{
  "id": 2529,
  "curve_key": "1897973001:-3270398011749",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-39541104",
    "3795068160"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 64.09215693617794,
  "faltings_height": 3.4091583960101435,
  "conductor": "14490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23"
  ],
  "discriminant": "3950448789976017960960000",
  "regulator": "21.81255577826578952012083145922991155950",
  "points": [
    [
      "-70572718389/17757796",
      "23593497514056903/74831352344"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational full 2- and 3-torsion family at (p,q)=(-24,1); 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=14490; local exponents {'2': 1, '3': 2, '5': 1, '7': 1, '23': 1}.",
  "created_at": "2026-09-26 20:07:17",
  "updated_at": "2026-09-26 20:07:17"
}