{
  "id": 2655,
  "curve_key": "654752547241:-249672218283773461",
  "ainvs": [
    "1",
    "0",
    "1",
    "-13640678068",
    "288971338142306"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 81.62256963218732,
  "faltings_height": 4.855013640470813,
  "conductor": "14112210",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "59",
    "67"
  ],
  "discriminant": "126363882213485593525160156250000",
  "regulator": "14.2990221736585560295718646337310950386413",
  "points": [
    [
      "-113580",
      "19371382"
    ],
    [
      "-50600",
      "29173817"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-4, q=21; A=(3q-p)(p+q)^3=329171, B=-(p+3q)(p-q)^3=921875. 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 20:15:53",
  "updated_at": "2026-09-26 20:15:53"
}