{
  "id": 2494,
  "curve_key": "30882089329:-1928474872753033",
  "ainvs": [
    "1",
    "0",
    "0",
    "-643376861",
    "2231977487985"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 72.46032665829615,
  "faltings_height": 4.0984437767818305,
  "conductor": "13946970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "23",
    "29",
    "41"
  ],
  "discriminant": "14891978896708922111587406400",
  "regulator": "6.477577735427672568479084633935711285649",
  "points": [
    [
      "-33809/4",
      "21299585/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=6; A=(3q-p)(p+q)^3=-201433, B=-(p+3q)(p-q)^3=-121945. 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 20:05:05",
  "updated_at": "2026-09-26 20:05:05"
}