{
  "id": 2425,
  "curve_key": "1351530645721:-1553103284859469981",
  "ainvs": [
    "1",
    "0",
    "1",
    "-28156888453",
    "1797570899957756"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 83.79677663323525,
  "faltings_height": 4.854482761127561,
  "conductor": "25571910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "29"
  ],
  "discriminant": "32768220065691079549952753062500",
  "regulator": "3.211103674384260056688816905753639578029",
  "points": [
    [
      "-189095",
      "19080122"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=5; A=(3q-p)(p+q)^3=-1195061, B=-(p+3q)(p-q)^3=-1127061. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 20:00:48",
  "updated_at": "2026-09-26 20:00:48"
}