{
  "id": 2219,
  "curve_key": "1641047465996929:-66307721919515550032833",
  "ainvs": [
    "1",
    "0",
    "0",
    "-34188488874936",
    "76745045668917072960"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 105.10233339493246,
  "faltings_height": 6.567647454097458,
  "conductor": "4929154230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "53",
    "163"
  ],
  "discriminant": "13129170590135535878354008725791805542400",
  "regulator": "3.417315333404163390631058587516207885877",
  "points": [
    [
      "3222768",
      "187865736"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-55, q=36; A=(3q-p)(p+q)^3=-1118017, B=-(p+3q)(p-q)^3=39939263. 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 19:47:51",
  "updated_at": "2026-09-26 19:47:51"
}