{
  "id": 2480,
  "curve_key": "1767296605561:-2349437625293684941",
  "ainvs": [
    "1",
    "0",
    "1",
    "-36818679283",
    "2719253442533306"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 84.60141646034491,
  "faltings_height": 4.605412684964512,
  "conductor": "45042690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "31",
    "37"
  ],
  "discriminant": "3610576700392350310992562500",
  "regulator": "4.200764067997474660470224062035369692473",
  "points": [
    [
      "-151235",
      "69562892"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=1; A=(3q-p)(p+q)^3=-1329669, B=-(p+3q)(p-q)^3=-1329125. 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 20:04:13",
  "updated_at": "2026-09-26 20:04:13"
}