{
  "id": 2518,
  "curve_key": "330603529:5149468653083",
  "ainvs": [
    "1",
    "0",
    "1",
    "-6887574",
    "-5960607128"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 58.849291253476146,
  "faltings_height": 2.896054786664466,
  "conductor": "30030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13"
  ],
  "discriminant": "5565686539253841000000",
  "regulator": "6.059393059634639821043147158887563028908",
  "points": [
    [
      "-6812731/4624",
      "10122095013/314432"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational full 2- and 3-torsion family at (p,q)=(-10,1); 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 20:06:35",
  "updated_at": "2026-09-26 20:06:35"
}