{
  "id": 2241,
  "curve_key": "729298409817121:-15646315377025431388081",
  "ainvs": [
    "1",
    "0",
    "0",
    "-15193716871190",
    "18109160049858584100"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 102.6693123164785,
  "faltings_height": 6.565771398366689,
  "conductor": "3425022510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "61",
    "131",
    "157"
  ],
  "discriminant": "82806285030662333416008295519617024000000",
  "regulator": "3.155818330594945098159137386892718416419",
  "points": [
    [
      "3156142",
      "1261235572"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=48; A=(3q-p)(p+q)^3=6731375, B=-(p+3q)(p-q)^3=29734511. 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 19:49:12",
  "updated_at": "2026-09-26 19:49:12"
}