{
  "id": 3698,
  "curve_key": "465977303046597508887447161353:-315456323419695258498508763274654278611450085",
  "ainvs": [
    "1",
    "1",
    "0",
    "-9707860480137448101821815861",
    "365111485439458059801777678001548174488125"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 204.94180331361036,
  "faltings_height": 14.935482787371505,
  "conductor": "1321043258541830079458759813032686",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "43",
    "101",
    "131",
    "179",
    "509",
    "587",
    "1367",
    "2141",
    "13217",
    "120917"
  ],
  "discriminant": "964825460567005894728668892146784215021796339926265191062199141002557012276667124784",
  "regulator": "243956883642.2575329775027833404935389483320418026183786484",
  "points": [
    [
      "61435597409838",
      "24117538879733583959"
    ],
    [
      "-490333896749952107302097/21789892996",
      "2433018901538236122147388880137627577/3216493264711544"
    ],
    [
      "8317707424784025/121",
      "200131788918325932684635/1331"
    ],
    [
      "17649623872748926/289",
      "20711172715370776160939/4913"
    ],
    [
      "8305391177311539257/179776",
      "9405140484931026536195017505/76225024"
    ],
    [
      "5340555814390784184878/32982049",
      "330185185862186825116505189040281/189415907407"
    ],
    [
      "2227846904064755674130350/36239594689",
      "175396223753844719113781864380281545/6898822922160863"
    ],
    [
      "61207878462315758738739094/145517072089",
      "466746429128827780582666251321021545501/55509960938574563"
    ],
    [
      "201012838324927296239137394775/3006045325927396",
      "20159072484016894271671227828055849024250465/164813691587386274433944"
    ],
    [
      "1036103050555591404471/14160169",
      "-11493951401532414889885430840059/53284715947"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 4455/18784 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 01:45:27",
  "updated_at": "2026-09-30 01:45:27"
}