{
  "id": 2513,
  "curve_key": "441659755321:254543414158211219",
  "ainvs": [
    "1",
    "0",
    "1",
    "-9201244903",
    "-294611199823894"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 80.44141691473912,
  "faltings_height": 4.69154049966264,
  "conductor": "39270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17"
  ],
  "discriminant": "12360692761105045152384575078400",
  "regulator": "5.537820651492723264200418504656400047997",
  "points": [
    [
      "-9661505/169",
      "14730247004/2197"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational full 2- and 3-torsion family at (p,q)=(-16,11); Velu quotient by rational order-3 subgroup. The mapped rank >=1 witness is non-torsion by the original exact 2-descent Kummer certificate and finite isogeny kernel. Conductor N=39270; local exponents {'2': 1, '3': 1, '5': 1, '7': 1, '11': 1, '17': 1}.",
  "created_at": "2026-09-26 20:06:16",
  "updated_at": "2026-09-26 20:06:16"
}