{
  "id": 2633,
  "curve_key": "8605986155809:-25119819771268257073",
  "ainvs": [
    "1",
    "0",
    "0",
    "-179291378246",
    "29073850535056740"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 89.35043742502901,
  "faltings_height": 5.281857863806331,
  "conductor": "159206190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "37",
    "59"
  ],
  "discriminant": "3692006737958854077154821675417600",
  "regulator": "10.4508497223344765402494959796681330748769",
  "points": [
    [
      "-442484",
      "147776650"
    ],
    [
      "-344804",
      "223556794"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=24; A=(3q-p)(p+q)^3=113135, B=-(p+3q)(p-q)^3=2988527. 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 20:14:10",
  "updated_at": "2026-09-26 20:14:10"
}