{
  "id": 2481,
  "curve_key": "82832805841:-22606404361614361",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1725683455",
    "26164676056025"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 75.42027007703402,
  "faltings_height": 4.226166609205831,
  "conductor": "1272810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "29"
  ],
  "discriminant": "33153377314362109938441000000",
  "regulator": "2.272854417564613083905797161552345129036",
  "points": [
    [
      "-43510",
      "4366865"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-19, q=10; A=(3q-p)(p+q)^3=-35721, B=-(p+3q)(p-q)^3=268279. 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 20:04:17",
  "updated_at": "2026-09-26 20:04:17"
}