{
  "id": 2610,
  "curve_key": "4103164940088769:-262832129910191177979553",
  "ainvs": [
    "1",
    "0",
    "0",
    "-85482602918516",
    "304203846939171027600"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 107.85160502231443,
  "faltings_height": 6.46876172719646,
  "conductor": "4294920630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "47",
    "179"
  ],
  "discriminant": "1536142732043788823072994061259673600",
  "regulator": "13.1520845709902824796775899713527779758570",
  "points": [
    [
      "5291344",
      "183755620"
    ],
    [
      "5334268",
      "12051976"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=44; A=(3q-p)(p+q)^3=-4833, B=-(p+3q)(p-q)^3=64053535. 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 20:12:35",
  "updated_at": "2026-09-26 20:12:35"
}