LMFDB - Modular curve search results

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Level	Index	Genus	Rank	Genus-rank difference

$\Q$-gonality	Cusps	$\Q$-cusps	Elliptic points of order 2	Elliptic points of order 3

Simple	Squarefree	CM points	Fiber product with	Minimally covers

Minimally covered by	Contains $-I$	Points	Obstructions	Family

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Results (1-50 of at least 1000)

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Label	CP label	Level	Index	Genus	$\Q$-gonality	Cusps	$\Q$-cusps	Conductor	Simple	Squarefree	Contains -1	Decomposition	Local obstruction	$\operatorname{GL}_2(\mathbb{Z}/N\mathbb{Z})$-generators
232.48.0-4.a.1.1	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}27&46\\2&229\end{bmatrix}$, $\begin{bmatrix}133&160\\124&49\end{bmatrix}$, $\begin{bmatrix}147&178\\38&225\end{bmatrix}$, $\begin{bmatrix}187&40\\24&63\end{bmatrix}$, $\begin{bmatrix}201&52\\108&153\end{bmatrix}$
232.48.0-4.a.1.2	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}167&2\\178&105\end{bmatrix}$, $\begin{bmatrix}173&70\\182&11\end{bmatrix}$, $\begin{bmatrix}191&20\\96&187\end{bmatrix}$, $\begin{bmatrix}191&76\\28&139\end{bmatrix}$, $\begin{bmatrix}217&218\\102&95\end{bmatrix}$
232.48.0-4.a.1.3	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}51&100\\156&115\end{bmatrix}$, $\begin{bmatrix}175&208\\48&199\end{bmatrix}$, $\begin{bmatrix}181&112\\112&225\end{bmatrix}$, $\begin{bmatrix}185&166\\66&175\end{bmatrix}$, $\begin{bmatrix}205&16\\28&77\end{bmatrix}$
232.48.0-8.a.1.1	4G0	$232$	$48$	$0$	$1$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}171&128\\150&39\end{bmatrix}$, $\begin{bmatrix}173&170\\92&227\end{bmatrix}$, $\begin{bmatrix}205&78\\108&171\end{bmatrix}$, $\begin{bmatrix}205&224\\6&89\end{bmatrix}$
232.48.0-8.a.1.2	4G0	$232$	$48$	$0$	$1$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}135&148\\156&159\end{bmatrix}$, $\begin{bmatrix}137&68\\40&169\end{bmatrix}$, $\begin{bmatrix}189&44\\110&145\end{bmatrix}$, $\begin{bmatrix}189&210\\154&123\end{bmatrix}$
232.48.0-8.a.1.3	4G0	$232$	$48$	$0$	$1$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}7&2\\224&41\end{bmatrix}$, $\begin{bmatrix}67&190\\152&5\end{bmatrix}$, $\begin{bmatrix}167&182\\118&137\end{bmatrix}$, $\begin{bmatrix}211&72\\134&183\end{bmatrix}$
232.48.0-8.a.1.4	4G0	$232$	$48$	$0$	$1$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}99&184\\128&131\end{bmatrix}$, $\begin{bmatrix}115&168\\146&231\end{bmatrix}$, $\begin{bmatrix}177&214\\46&183\end{bmatrix}$, $\begin{bmatrix}201&140\\94&117\end{bmatrix}$
232.48.0-116.a.1.1	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}33&40\\70&157\end{bmatrix}$, $\begin{bmatrix}35&116\\132&199\end{bmatrix}$, $\begin{bmatrix}105&10\\188&227\end{bmatrix}$, $\begin{bmatrix}127&102\\198&81\end{bmatrix}$
