{
  "id": 2511,
  "curve_key": "4082372361:-257172362391141",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-85049424",
    "297674459568"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 66.38983235222679,
  "faltings_height": 3.412635899064964,
  "conductor": "131670",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19"
  ],
  "discriminant": "1098513156172746872250000",
  "regulator": "2.521151845915205589387793252125812550149",
  "points": [
    [
      "-8868",
      "599784"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-12, q=7; A=(3q-p)(p+q)^3=-4125, B=-(p+3q)(p-q)^3=61731. 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 20:06:08",
  "updated_at": "2026-09-26 20:06:08"
}