{
  "id": 2123,
  "curve_key": "62169629483942416:-8661273218257934174745536",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-1295200614248800",
    "10024622212124665600000"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "naive_height": 116.00592901034972,
  "faltings_height": 7.712994823542747,
  "conductor": "63897470352240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "31",
    "41",
    "271",
    "4801"
  ],
  "discriminant": "95643443473701972219342591688748275569469440000",
  "regulator": "14352.2997251386372781408093898120145446010129201",
  "points": [
    [
      "52433250",
      "293708919250"
    ],
    [
      "-469672062525680/37075921",
      "35263495560386170733040/225755282969"
    ],
    [
      "-150353315/4",
      "598727020815/8"
    ],
    [
      "105691600/121",
      "125523612068400/1331"
    ],
    [
      "195168929250/49",
      "86218075534945250/343"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found by a conductor-oriented search in the standard Z/2Z x Z/4Z family\r\ny^2 = x(x+u^2)(x+v^2), with (u,v) = (4801,8401). Here\r\nv-u = 3600 = 60^2. The search used the same smooth-support / Nagao-filter\r\nstrategy used for curve#1829. PARI/GP 2.17.4 gives exact rank 5 and\r\ntorsion Z/2Z x Z/4Z. Conductor N = 63897470352240.\r\nThis substantially improves the conductor of curve#1829 that I previously submitted.",
  "created_at": "2026-09-26 10:03:45",
  "updated_at": "2026-09-26 10:03:45"
}