232.48.0-116.a.1.2	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}15&58\\226&205\end{bmatrix}$, $\begin{bmatrix}157&76\\18&61\end{bmatrix}$, $\begin{bmatrix}171&176\\224&7\end{bmatrix}$, $\begin{bmatrix}195&212\\204&179\end{bmatrix}$
232.48.0-116.a.1.3	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}65&82\\142&23\end{bmatrix}$, $\begin{bmatrix}73&18\\192&127\end{bmatrix}$, $\begin{bmatrix}123&2\\180&181\end{bmatrix}$, $\begin{bmatrix}205&152\\6&189\end{bmatrix}$
232.48.0-116.a.1.4	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}133&82\\22&87\end{bmatrix}$, $\begin{bmatrix}137&170\\56&119\end{bmatrix}$, $\begin{bmatrix}179&12\\176&79\end{bmatrix}$, $\begin{bmatrix}197&156\\198&157\end{bmatrix}$
232.48.0-116.a.1.5	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}95&134\\68&181\end{bmatrix}$, $\begin{bmatrix}115&102\\160&133\end{bmatrix}$, $\begin{bmatrix}121&166\\68&103\end{bmatrix}$, $\begin{bmatrix}159&104\\162&111\end{bmatrix}$
232.48.0-116.a.1.6	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}35&120\\164&95\end{bmatrix}$, $\begin{bmatrix}35&214\\226&53\end{bmatrix}$, $\begin{bmatrix}41&128\\62&97\end{bmatrix}$, $\begin{bmatrix}181&132\\190&153\end{bmatrix}$
232.48.0.a.1	8N0	$232$	$48$	$0$	$2$	$10$	$0$	$?$	?	?	✓	not computed	✓	$\begin{bmatrix}35&184\\0&93\end{bmatrix}$, $\begin{bmatrix}47&120\\8&95\end{bmatrix}$, $\begin{bmatrix}49&188\\84&215\end{bmatrix}$, $\begin{bmatrix}89&96\\156&19\end{bmatrix}$, $\begin{bmatrix}117&48\\140&191\end{bmatrix}$, $\begin{bmatrix}117&48\\176&15\end{bmatrix}$
232.48.0-232.a.1.1	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}137&122\\166&23\end{bmatrix}$, $\begin{bmatrix}161&166\\98&63\end{bmatrix}$, $\begin{bmatrix}177&10\\194&131\end{bmatrix}$, $\begin{bmatrix}209&30\\60&103\end{bmatrix}$
232.48.0-232.a.1.2	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}25&158\\98&123\end{bmatrix}$, $\begin{bmatrix}45&212\\92&101\end{bmatrix}$, $\begin{bmatrix}59&176\\16&167\end{bmatrix}$, $\begin{bmatrix}215&28\\218&15\end{bmatrix}$
232.48.0-232.a.1.3	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}35&44\\166&87\end{bmatrix}$, $\begin{bmatrix}53&152\\182&117\end{bmatrix}$, $\begin{bmatrix}79&186\\154&129\end{bmatrix}$, $\begin{bmatrix}111&52\\202&135\end{bmatrix}$
232.48.0-232.a.1.4	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}29&198\\110&107\end{bmatrix}$, $\begin{bmatrix}95&124\\220&135\end{bmatrix}$, $\begin{bmatrix}163&122\\162&121\end{bmatrix}$, $\begin{bmatrix}197&50\\124&231\end{bmatrix}$
