{
  "id": 3694,
  "curve_key": "1504058671905526414575720225:-56681548715479564326491250148075037756625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-31334555664698466970327505",
    "65603644346627699757540306732570171872"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "naive_height": 187.73389423854442,
  "faltings_height": 13.55667155739569,
  "conductor": "242574104114218087554953925",
  "bad_primes": [
    "3",
    "5",
    "7",
    "31",
    "43",
    "47",
    "59",
    "73",
    "101",
    "137",
    "311",
    "353",
    "401",
    "937"
  ],
  "discriminant": "109764042311428002918110138859392466498889591083535967987747292101080610390625",
  "regulator": "23495112.899865026232030790397532213802541551536589760340",
  "points": [
    [
      "-4293314553312",
      "10999820947981814815"
    ],
    [
      "8486511603147/4",
      "23560597224186783305/8"
    ],
    [
      "4808975766624",
      "5111757697129571200"
    ],
    [
      "194304065100084/25",
      "2134374469033702018892/125"
    ],
    [
      "346502834659146/25",
      "5986793130328640969354/125"
    ],
    [
      "481437979901076/289",
      "20859843300714263004860/4913"
    ],
    [
      "739826936966181/169",
      "7713015403703935456825/2197"
    ],
    [
      "8203936891014204624/1437601",
      "14690046989164043479369046225/1723683599"
    ],
    [
      "47556559464052337469/17986081",
      "84865211962797690714859652525/76278969521"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 1553/5074 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:44:41",
  "updated_at": "2026-09-30 01:44:41"
}