{
  "id": 3659,
  "curve_key": "-83780225150400:-111427834708178496000",
  "ainvs": [
    "0",
    "0",
    "0",
    "1745421357300",
    "128967401282614000"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4
  ],
  "naive_height": 96.17765435653249,
  "faltings_height": 6.08467813025915,
  "conductor": "198468505684800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "31",
    "151",
    "293",
    "773"
  ],
  "discriminant": "-347500074979269068090778585999360000000",
  "regulator": "15830.856382367845382804284349234198066702910120403",
  "points": [
    [
      "784830",
      "1407923600"
    ],
    [
      "38000990",
      "234398689200"
    ],
    [
      "77705534",
      "685079140752"
    ],
    [
      "4885316/49",
      "189110155536/343"
    ],
    [
      "12698446/9",
      "62745068656/27"
    ],
    [
      "119020145/1024",
      "18920761180425/32768"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -11/16 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": "2026-09-29 19:28:28",
  "updated_at": "2026-09-29 19:28:28"
}