232.48.0-232.a.1.5	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}57&90\\110&219\end{bmatrix}$, $\begin{bmatrix}73&148\\36&1\end{bmatrix}$, $\begin{bmatrix}115&206\\52&153\end{bmatrix}$, $\begin{bmatrix}197&118\\8&187\end{bmatrix}$
232.48.0-232.a.1.6	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}9&174\\190&199\end{bmatrix}$, $\begin{bmatrix}71&178\\56&5\end{bmatrix}$, $\begin{bmatrix}73&188\\164&105\end{bmatrix}$, $\begin{bmatrix}95&48\\18&147\end{bmatrix}$
232.48.0-232.a.1.7	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}55&70\\24&77\end{bmatrix}$, $\begin{bmatrix}59&26\\198&201\end{bmatrix}$, $\begin{bmatrix}225&174\\44&99\end{bmatrix}$, $\begin{bmatrix}231&54\\182&25\end{bmatrix}$
232.48.0-232.a.1.8	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}75&118\\36&105\end{bmatrix}$, $\begin{bmatrix}131&10\\130&45\end{bmatrix}$, $\begin{bmatrix}143&20\\104&167\end{bmatrix}$, $\begin{bmatrix}187&166\\228&221\end{bmatrix}$
232.48.0-4.b.1.1	4G0	$232$	$48$	$0$	$1$	$6$	$4$	$?$	?	?		not computed		$\begin{bmatrix}45&8\\224&123\end{bmatrix}$, $\begin{bmatrix}55&28\\120&47\end{bmatrix}$, $\begin{bmatrix}75&116\\76&215\end{bmatrix}$, $\begin{bmatrix}99&168\\184&211\end{bmatrix}$, $\begin{bmatrix}139&112\\48&143\end{bmatrix}$, $\begin{bmatrix}207&224\\168&183\end{bmatrix}$
232.48.0-4.b.1.2	4G0	$232$	$48$	$0$	$1$	$6$	$4$	$?$	?	?		not computed		$\begin{bmatrix}33&128\\20&3\end{bmatrix}$, $\begin{bmatrix}87&108\\216&201\end{bmatrix}$, $\begin{bmatrix}109&156\\92&85\end{bmatrix}$, $\begin{bmatrix}123&136\\172&159\end{bmatrix}$, $\begin{bmatrix}143&56\\36&147\end{bmatrix}$, $\begin{bmatrix}153&104\\72&141\end{bmatrix}$
232.48.0-4.b.1.3	4G0	$232$	$48$	$0$	$1$	$6$	$4$	$?$	?	?		not computed		$\begin{bmatrix}39&228\\136&209\end{bmatrix}$, $\begin{bmatrix}47&176\\212&93\end{bmatrix}$, $\begin{bmatrix}57&176\\100&149\end{bmatrix}$, $\begin{bmatrix}65&64\\112&147\end{bmatrix}$, $\begin{bmatrix}133&148\\172&221\end{bmatrix}$, $\begin{bmatrix}229&160\\140&1\end{bmatrix}$
232.48.0-4.b.1.4	4G0	$232$	$48$	$0$	$1$	$6$	$4$	$?$	?	?		not computed		$\begin{bmatrix}39&224\\112&107\end{bmatrix}$, $\begin{bmatrix}43&120\\128&229\end{bmatrix}$, $\begin{bmatrix}93&112\\104&213\end{bmatrix}$, $\begin{bmatrix}95&108\\168&171\end{bmatrix}$, $\begin{bmatrix}115&176\\24&161\end{bmatrix}$, $\begin{bmatrix}217&80\\100&161\end{bmatrix}$
232.48.0-4.b.1.5	4G0	$232$	$48$	$0$	$1$	$6$	$4$	$?$	?	?		not computed		$\begin{bmatrix}7&148\\16&129\end{bmatrix}$, $\begin{bmatrix}39&168\\8&185\end{bmatrix}$, $\begin{bmatrix}73&72\\196&143\end{bmatrix}$, $\begin{bmatrix}141&200\\156&67\end{bmatrix}$, $\begin{bmatrix}211&112\\212&95\end{bmatrix}$, $\begin{bmatrix}219&188\\52&197\end{bmatrix}$
