History of Number of elliptic curves over $\mathbb{Q}$ with good redution outside $S$

+Title: Number of elliptic curves over $\mathbb{Q}$ with good redution outside $S$+Definition: 'Let $S$ be a finite set of primes. An elliptic curve $E/\mathbb{Q}$ is+  said to have  good reduction outside $S$ if its minimal discriminant  (equivalently,+  its conductor) is only divisible by primes in $S$. This table lists the numbers+  of elliptic curves $E/\mathbb{Q}$ with good reduction outside $S$ counted in two+  different ways:  up to $\mathbb{Q}$-isomorphism, and up to $\overline{\mathbb{Q}}$-isomorphism.'+Parameters:+  S:+    title: set of primes+    type: Set+  variable:+    display: ''+    title: ''+    type: Symbolic+    show-in-parameter-list: 'no'+Comments:+  comment-first-n-primes: 'Elliptic curves over $\mathbb{Q}$ with good reduction  outside+    of the first $n$ have been computed by several authors: $n=0$ by Tate (see CITE{Ogg}),  $n=1$+    by Ogg CITE{Ogg}, $n=2$ by Coghlan CITE{Cog} and Stephens CITE{Ste}, $n=3,4,5$+    by von Känel and Matschke CITE{vKanMat} and  Bennett, Gherga and Rechnitzer CITE{BeGhRe},+    $n=6$ heuristically by Best and matschke CITE{BesMat}, $n=7,8,9^*$ by Matschke+    CITE{M-ECDB} ($n=9$ assumes GRH).'+Formulas: {}+Programs: {}+References:+  BeGhRe:+    bib: Michael A. Bennett, Adela Gherga, and Andrew Rechnitzer, "Computing elliptic+      curves over Q". Math. Comp., 88(317):1341–1390, 2019.+  BesMat:+    bib: A. Best, B. Matschke, "Elliptic curves with good reduction outside of the+      first six primes". 2020+    arxiv: '2007.10535'+    github: https://github.com/elliptic-curve-data/ec-data-S6+  Cog:+    bib: Francis Coghlan, "Elliptic Curves with Conductor $2^m 3^n$". Ph.D. thesis,+      Manchester, England, 1967.+  vKanMat:+    bib: R. von Känel, B. Matschke, "Solving S-unit, Mordell, Thue, Thue-Mahler and+      generalized  Ramanujan-Nagell equations via Shimura-Taniyama conjecture". 2016+    arxiv: '1605.06079'+    github: https://github.com/bmatschke/solving-classical-diophantine-equations+  Kou:+    bib: Angelos Koutsianas, "Computing all elliptic curves over  an arbitrary number+      field with prescribed primes of bad reduction". Exp. Math., 28(1):1–15, 2019.+    arXiv: '1511.05108'+    github: https://github.com/akoutsianas/ERGOS+  Ogg:+    bib: Andrew P. Ogg, "Abelian curves of 2-power conductor". Math. Proc. Camb. Philos.+      Soc., 62(2):143–148, 1966.+  Ste:+    bib: Nelson M. Stephens, "The Birch Swinnerton-Dyer Conjecture for  Selmer curves+      of positive rank". Ph.D. Thesis, Manchester, 1965.+Links:+  M-ECDB:+    title: Matschke - Tables of elliptic curves+    url: https://github.com/bmatschke/s-unit-equations/tree/master/elliptic-curve-tables/+  Wiki:+    title: 'Wikipedia: Elliptic curves over the rational numbers'+    url: https://en.wikipedia.org/wiki/Elliptic_curve#Elliptic_curves_over_the_rational_numbers+Similar tables: ''+Keywords: ''+Tags:+- number theory+- elliptic curves+Data properties:+  type: R+  complete: 'no'+  sources:+  - CITE{M-ECDB}+  reliability: Assumes GRH if $23\in S$.  Needs to be recomputed to be provably correct+    (see readme.md in CITE{M-ECDB}).+Display properties:+  number-header: count+Numbers:+  '1':+    param_latex: $\{\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '0'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '0'+  '2':+    param_latex: $\{2\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '24'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '5'+  '3':+    param_latex: $\{3\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '8'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2'+  '6':+    param_latex: $\{2, 3\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '752'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '83'+  '5':+    param_latex: $\{5\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '0'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '0'+  '10':+    param_latex: $\{2, 5\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '280'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '32'+  '15':+    param_latex: $\{3, 5\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '148'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '29'+  '30':+    param_latex: $\{2, 3, 5\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7600'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '442'+  '7':+    param_latex: $\{7\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '4'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2'+  '14':+    param_latex: $\{2, 7\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '288'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '33'+  '21':+    param_latex: $\{3, 7\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '148'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '29'+  '42':+    param_latex: $\{2, 3, 7\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7168'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '415'+  '35':+    param_latex: $\{5, 7\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '40'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '10'+  '70':+    param_latex: $\{2, 5, 7\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3088'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '186'+  '105':+    param_latex: $\{3, 5, 7\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1080'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '109'+  '210':+    param_latex: $\{2, 3, 5, 7\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '71520'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2140'+  '11':+    param_latex: $\{11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '12'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '6'+  '22':+    param_latex: $\{2, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '232'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '26'+  '33':+    param_latex: $\{3, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '132'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '25'+  '66':+    param_latex: $\{2, 3, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '6640'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '382'+  '55':+    param_latex: $\{5, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '44'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '11'+  '110':+    param_latex: $\{2, 5, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2912'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '175'+  '165':+    param_latex: $\{3, 5, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '968'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '95'+  '330':+    param_latex: $\{2, 3, 5, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '64160'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1910'+  '77':+    param_latex: $\{7, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '56'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '14'+  '154':+    param_latex: $\{2, 7, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2656'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '159'+  '231':+    