{
  "id": 2393,
  "curve_key": "13273971447529:-48357230613481110133",
  "ainvs": [
    "1",
    "0",
    "1",
    "-276541071824",
    "55968993868661966"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 90.65047859892798,
  "faltings_height": 5.247197021921364,
  "conductor": "235922610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "41",
    "47",
    "53"
  ],
  "discriminant": "248662901647450179098424462416400",
  "regulator": "4.550288010296718012881941162302374653213",
  "points": [
    [
      "-393615",
      "322432567"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-44, q=3; A=(3q-p)(p+q)^3=-3652813, B=-(p+3q)(p-q)^3=-3633805. 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 19:58:47",
  "updated_at": "2026-09-26 19:58:47"
}