{
  "id": 3693,
  "curve_key": "16807565015219262661767956488580614863361:-2169016003071705032062885637684524200833016838923280632272641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-350157604483734638786832426845429476320",
    "2510435188740399342636197095094554753287459379850011238400"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
  ],
  "naive_height": 277.867943131044,
  "faltings_height": 20.98792263983642,
  "conductor": "120600636120040262281305547153244997893031818350820655996701181065730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "61",
    "127",
    "173",
    "313",
    "337",
    "491",
    "541",
    "1721",
    "2161",
    "2423",
    "3469",
    "3907",
    "4547",
    "8221",
    "13477",
    "203713",
    "1365868604929"
  ],
  "discriminant": "25121477374297765527923282858800055355877054995479383055579862153334243664419119090461139063381908579398890000000000",
  "regulator": "71386248750004333047936.2426575487895370085139415317925700501538279329591",
  "points": [
    [
      "800217818841917979390",
      "22630524388919943871694782174230"
    ],
    [
      "5298998356394073012914940/579121",
      "3753734203522087893404393107446081780/440711081"
    ],
    [
      "6202442093718931977556920/543169",
      "390019107850172647869363372610633320/400315553"
    ],
    [
      "211302933108280610926636110/4012009",
      "2899244872652760548492957636732977080210/8036054027"
    ],
    [
      "265170418237568144511583360/1830609",
      "4283665989768466336499891229482661088960/2476813977"
    ],
    [
      "1688533734929422327635758720/173106649",
      "10917887793990137573275726797924721195840/2277564180893"
    ],
    [
      "412617494424846529298617367160/6004855081",
      "256092319882702733363319661507175578920437880/465322225081771"
    ],
    [
      "935028922007813837873439755640/432738993241",
      "11955828145014979117789028732272083966169530720/284668259184733789"
    ],
    [
      "13965179968744727832820167894840/556395154561",
      "40523587438277921090670039596075449578551287320/415025717294986559"
    ],
    [
      "29102909738762127678599902429560/2499981563689",
      "13561080137382122919935700613206364498147226760/3952803349740279637"
    ],
    [
      "410906959932442342750047359448240/8909660881",
      "8329428611173434662084585048157672899816882824080/840991800218471"
    ],
    [
      "271102523916019909110833715373103835/26890470860192164",
      "9821210036248151877367420189920826550691720110006565/4409583901513753776499288"
    ],
    [
      "29106171926731708797638610635850806810/668012582313014689",
      "144423775393265094724004170220604855799851342263303171990/545980288936690874489870863"
    ],
    [
      "326229636668925011902265778590246334040/45080374253149152009",
      "5706504470178611986985163297714687414160012026083803647320/302678288302741133985059184027"
    ],
    [
      "29036189118070977912280984113326997748890660/1653128578637135139540529",
      "89646478154072703642657221390080867576998130283054224929880893840/2125494330094195199532633703278826583"
    ],
    [
      "68456839435017863108945575192537856070462346740/4535836359563298452915354281",
      "7868675074789570992759096597765727747219907118031214033841824250607920/305482310730302600094306871579307726017429"
    ],
    [
      "2558503412531632913047226631053005866385803390927429862060598426921803129849/105191608143388803730163181285001030737602266595726361600",
      "-98776205186262709269303402410496914878420052374432464504622278214963919966269111380719127036811251203257625372413/1078876272418027519324878504896246485994821511401013635043010581567410634808078336000"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -942/47, u = 11/5 of the Elkies-Klagsbrun family y^2 = x^3 + 2A(t,u)x^2 + B(t,u)x (arXiv:2003.00077, Sec. 9, eqs. (3)-(4)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:44:30",
  "updated_at": "2026-09-30 01:44:30"
}