{
  "id": 2268,
  "curve_key": "261169051264641:-2316760413789037146561",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-5441021901347",
    "2681437024363157219"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 99.58856705872512,
  "faltings_height": 6.345809310589474,
  "conductor": "707767830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "41",
    "47",
    "53"
  ],
  "discriminant": "7202993281458061907388018044460096000000",
  "regulator": "5.537459445021880653971392715361547862548",
  "points": [
    [
      "2215867",
      "1225638546"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-9, q=44; A=(3q-p)(p+q)^3=6045375, B=-(p+3q)(p-q)^3=18311871. 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 19:50:55",
  "updated_at": "2026-09-26 19:50:55"
}