232.48.0-4.b.1.6	4G0	$232$	$48$	$0$	$1$	$6$	$4$	$?$	?	?		not computed		$\begin{bmatrix}49&208\\148&13\end{bmatrix}$, $\begin{bmatrix}73&76\\96&117\end{bmatrix}$, $\begin{bmatrix}169&20\\100&223\end{bmatrix}$, $\begin{bmatrix}175&80\\180&117\end{bmatrix}$, $\begin{bmatrix}187&224\\52&43\end{bmatrix}$, $\begin{bmatrix}195&80\\96&13\end{bmatrix}$
232.48.0-4.b.1.7	4G0	$232$	$48$	$0$	$1$	$6$	$4$	$?$	?	?		not computed		$\begin{bmatrix}33&76\\148&225\end{bmatrix}$, $\begin{bmatrix}97&144\\200&15\end{bmatrix}$, $\begin{bmatrix}111&4\\112&39\end{bmatrix}$, $\begin{bmatrix}135&24\\20&181\end{bmatrix}$, $\begin{bmatrix}139&216\\216&125\end{bmatrix}$, $\begin{bmatrix}225&168\\28&155\end{bmatrix}$
232.48.0-4.b.1.8	4G0	$232$	$48$	$0$	$1$	$6$	$4$	$?$	?	?		not computed		$\begin{bmatrix}29&208\\68&23\end{bmatrix}$, $\begin{bmatrix}45&148\\68&53\end{bmatrix}$, $\begin{bmatrix}115&4\\132&67\end{bmatrix}$, $\begin{bmatrix}125&56\\188&161\end{bmatrix}$, $\begin{bmatrix}137&8\\168&219\end{bmatrix}$, $\begin{bmatrix}147&136\\152&57\end{bmatrix}$
232.48.0-4.b.1.9	4G0	$232$	$48$	$0$	$1$	$6$	$4$	$?$	?	?		not computed		$\begin{bmatrix}29&188\\40&73\end{bmatrix}$, $\begin{bmatrix}55&92\\48&21\end{bmatrix}$, $\begin{bmatrix}95&164\\204&1\end{bmatrix}$, $\begin{bmatrix}135&92\\180&35\end{bmatrix}$, $\begin{bmatrix}149&76\\136&205\end{bmatrix}$, $\begin{bmatrix}175&192\\152&205\end{bmatrix}$
232.48.0-4.b.1.10	4G0	$232$	$48$	$0$	$1$	$6$	$4$	$?$	?	?		not computed		$\begin{bmatrix}45&112\\204&137\end{bmatrix}$, $\begin{bmatrix}157&152\\216&27\end{bmatrix}$, $\begin{bmatrix}159&8\\4&9\end{bmatrix}$, $\begin{bmatrix}165&60\\176&31\end{bmatrix}$, $\begin{bmatrix}185&36\\220&177\end{bmatrix}$, $\begin{bmatrix}187&56\\108&151\end{bmatrix}$
232.48.0-8.b.1.1	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}87&146\\126&133\end{bmatrix}$, $\begin{bmatrix}109&22\\68&135\end{bmatrix}$, $\begin{bmatrix}171&206\\8&113\end{bmatrix}$, $\begin{bmatrix}179&14\\90&9\end{bmatrix}$
232.48.0-8.b.1.2	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}5&28\\120&53\end{bmatrix}$, $\begin{bmatrix}41&226\\10&35\end{bmatrix}$, $\begin{bmatrix}59&190\\86&1\end{bmatrix}$, $\begin{bmatrix}137&6\\128&227\end{bmatrix}$
232.48.0-8.b.1.3	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}3&158\\230&153\end{bmatrix}$, $\begin{bmatrix}103&146\\124&53\end{bmatrix}$, $\begin{bmatrix}153&86\\86&3\end{bmatrix}$, $\begin{bmatrix}175&100\\2&51\end{bmatrix}$
232.48.0-8.b.1.4	4G0	$232$	$48$	$0$	$2$	$6$	$0$	$?$	?	?		not computed	✓	$\begin{bmatrix}47&62\\150&85\end{bmatrix}$, $\begin{bmatrix}55&142\\224&13\end{bmatrix}$, $\begin{bmatrix}131&28\\166&199\end{bmatrix}$, $\begin{bmatrix}189&60\\106&209\end{bmatrix}$
232.48.0-116.b.1.1	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}5&114\\160&149\end{bmatrix}$, $\begin{bmatrix}117&172\\90&203\end{bmatrix}$, $\begin{bmatrix}139&178\\142&21\end{bmatrix}$, $\begin{bmatrix}183&2\\164&131\end{bmatrix}$, $\begin{bmatrix}193&118\\164&177\end{bmatrix}$
