{
  "id": 2254,
  "curve_key": "487417686518161:-10535860034734309350841",
  "ainvs": [
    "1",
    "0",
    "0",
    "-10154535135795",
    "12194281601397893025"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 101.46042763182635,
  "faltings_height": 6.353219615972418,
  "conductor": "16059825210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "23",
    "37",
    "53",
    "83"
  ],
  "discriminant": "2774535979084538593013300527768881000000",
  "regulator": "8.424878144590969797533622978624002931359",
  "points": [
    [
      "8251635/4",
      "1264284315/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=30; A=(3q-p)(p+q)^3=-1739881, B=-(p+3q)(p-q)^3=21156119. 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 19:50:01",
  "updated_at": "2026-09-26 19:50:01"
}