{
  "id": 2608,
  "curve_key": "241029714017449:-3740520931794817401493",
  "ainvs": [
    "1",
    "0",
    "1",
    "-5021452375364",
    "4329306215567414786"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 99.34782400949175,
  "faltings_height": 6.020013110277931,
  "conductor": "1313836590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "23",
    "29",
    "47",
    "127"
  ],
  "discriminant": "6482787457546589305113119160368193600",
  "regulator": "40.8161357598636249480470602557701809313496",
  "points": [
    [
      "1263828",
      "40816213"
    ],
    [
      "1432689",
      "274713127"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-40, q=29; A=(3q-p)(p+q)^3=-169037, B=-(p+3q)(p-q)^3=15439923. 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 20:12:27",
  "updated_at": "2026-09-26 20:12:27"
}