{
  "id": 2291,
  "curve_key": "86580946957761:-798784210357016942241",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1803769728287",
    "924519212929720199"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 96.27630268576694,
  "faltings_height": 5.881146918214117,
  "conductor": "1711710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19"
  ],
  "discriminant": "6352492644226678205708502994944000000",
  "regulator": "3.409857796625362971005525103039801007602",
  "points": [
    [
      "-1318253",
      "1006390006"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-57, q=8; A=(3q-p)(p+q)^3=-9529569, B=-(p+3q)(p-q)^3=-9062625. 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 19:52:25",
  "updated_at": "2026-09-26 19:52:25"
}