{
  "id": 2360,
  "curve_key": "10140449230849:29362248747372791807",
  "ainvs": [
    "1",
    "0",
    "0",
    "-211259358976",
    "-33984101803294720"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 89.84266024786594,
  "faltings_height": 5.455826104258235,
  "conductor": "18853890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "31",
    "97"
  ],
  "discriminant": "104506752225180137953045566298521600",
  "regulator": "5.189794376152759453580775800624947687228",
  "points": [
    [
      "-218752",
      "42079616"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=32; A=(3q-p)(p+q)^3=2889727, B=-(p+3q)(p-q)^3=3414015. 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 19:56:44",
  "updated_at": "2026-09-26 19:56:44"
}