{
  "id": 2278,
  "curve_key": "163790272403641:-1153567504899765750061",
  "ainvs": [
    "1",
    "0",
    "1",
    "-3412297341743",
    "1335147290757357806"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 98.18882369564663,
  "faltings_height": 6.229033093261583,
  "conductor": "1795934910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "29",
    "83"
  ],
  "discriminant": "1772757605941160919797732262618164062500",
  "regulator": "5.112579199833635809491981385033606014358",
  "points": [
    [
      "-1982115",
      "559041682"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-58, q=25; A=(3q-p)(p+q)^3=-4779621, B=-(p+3q)(p-q)^3=9720379. 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 19:51:35",
  "updated_at": "2026-09-26 19:51:35"
}