{
  "id": 2209,
  "curve_key": "2723151767927761:-131571494626169172297241",
  "ainvs": [
    "1",
    "0",
    "0",
    "-56732328498495",
    "152281817756298056025"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 106.62169902782509,
  "faltings_height": 6.8440037177136785,
  "conductor": "7538941410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "73",
    "181"
  ],
  "discriminant": "1668185770350604092654789636225152841000000",
  "regulator": "3.469427876975316033505372885565812678417",
  "points": [
    [
      "5508960",
      "2630711355"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-19, q=54; A=(3q-p)(p+q)^3=7760375, B=-(p+3q)(p-q)^3=55629431. 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 19:47:14",
  "updated_at": "2026-09-26 19:47:14"
}