param_latex: $\{3, 7, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1088'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '110'+  '462':+    param_latex: $\{2, 3, 7, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '59360'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1760'+  '385':+    param_latex: $\{5, 7, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '424'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '53'+  '770':+    param_latex: $\{2, 5, 7, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '26784'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '822'+  '1155':+    param_latex: $\{3, 5, 7, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '10000'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '545'+  '2310':+    param_latex: $\{2, 3, 5, 7, 11\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '592192'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '8980'+  '13':+    param_latex: $\{13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '0'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '0'+  '26':+    param_latex: $\{2, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '336'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '39'+  '39':+    param_latex: $\{3, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '96'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '16'+  '78':+    param_latex: $\{2, 3, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '6192'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '354'+  '65':+    param_latex: $\{5, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '44'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '11'+  '130':+    param_latex: $\{2, 5, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2880'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '173'+  '195':+    param_latex: $\{3, 5, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1248'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '130'+  '390':+    param_latex: $\{2, 3, 5, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '62912'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1871'+  '91':+    param_latex: $\{7, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '40'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '10'+  '182':+    param_latex: $\{2, 7, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2912'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '175'+  '273':+    param_latex: $\{3, 7, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '904'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '87'+  '546':+    param_latex: $\{2, 3, 7, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '57056'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1688'+  '455':+    param_latex: $\{5, 7, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '400'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '50'+  '910':+    param_latex: $\{2, 5, 7, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '24864'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '762'+  '1365':+    param_latex: $\{3, 5, 7, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '9936'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '541'+  '2730':+    param_latex: $\{2, 3, 5, 7, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '575296'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '8716'+  '143':+    param_latex: $\{11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '32'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '8'+  '286':+    param_latex: $\{2, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2688'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '161'+  '429':+    param_latex: $\{3, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '976'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '96'+  '858':+    param_latex: $\{2, 3, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '52672'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1551'+  '715':+    param_latex: $\{5, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '280'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '35'+  '1430':+    param_latex: $\{2, 5, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '22528'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '689'+  '2145':+    param_latex: $\{3, 5, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '8144'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '429'+  '4290':+    param_latex: $\{2, 3, 5, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '507072'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '7650'+  '1001':+    param_latex: $\{7, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '384'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '48'+  '2002':+    param_latex: $\{2, 7, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '20704'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '632'+  '3003':+    param_latex: $\{3, 7, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '8480'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '450'+  '6006':+    param_latex: $\{2, 3, 7, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '469440'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '7062'+  '5005':+    param_latex: $\{5, 7, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3264'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '204'+  '10010':+    param_latex: $\{2, 5, 7, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '205824'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '3185'+  '15015':+    param_latex: $\{3, 5, 7, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '81152'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2294'+  '30030':+    param_latex: $\{2, 3, 5, 7, 11, 13\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '4576128'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '34960'+  '17':+    param_latex: $\{17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '8'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '4'+  '34':+    param_latex: $\{2, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '256'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '29'+  '51':+    param_latex: $\{3, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '120'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '22'+  '102':+    param_latex: $\{2, 3, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '6080'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '347'+  '85':+    param_latex: $\{5, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '40'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '10'+  '170':+    param_latex: $\{2, 5, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2688'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '161'+  '255':+    param_latex: $\{3, 5, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '968'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '95'+  '510':+    param_latex: $\{2, 3, 5, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '60128'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1784'+  '119':+    param_latex: $\{7, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '28'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '7'+  '238':+    param_latex: $\{2, 7, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2384'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '142'+  '357':+    param_latex: $\{3, 7, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1008'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '100'+  '714':+    param_latex: $\{2, 3, 7, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '55008'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1624'+  '595':+    param_latex: $\{5, 7, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '384'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '48'+  '1190':+    param_latex: $\{2, 5, 7, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '22816'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '698'+  '1785':+    param_latex: $\{3, 5, 7, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '9936'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '541'+  '3570':+    param_latex: $\{2, 3, 5, 7, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '536384'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '8108'+  '187':+    param_latex: $\{11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '64'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '16'+  '374':+    param_latex: $\{2, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1920'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '113'+  '561':+    param_latex: $\{3, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1000'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '99'+  '1122':+    param_latex: $\{2, 3, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '49888'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1464'+  '935':+    param_latex: $\{5, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '400'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '50'+  '1870':+    param_latex: $\{2, 5, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '21408'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '654'+  '2805':+    param_latex: $\{3, 5, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7952'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '417'+  '5610':+    param_latex: $\{2, 3, 5, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '488960'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '7367'+  '1309':+    param_latex: $\{7, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '320'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '40'+  '2618':+    param_latex: $\{2, 7, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '19904'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '607'+  '3927':+    param_latex: $\{3, 7, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7184'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '369'+  '7854':+    param_latex: $\{2, 3, 7, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '430912'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '6460'+  '6545':+    param_latex: $\{5, 7, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3536'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '221'+  '13090':+    param_latex: $\{2, 5, 7, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '191808'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2966'+  '19635':+    param_latex: $\{3, 5, 7, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '75424'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2115'+  '39270':+    param_latex: $\{2, 3, 5, 7, 11, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '4283008'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '32670'+  '221':+    param_latex: $\{13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '40'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '10'+  '442':+    param_latex: $\{2, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2064'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '122'+  '663':+    param_latex: $\{3, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1000'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '99'+  '1326':+    param_latex: $\{2, 3, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '45216'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1318'+  '1105':+    param_latex: $\{5, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '288'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '36'+  '2210':+    param_latex: $\{2, 5, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '18944'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '577'+  '3315':+    param_latex: $\{3, 5, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7904'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '414'+  '6630':+    param_latex: $\{2, 3, 5, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '457280'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '6872'+  '1547':+    param_latex: $\{7, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '224'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '28'+  '3094':+    param_latex: $\{2, 7, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '20320'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '620'+  '4641':+    param_latex: $\{3, 7, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '6816'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '346'+  '9282':+    param_latex: $\{2, 3, 7, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '406592'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '6080'+  '7735':+    param_latex: $\{5, 7, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3104'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '194'+  '15470':+    param_latex: $\{2, 5, 7, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '181824'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2810'+  '23205':+    param_latex: $\{3, 5, 7, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '73024'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2040'+  '46410':+    param_latex: $\{2, 3, 5, 7, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '4127872'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '31458'+  '2431':+    param_latex: $\{11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '344'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '43'+  '4862':+    param_latex: $\{2, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '15200'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '460'+  '7293':+    param_latex: $\{3, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7440'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '385'+  '14586':+    param_latex: $\{2, 3, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '342720'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '5082'+  '12155':+    param_latex: $\{5, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2464'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '154'+  '24310':+    param_latex: $\{2, 5, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '166208'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2566'+  '36465':+    param_latex: $\{3, 5, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '63808'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1752'+  '72930':+    