{
  "id": 2619,
  "curve_key": "56752271974729:-420258262187216625733",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1182338999474",
    "486409927151398916"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 95.00915041885703,
  "faltings_height": 5.8062206470847,
  "conductor": "259549710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "29",
    "109"
  ],
  "discriminant": "3571682249444523930229353956385998400",
  "regulator": "18.0386134745782688233569685206620668602776",
  "points": [
    [
      "476460",
      "176498572"
    ],
    [
      "518688",
      "112396468"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-40, q=23; A=(3q-p)(p+q)^3=-535517, B=-(p+3q)(p-q)^3=7251363. 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 20:13:08",
  "updated_at": "2026-09-26 20:13:08"
}