{
  "id": 4018,
  "curve_key": "3174111841390922712232259277723876728615665:2556057946626923551849128788690031278897612266950768495495761975",
  "ainvs": [
    "1",
    "0",
    "0",
    "-66127330028977556504838734952580765179493",
    "-2958400401188568925756817079226988035840232240587215637255423"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
  ],
  "naive_height": 293.59080529189936,
  "faltings_height": 22.520380428101408,
  "conductor": "608480130869274673011093246882337748935299188663528462593209259950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "23",
    "43",
    "53",
    "61",
    "101",
    "167",
    "233",
    "563",
    "587",
    "607",
    "1033",
    "1123",
    "2473",
    "9161",
    "67271",
    "97987",
    "3788861",
    "25217561"
  ],
  "discriminant": "14725520879464003410482889962294353725325097436344970243714146812376316203416042032360017287336937170105961887375155951168000",
  "regulator": "6158642925084880311390825449.71079424890126790075614267437847057266189715",
  "points": [
    [
      "453358467784461190337371/100",
      "304758563245016225449785664623952051/1000"
    ],
    [
      "-32330935312804639752618171967215284226778972/643905877533831458960401",
      "-250641705343154538410510335957971519641092565741500640432933929603/516694196976743861380578542272500601"
    ],
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      "226441399109839715825054012782154813025734/721820765157179841169",
      "-51927969847183479035880891041162631424976475192754034330425187/19392958021144098333029976245447"
    ],
    [
      "7485500981660996240506413293565254/146516700625",
      "-647628274656251146665195597352188510739080071964167/56082930081734375"
    ],
    [
      "13662953414919025777190242016044175158/31427198903306761",
      "39577370992629772380333791520891225182008748398657694375/5571325228304514168320741"
    ],
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      "78984828798024095218648634750001956/185158368358681",
      "17172946955159598866193824706070765029933933250097935/2519503799341764743171"
    ],
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      "-8854132747489221584325389978570646958726/161756020117106020225",
      "-1450693690681239243947250037179873431402565371753041596951887/2057267092786413780388895453375"
    ],
    [
      "-18917198913417933378710204320812468759466/375401722423265222689",
      "3606944809550585218563985354221382301925628313058680627440133/7273515880622236431563644343887"
    ],
    [
      "-149607588523535355120790357432822526494/1326046050545851441",
      "-2673829362603306812704148707686299381316613256707205897489/1526996035733140616294840489"
    ],
    [
      "767692147821992965785584544028089204314/561044003910091849",
      "-20879138078190990412146138667935418438315094414141802014003/420238064818879041907709243"
    ],
    [
      "12169190460043764819411880467049057127894/42439719417194277025",
      "-355793578664061426528360082580614704379558437518130914257807/276476839311779576462089471375"
    ],
    [
      "3684530494227606831190212368907733298/13189369660890361",
      "-920659242787224698379464197436700577382547120360665605/1514732908106929952128141"
    ],
    [
      "103509248362404538588493793533268933682853462114/179496769218928554850171009",
      "29519029664409727397653123718368381431955542613539592647386771166139495/2404833173195044871839691123795156675777"
    ],
    [
      "-29430531133062154366553091448605650478754/197867329230826353121",
      "-5271202089918235056766524029421250624806280258849049049064259/2783307165670245968787344767919"
    ],
    [
      "-27527365192671193289763661044307755593870228056/121032607924370789836060369",
      "-749196457091435005572828494196390318981769591619179649737449553089545/1331538066998560534263509821821531200153"
    ],
    [
      "165903886265539388195751605380708973675549271998/4117264762972862834624641",
      "-67573433297833681300250257041285160572592422902182256709847442927780275/8354360144796420215258540126845205311"
    ],
    [
      "380131134362263177780198460747520806910788486/239281401101192338839721",
      "7310886358008775960926538409001763650092998039988101635578729256085/117047842935974244606605832088314731"
    ]
  ],
  "submitter": "Odbayar Shinebayar",
  "history": [],
  "commentary": "Unlisted rational-isogeny neighbor of curve#3692 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 17: 17 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.",
  "created_at": "2026-10-05 04:46:55",
  "updated_at": "2026-10-05 04:46:55"
}