{
  "id": 3679,
  "curve_key": "-10550042757737930349827487:17943801646363745586510985502817229551",
  "ainvs": [
    "1",
    "-1",
    "1",
    "219792557452873548954739",
    "-20768288942605579605232414571054923"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "naive_height": 172.85451643391133,
  "faltings_height": 12.4917790148093,
  "conductor": "4145713793217534004171727022",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "19",
    "37",
    "47",
    "59",
    "73",
    "107",
    "827",
    "1031",
    "3517",
    "5039"
  ],
  "discriminant": "-865877123675513667546144864225764936876515883437330647051983056520122368",
  "regulator": "142874122.51398487915473900357099740206272333545495702944",
  "points": [
    [
      "124172461155",
      "91861160513326756"
    ],
    [
      "2558819437095",
      "4158803485209640408"
    ],
    [
      "2361155322765/16",
      "7807141743258902227/64"
    ],
    [
      "68419808060925/169",
      "805947481079413498006/2197"
    ],
    [
      "15494441189301201/1849",
      "1931678103277911268475908/79507"
    ],
    [
      "30817122310006843/841",
      "5410327282976213628505908/24389"
    ],
    [
      "122434998154223295/58081",
      "43841187465607730120553016/13997521"
    ],
    [
      "134060973317874255/185761",
      "57384965287306036381519496/80062991"
    ],
    [
      "5026830767603606991/53919649",
      "9139609820186385991126263272/395931982607"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -1391/1824 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 19:31:49",
  "updated_at": "2026-09-29 19:31:49"
}