param_latex: $\{2, 3, 5, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3625984'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '27537'+  '17017':+    param_latex: $\{7, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2224'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '139'+  '34034':+    param_latex: $\{2, 7, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '137728'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2121'+  '51051':+    param_latex: $\{3, 7, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '56608'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1527'+  '102102':+    param_latex: $\{2, 3, 7, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3210752'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '24293'+  '85085':+    param_latex: $\{5, 7, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '24352'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '761'+  '170170':+    param_latex: $\{2, 5, 7, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1479168'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '11493'+  '255255':+    param_latex: $\{3, 5, 7, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '565440'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '8107'+  '510510':+    param_latex: $\{2, 3, 5, 7, 11, 13, 17\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '32367872'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '124124'+  '19':+    param_latex: $\{19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '8'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '4'+  '38':+    param_latex: $\{2, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '336'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '39'+  '57':+    param_latex: $\{3, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '140'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '27'+  '114':+    param_latex: $\{2, 3, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '5936'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '338'+  '95':+    param_latex: $\{5, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '40'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '10'+  '190':+    param_latex: $\{2, 5, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2304'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '137'+  '285':+    param_latex: $\{3, 5, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1096'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '111'+  '570':+    param_latex: $\{2, 3, 5, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '58336'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1728'+  '133':+    param_latex: $\{7, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '32'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '8'+  '266':+    param_latex: $\{2, 7, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1904'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '112'+  '399':+    param_latex: $\{3, 7, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1024'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '102'+  '798':+    param_latex: $\{2, 3, 7, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '53760'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1585'+  '665':+    param_latex: $\{5, 7, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '408'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '51'+  '1330':+    param_latex: $\{2, 5, 7, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '24608'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '754'+  '1995':+    param_latex: $\{3, 5, 7, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '8768'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '468'+  '3990':+    param_latex: $\{2, 3, 5, 7, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '523584'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '7908'+  '209':+    param_latex: $\{11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '56'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '14'+  '418':+    param_latex: $\{2, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2576'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '154'+  '627':+    param_latex: $\{3, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '944'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '92'+  '1254':+    param_latex: $\{2, 3, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '49312'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1446'+  '1045':+    param_latex: $\{5, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '280'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '35'+  '2090':+    param_latex: $\{2, 5, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '20864'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '637'+  '3135':+    param_latex: $\{3, 5, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '8192'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '432'+  '6270':+    param_latex: $\{2, 3, 5, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '461568'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '6939'+  '1463':+    param_latex: $\{7, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '296'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '37'+  '2926':+    param_latex: $\{2, 7, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '18144'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '552'+  '4389':+    param_latex: $\{3, 7, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7616'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '396'+  '8778':+    param_latex: $\{2, 3, 7, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '423232'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '6340'+  '7315':+    param_latex: $\{5, 7, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2832'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '177'+  '14630':+    param_latex: $\{2, 5, 7, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '191872'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2967'+  '21945':+    param_latex: $\{3, 5, 7, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '73728'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2062'+  '43890':+    param_latex: $\{2, 3, 5, 7, 11, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '4233984'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '32287'+  '247':+    param_latex: $\{13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '16'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '4'+  '494':+    param_latex: $\{2, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2192'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '130'+  '741':+    param_latex: $\{3, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '848'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '80'+  '1482':+    param_latex: $\{2, 3, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '44768'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1304'+  '1235':+    param_latex: $\{5, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '288'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '36'+  '2470':+    param_latex: $\{2, 5, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '22016'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '673'+  '3705':+    param_latex: $\{3, 5, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7760'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '405'+  '7410':+    param_latex: $\{2, 3, 5, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '448640'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '6737'+  '1729':+    param_latex: $\{7, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '240'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '30'+  '3458':+    param_latex: $\{2, 7, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '17664'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '537'+  '5187':+    param_latex: $\{3, 7, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7520'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '390'+  '10374':+    param_latex: $\{2, 3, 7, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '399616'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '5971'+  '8645':+    param_latex: $\{5, 7, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2848'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '178'+  '17290':+    param_latex: $\{2, 5, 7, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '180032'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2782'+  '25935':+    param_latex: $\{3, 5, 7, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '70336'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1956'+  '51870':+    param_latex: $\{2, 3, 5, 7, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '4071552'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '31018'+  '2717':+    param_latex: $\{11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '232'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '29'+  '5434':+    param_latex: $\{2, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '17088'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '519'+  '8151':+    param_latex: $\{3, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '6480'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '325'+  '16302':+    param_latex: $\{2, 3, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '348352'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '5170'+  '13585':+    param_latex: $\{5, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2288'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '143'+  '27170':+    param_latex: $\{2, 5, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '165760'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2559'+  '40755':+    param_latex: $\{3, 5, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '64192'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1764'+  '81510':+    param_latex: $\{2, 3, 5, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3564288'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '27055'+  '19019':+    param_latex: $\{7, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2256'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '141'+  '38038':+    param_latex: $\{2, 7, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '135808'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2091'+  '57057':+    param_latex: $\{3, 7, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '59040'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1603'+  '114114':+    param_latex: $\{2, 3, 7, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3148672'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '23808'+  '95095':+    param_latex: $\{5, 7, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '22176'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '693'+  '190190':+    param_latex: $\{2, 5, 7, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1420672'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '11036'+  '285285':+    param_latex: $\{3, 5, 7, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '555200'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '7947'+  '570570':+    param_latex: $\{2, 3, 5, 7, 11, 13, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '31490048'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '120695'+  '323':+    param_latex: $\{17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '52'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '13'+  '646':+    param_latex: $\{2, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2080'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '123'+  '969':+    param_latex: $\{3, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '880'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '84'+  '1938':+    param_latex: $\{2, 3, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '43520'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1265'+  '1615':+    param_latex: $\{5, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '336'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '42'+  '3230':+    param_latex: $\{2, 5, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '20512'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '626'+  '4845':+    param_latex: $\{3, 5, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7664'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '399'+  '9690':+    param_latex: $\{2, 3, 5, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '417408'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '6249'+  '2261':+    param_latex: $\{7, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '304'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '38'+  '4522':+    param_latex: $\{2, 7, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '18112'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '551'+  '6783':+    param_latex: $\{3, 7, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7120'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '365'+  '13566':+    param_latex: $\{2, 3, 7, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '379904'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '5663'+  '11305':+    param_latex: $\{5, 7, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3344'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '209'+  '22610':+    param_latex: $\{2, 5, 7, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '177984'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2750'+  '33915':+    param_latex: $\{3, 5, 7, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '69696'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1936'+  '67830':+    param_latex: $\{2, 3, 5, 7, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3721728'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '28285'+  '3553':+    param_latex: $\{11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '392'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '49'+  '7106':+    param_latex: $\{2, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '15456'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '468'+  '10659':+    param_latex: $\{3, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '7328'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '378'+  '21318':+    param_latex: $\{2, 3, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '352384'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '5233'+  '17765':+    param_latex: $\{5, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2640'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '165'+  '35530':+    param_latex: $\{2, 5, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '149120'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2299'+  '53295':+    param_latex: $\{3, 5, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '60640'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1653'+  '106590':+    param_latex: $\{2, 3, 5, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3302784'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '25012'+  '24871':+    param_latex: $\{7, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2400'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '150'+  '49742':+    param_latex: $\{2, 7, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '138176'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2128'+  '74613':+    param_latex: $\{3, 7, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '57504'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1555'+  '149226':+    param_latex: $\{2, 3, 7, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2947840'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '22239'+  '124355':+    param_latex: $\{5, 7, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '23552'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '736'+  '248710':+    param_latex: $\{2, 5, 7, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1346560'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '10457'+  '373065':+    param_latex: $\{3, 5, 7, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '528704'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '7533'+  '746130':+    param_latex: $\{2, 3, 5, 7, 11, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '29356544'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '112361'+  '4199':+    param_latex: $\{13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '208'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '26'+  '8398':+    param_latex: $\{2, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '13792'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '416'+  '12597':+    param_latex: $\{3, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '6048'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '298'+  '25194':+    param_latex: $\{2, 3, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '332800'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '4927'+  '20995':+    param_latex: $\{5, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2080'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '130'+  '41990':+    param_latex: $\{2, 5, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '146944'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2265'+  '62985':+    param_latex: $\{3, 5, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '53856'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1441'+  '125970':+    param_latex: $\{2, 3, 5, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3148800'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '23809'+  '29393':+    param_latex: $\{7, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1856'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '116'+  '58786':+    param_latex: $\{2, 7, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '129728'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1996'+  '88179':+    param_latex: $\{3, 7, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '50816'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1346'+  '176358':+    param_latex: $\{2, 3, 7, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2803456'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '21111'+  '146965':+    param_latex: $\{5, 7, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '22560'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '705'+  '293930':+    param_latex: $\{2, 5, 7, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1292928'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '10038'+  '440895':+    param_latex: $\{3, 5, 7, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '496768'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '7034'+  '881790':+    param_latex: $\{2, 3, 5, 7, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '28140800'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '107612'+  '46189':+    param_latex: $\{11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1952'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '122'+  '92378':+    param_latex: $\{2, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '111744'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1715'+  '138567':+    param_latex: $\{3, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '48736'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '1281'+  '277134':+    param_latex: $\{2, 3, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '2497280'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '18719'+  '230945':+    param_latex: $\{5, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '16928'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '529'+  '461890':+    param_latex: $\{2, 5, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1131520'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '8777'+  '692835':+    param_latex: $\{3, 5, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '442944'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '6193'+  '1385670':+    param_latex: $\{2, 3, 5, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '24646912'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '93964'+  '323323':+    param_latex: $\{7, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '17152'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '536'+  '646646':+    param_latex: $\{2, 7, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '1022336'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '7924'+  '969969':+    param_latex: $\{3, 7, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '417280'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '5792'+  '1939938':+    param_latex: $\{2, 3, 7, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '22180864'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '84331'+  '1616615':+    param_latex: $\{5, 7, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '167744'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '2621'+  '3233230':+    param_latex: $\{2, 5, 7, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '10008064'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '38967'+  '4849845':+    param_latex: $\{3, 5, 7, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '3837184'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '27792'+  '9699690':+    param_latex: $\{2, 3, 5, 7, 11, 13, 17, 19\}$+    numbers:+      Q:+        param-latex: $\mathbb{Q}$+        number: '217923072'+      Qbar:+        param-latex: $\overline{\mathbb{Q}}$+        number: '418816'