{
  "id": 2668,
  "curve_key": "217845074881:-101607607179810721",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4538439060",
    "117601018995600"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 78.32114994422837,
  "faltings_height": 4.286293556960776,
  "conductor": "14893530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "29",
    "53"
  ],
  "discriminant": "8133028114017017756736000000",
  "regulator": "10.2399912599585977870957807088941257921710",
  "points": [
    [
      "-62280",
      "12628140"
    ],
    [
      "15240",
      "7201740"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=12; A=(3q-p)(p+q)^3=-6625, B=-(p+3q)(p-q)^3=463391. 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 20:16:52",
  "updated_at": "2026-09-26 20:16:52"
}