{
  "id": 2558,
  "curve_key": "160294201:-1681996056301",
  "ainvs": [
    "1",
    "0",
    "1",
    "-3339463",
    "1946476406"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 56.6775643230158,
  "faltings_height": 2.7239962988134825,
  "conductor": "91770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "23"
  ],
  "discriminant": "746253168334407562500",
  "regulator": "1.887047788020050409991781388840558949457",
  "points": [
    [
      "-1775",
      "48662"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=5; A=(3q-p)(p+q)^3=-221616, B=-(p+3q)(p-q)^3=-175616. 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 20:09:06",
  "updated_at": "2026-09-26 20:09:06"
}