{
  "id": 3678,
  "curve_key": "55393391394192027272648256:-412019846861613448112105588303802683904",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1154028987379000568180172",
    "476874822756497046426048134610882736"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "naive_height": 177.82950758874404,
  "faltings_height": 12.575315685366268,
  "conductor": "3716012842930786646909643840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "23",
    "37",
    "59",
    "109",
    "137",
    "157",
    "163",
    "199",
    "277",
    "449"
  ],
  "discriminant": "121683127663925100703696233445816670418082806365744147280371891343360000",
  "regulator": "262728408.57869427728325803809422130764604041941356805625",
  "points": [
    [
      "-1228249730203",
      "203411567839680585"
    ],
    [
      "465995200637",
      "200734707120348555"
    ],
    [
      "638827377752",
      "18847576795544820"
    ],
    [
      "761137413912",
      "198620355656933420"
    ],
    [
      "2812754631197",
      "4414094693347425435"
    ],
    [
      "-6639186955232764/7225",
      "535870489507141071035016/614125"
    ],
    [
      "-239486334726312/289",
      "4567079779170840855220/4913"
    ],
    [
      "141729115619057/196",
      "392781104293493253015/2744"
    ],
    [
      "75109015713764849/484",
      "20583903048061848895839465/10648"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 247/45 of the Elkies-Klagsbrun Z/4 fibration E2: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = -8(80t+9), c = 2(t-2)(2t-1)(18t-1)(2t-81) (arXiv:2003.00077, eq. (6)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:31:39",
  "updated_at": "2026-09-29 19:31:39"
}