{
  "id": 2488,
  "curve_key": "71347307761:-19049706962967241",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1486402245",
    "22048148081025"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 74.97247634191565,
  "faltings_height": 3.9895713571111218,
  "conductor": "2381190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "29"
  ],
  "discriminant": "172300010934522515625000000",
  "regulator": "3.227340082530063723860144340104583476142",
  "points": [
    [
      "-38610",
      "4697055"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=2; A=(3q-p)(p+q)^3=-268569, B=-(p+3q)(p-q)^3=-265625. 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 20:04:43",
  "updated_at": "2026-09-26 20:04:43"
}