{
  "id": 2417,
  "curve_key": "1949890079281:2354854684628398679",
  "ainvs": [
    "1",
    "0",
    "0",
    "-40622709985",
    "-2725529640582775"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 84.89638235194768,
  "faltings_height": 5.06367300844506,
  "conductor": "2372370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "79"
  ],
  "discriminant": "1081180882154725982145140625000000",
  "regulator": "5.441478977205405787161283590006914562062",
  "points": [
    [
      "-320845/4",
      "33114595/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=26; A=(3q-p)(p+q)^3=1234375, B=-(p+3q)(p-q)^3=1515591. 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 20:00:18",
  "updated_at": "2026-09-26 20:00:18"
}