941232",
      "21150984"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-24, q=31; A=(3q-p)(p+q)^3=40131, B=-(p+3q)(p-q)^3=11479875. 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 19:54:30",
  "updated_at": "2026-09-26 19:54:30"
}