{
  "id": 3695,
  "curve_key": "4890109440586125590386867008:-336295438040265506131551592331228872826880",
  "ainvs": [
    "0",
    "0",
    "0",
    "-101877280012210949799726396",
    "389230831065122113578184713346329713920"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 191.2710365836906,
  "faltings_height": 13.826815018016244,
  "conductor": "282976117803100217896404857655264",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "29",
    "31",
    "43",
    "59",
    "61",
    "67",
    "83",
    "107",
    "113",
    "151",
    "277",
    "4397",
    "7417"
  ],
  "discriminant": "2224188884104094034322632122718427516963876101332038285802870000202356187131904",
  "regulator": "13112560845.10097020991104734920504641138557178642649554564",
  "points": [
    [
      "3831814776653",
      "7424133032762786403"
    ],
    [
      "-30460542435926462070/3301489",
      "139888659168364687981069672660/5998805513"
    ],
    [
      "-282430881219454/25",
      "1239482402141023478844/125"
    ],
    [
      "-31443375429783/4",
      "212313451224433117909/8"
    ],
    [
      "304275607581588/121",
      "16243894084540941931532/1331"
    ],
    [
      "12024313702738769/1600",
      "443624956529479789291353/64000"
    ],
    [
      "38167047320189066/13225",
      "16608361898303355519374364/1520875"
    ],
    [
      "38791388080448720/841",
      "7470512902108147173803640/24389"
    ],
    [
      "101996256370422153/20164",
      "5223284915079830056569797/2863288"
    ],
    [
      "2106204613179794186/727609",
      "6758616905594134705701383940/620650477"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 565/2324 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 01:44:55",
  "updated_at": "2026-09-30 01:44:55"
}