{
  "id": 2211,
  "curve_key": "2267731180392489:-107295653136383898009813",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-47244399591510",
    "124184795533766446500"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 106.07266873976246,
  "faltings_height": 6.685753444317357,
  "conductor": "2399641290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "23",
    "37",
    "97"
  ],
  "discriminant": "86624918666168144925311117260290006080400",
  "regulator": "5.514558827646099244174266389350976877654",
  "points": [
    [
      "-7929213",
      "520545009"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-60, q=37; A=(3q-p)(p+q)^3=-2080557, B=-(p+3q)(p-q)^3=46546323. 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 19:47:22",
  "updated_at": "2026-09-26 19:47:22"
}