{
  "id": 2527,
  "curve_key": "1653866449:-52076620397593",
  "ainvs": [
    "1",
    "0",
    "0",
    "-34455551",
    "60270994905"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 63.67914505809471,
  "faltings_height": 3.321217232664942,
  "conductor": "1607970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "31"
  ],
  "discriminant": "1048497620162995169294400",
  "regulator": "3.795196800582035512261648364052845410000",
  "points": [
    [
      "-4892",
      "336751"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=6; A=(3q-p)(p+q)^3=-10633, B=-(p+3q)(p-q)^3=34295. 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 20:07:09",
  "updated_at": "2026-09-26 20:07:09"
}