{
  "id": 2361,
  "curve_key": "12678639034681:-44976351037898973421",
  "ainvs": [
    "1",
    "0",
    "1",
    "-264138313223",
    "52055939837894006"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 90.51281918258223,
  "faltings_height": 5.366689830343593,
  "conductor": "163032870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "61",
    "89"
  ],
  "discriminant": "8791835625547574724429969726562500",
  "regulator": "7.327047884495483178115789654747984962426",
  "points": [
    [
      "859143/4",
      "577773677/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-14, q=25; A=(3q-p)(p+q)^3=118459, B=-(p+3q)(p-q)^3=3618459. 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 19:56:48",
  "updated_at": "2026-09-26 19:56:48"
}