{
  "id": 2514,
  "curve_key": "2684889769:-130811682216853",
  "ainvs": [
    "1",
    "0",
    "1",
    "-55935204",
    "151397748706"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 65.13271652906496,
  "faltings_height": 3.3759032778540163,
  "conductor": "51870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19"
  ],
  "discriminant": "1297852417956067777440000",
  "regulator": "5.755875100150346457441786253559087504384",
  "points": [
    [
      "-5039",
      "555071"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-16, q=3; A=(3q-p)(p+q)^3=-54925, B=-(p+3q)(p-q)^3=-48013. 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 20:06:20",
  "updated_at": "2026-09-26 20:06:20"
}