{
  "id": 2638,
  "curve_key": "4157721436729:-8270960479243674733",
  "ainvs": [
    "1",
    "0",
    "1",
    "-86619196599",
    "9572863706784166"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 87.16796492575939,
  "faltings_height": 5.169289292521952,
  "conductor": "459900870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "23",
    "59",
    "79"
  ],
  "discriminant": "2004790404876543590819949689724900",
  "regulator": "12.2465390663756417614454192298079326712657",
  "points": [
    [
      "-314959",
      "75062166"
    ],
    [
      "-1093813/4",
      "906588399/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-10, q=23; A=(3q-p)(p+q)^3=173563, B=-(p+3q)(p-q)^3=2120283. 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 20:14:31",
  "updated_at": "2026-09-26 20:14:31"
}