{
  "id": 3697,
  "curve_key": "1406823856392887894212894670400:-1668419185296890253015074790519095670821568000",
  "ainvs": [
    "0",
    "0",
    "0",
    "-29308830341518497796101972300",
    "1931040723723252607656336563100805174562000"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 208.2566621076267,
  "faltings_height": 15.057465647774634,
  "conductor": "1213220854870659463310025004843200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "29",
    "37",
    "41",
    "79",
    "83",
    "127",
    "131",
    "163",
    "191",
    "433",
    "853",
    "883"
  ],
  "discriminant": "403697074028694232968736559056369542215527690792931635499597961550890829831680000000",
  "regulator": "145460322436.3369699931235563325387062184144280510292995872",
  "points": [
    [
      "94001313916130",
      "81184925024236407400"
    ],
    [
      "12026986356420865/1024",
      "41298414994636945520219775/32768"
    ],
    [
      "63842075187351490/529",
      "4738228713902535098045400/12167"
    ],
    [
      "160712046488469865/1764",
      "9669888554882894693456725/74088"
    ],
    [
      "2232410059367876944/2809",
      "3263754317013718086717886572/148877"
    ],
    [
      "14600119728273147721/77284",
      "38049238726836276872633330331/21484952"
    ],
    [
      "2143692406464508718365/25030009",
      "27747604262628792667853528325525/125225135027"
    ],
    [
      "4826585959622122913410/15673681",
      "291758738321991425286308181859800/62052103079"
    ],
    [
      "646341162093352966642210/5611657921",
      "121297930876731740812550643351778200/420374906520031"
    ],
    [
      "1108590519573517338899410/11107262881",
      "7011186557986772879363727250390200/1170605542291471"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -15653/10496 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 01:45:15",
  "updated_at": "2026-09-30 01:45:15"
}