{
  "id": 2659,
  "curve_key": "598552773721:441489682079818019",
  "ainvs": [
    "1",
    "0",
    "1",
    "-12469849453",
    "-510984467487244"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 81.35334160410115,
  "faltings_height": 4.715515630963802,
  "conductor": "8645010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "23",
    "67"
  ],
  "discriminant": "11300707893288624291305123062500",
  "regulator": "11.9662052506001572143583411612297068344079",
  "points": [
    [
      "-74129",
      "2496224"
    ],
    [
      "-55175",
      "3039572"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=11; A=(3q-p)(p+q)^3=-815189, B=-(p+3q)(p-q)^3=-91125. 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 20:16:11",
  "updated_at": "2026-09-26 20:16:11"
}