{
  "id": 2251,
  "curve_key": "642188096523649:-16230571227257888918593",
  "ainvs": [
    "1",
    "0",
    "0",
    "-13378918677576",
    "18785382249971926080"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 102.28770708583814,
  "faltings_height": 6.334538578951772,
  "conductor": "4865910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "29",
    "47"
  ],
  "discriminant": "816257889320087343675853262678497689600",
  "regulator": "5.100158673923007771280879039795287411948",
  "points": [
    [
      "1992336",
      "195131064"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=32; A=(3q-p)(p+q)^3=-712385, B=-(p+3q)(p-q)^3=24977727. 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 19:49:50",
  "updated_at": "2026-09-26 19:49:50"
}