{
  "id": 2593,
  "curve_key": "2139267778732561:-98896295308907533240441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-44568078723595",
    "114463301041673455025"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 105.89772001777132,
  "faltings_height": 6.57361358791651,
  "conductor": "28005183570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "53",
    "61",
    "167"
  ],
  "discriminant": "5677299943139103092134344667860489000000",
  "regulator": "18.7224816969661586268654087639350518521724",
  "points": [
    [
      "3765272",
      "181572041"
    ],
    [
      "3954650",
      "242846345"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=38; A=(3q-p)(p+q)^3=-563625, B=-(p+3q)(p-q)^3=45967831. 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 20:11:30",
  "updated_at": "2026-09-26 20:11:30"
}