{
  "id": 3682,
  "curve_key": "5694129565536021162987228939873:-13229774371802885216412180526441682942479068945",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-118627699282000440895567269581",
    "15312238856253369027772251664973282853020021"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 212.45096559949948,
  "faltings_height": 15.613093836485286,
  "conductor": "21231627710474670364487625916840938",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "29",
    "31",
    "47",
    "53",
    "59",
    "107",
    "127",
    "431",
    "587",
    "647",
    "739",
    "319147"
  ],
  "discriminant": "5552354121464264359119776804092484878421316221894232282879829221960525219126247176536064",
  "regulator": "3541592163.428384239994955593359554223442026622831841250519",
  "points": [
    [
      "-162370659524649",
      "5503918597946059842520"
    ],
    [
      "-92750752371489",
      "5051449356004927390120"
    ],
    [
      "168641533366887",
      "320688792342061404568"
    ],
    [
      "240939414916807",
      "846827799037763480088"
    ],
    [
      "242383331141103",
      "893758733474348821048"
    ],
    [
      "476785915228047",
      "8193746754079314150328"
    ],
    [
      "1269911786812303",
      "43733530182843243197368"
    ],
    [
      "6564566673785337",
      "531156245432320184322394"
    ],
    [
      "7201189343163295/49",
      "351884996618969070417096/343"
    ],
    [
      "9911567807853269295/37249",
      "11562439263330195418875784504/7189057"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 368/1183 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 19:32:20",
  "updated_at": "2026-09-29 19:32:20"
}