{
  "id": 2517,
  "curve_key": "813893809:-2046208358377",
  "ainvs": [
    "1",
    "0",
    "0",
    "-16956121",
    "2366883701"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 61.55202137904829,
  "faltings_height": 3.1971020864468414,
  "conductor": "30030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13"
  ],
  "discriminant": "309580507925165039062500",
  "regulator": "9.810336964750826692646418134680001539420",
  "points": [
    [
      "-1984099/784",
      "3770675831/21952"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational full 2- and 3-torsion family at (p,q)=(-25,1); 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=30030; local exponents {'2': 1, '3': 1, '5': 1, '7': 1, '11': 1, '13': 1}.",
  "created_at": "2026-09-26 20:06:31",
  "updated_at": "2026-09-26 20:06:31"
}