{
  "id": 2296,
  "curve_key": "469672017178081:-10178531796257818877521",
  "ainvs": [
    "1",
    "0",
    "0",
    "-9784833691210",
    "11780707282117816100"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 101.34916719372181,
  "faltings_height": 6.086865474535134,
  "conductor": "856856910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "29",
    "79",
    "137"
  ],
  "discriminant": "1902719185317152093529379699776000000",
  "regulator": "3.521205513981447330031567446071543660073",
  "points": [
    [
      "1679282",
      "290309882"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=36; A=(3q-p)(p+q)^3=46991, B=-(p+3q)(p-q)^3=21695375. 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 19:52:44",
  "updated_at": "2026-09-26 19:52:44"
}