{
  "id": 2387,
  "curve_key": "4154329737121:151038077187931919",
  "ainvs": [
    "1",
    "0",
    "0",
    "-86548536190",
    "-174819801715900"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 87.16551664935302,
  "faltings_height": 5.332014135377454,
  "conductor": "243259170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "43",
    "79"
  ],
  "discriminant": "41478300155422237766151721536000000",
  "regulator": "7.121397448390479105885124432017391851090",
  "points": [
    [
      "-8554",
      "23771702"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-43, q=12; A=(3q-p)(p+q)^3=-2353489, B=-(p+3q)(p-q)^3=-1164625. 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 19:58:23",
  "updated_at": "2026-09-26 19:58:23"
}