{
  "id": 2609,
  "curve_key": "156851313858001:-1799279129174032287001",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3267735705375",
    "2082498719788265625"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 98.05895828116651,
  "faltings_height": 6.136712468898145,
  "conductor": "1615817190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "101",
    "127"
  ],
  "discriminant": "359666163515140211088355838765625000000",
  "regulator": "26.2314714362678951965304923824865213742089",
  "points": [
    [
      "-1963968",
      "962683077"
    ],
    [
      "694056",
      "385455477"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=38; A=(3q-p)(p+q)^3=1984375, B=-(p+3q)(p-q)^3=13397751. 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 20:12:31",
  "updated_at": "2026-09-26 20:12:31"
}