{
  "id": 2531,
  "curve_key": "235148841:3605770247211",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-4898934",
    "-4172120460"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 57.82718771272294,
  "faltings_height": 2.484643584097558,
  "conductor": "10710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17"
  ],
  "discriminant": "561793182180249600",
  "regulator": "9.371923012302226390434740618139596382595",
  "points": [
    [
      "-1661939/1296",
      "42252227/46656"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational full 2- and 3-torsion family at (p,q)=(-12,5); 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=10710; local exponents {'2': 1, '3': 2, '5': 1, '7': 1, '17': 1}.",
  "created_at": "2026-09-26 20:07:25",
  "updated_at": "2026-09-26 20:07:25"
}