232.48.0-116.b.1.2	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}9&104\\2&43\end{bmatrix}$, $\begin{bmatrix}15&146\\8&167\end{bmatrix}$, $\begin{bmatrix}27&192\\48&127\end{bmatrix}$, $\begin{bmatrix}133&92\\136&217\end{bmatrix}$, $\begin{bmatrix}203&218\\212&3\end{bmatrix}$
232.48.0-116.b.1.3	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}49&22\\226&131\end{bmatrix}$, $\begin{bmatrix}89&162\\206&163\end{bmatrix}$, $\begin{bmatrix}99&112\\14&65\end{bmatrix}$, $\begin{bmatrix}149&28\\74&87\end{bmatrix}$, $\begin{bmatrix}219&6\\120&35\end{bmatrix}$
232.48.0-116.b.1.4	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}69&200\\78&127\end{bmatrix}$, $\begin{bmatrix}99&174\\106&53\end{bmatrix}$, $\begin{bmatrix}101&204\\44&125\end{bmatrix}$, $\begin{bmatrix}161&156\\20&17\end{bmatrix}$, $\begin{bmatrix}211&148\\222&149\end{bmatrix}$
232.48.0-116.b.1.5	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}49&192\\80&197\end{bmatrix}$, $\begin{bmatrix}95&142\\142&105\end{bmatrix}$, $\begin{bmatrix}143&184\\62&53\end{bmatrix}$, $\begin{bmatrix}215&130\\6&61\end{bmatrix}$, $\begin{bmatrix}225&16\\86&51\end{bmatrix}$
232.48.0-116.b.1.6	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}31&156\\162&125\end{bmatrix}$, $\begin{bmatrix}41&92\\54&47\end{bmatrix}$, $\begin{bmatrix}47&106\\156&55\end{bmatrix}$, $\begin{bmatrix}117&192\\162&7\end{bmatrix}$, $\begin{bmatrix}123&64\\186&201\end{bmatrix}$
232.48.0-116.b.1.7	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}17&154\\122&15\end{bmatrix}$, $\begin{bmatrix}21&98\\30&95\end{bmatrix}$, $\begin{bmatrix}135&220\\146&189\end{bmatrix}$, $\begin{bmatrix}137&60\\98&63\end{bmatrix}$, $\begin{bmatrix}199&72\\48&155\end{bmatrix}$
232.48.0-116.b.1.8	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}17&198\\64&149\end{bmatrix}$, $\begin{bmatrix}75&70\\210&173\end{bmatrix}$, $\begin{bmatrix}109&216\\78&47\end{bmatrix}$, $\begin{bmatrix}139&118\\46&161\end{bmatrix}$, $\begin{bmatrix}143&106\\104&231\end{bmatrix}$
232.48.0-116.b.1.9	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}13&110\\44&133\end{bmatrix}$, $\begin{bmatrix}165&20\\176&69\end{bmatrix}$, $\begin{bmatrix}169&120\\184&157\end{bmatrix}$, $\begin{bmatrix}217&180\\130&183\end{bmatrix}$, $\begin{bmatrix}231&48\\4&215\end{bmatrix}$
232.48.0-116.b.1.10	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}5&60\\230&203\end{bmatrix}$, $\begin{bmatrix}35&4\\126&17\end{bmatrix}$, $\begin{bmatrix}55&132\\60&55\end{bmatrix}$, $\begin{bmatrix}97&80\\196&57\end{bmatrix}$, $\begin{bmatrix}177&38\\2&63\end{bmatrix}$
232.48.0.b.1	8N0	$232$	$48$	$0$	$1$	$10$	$2$	$?$	?	?	✓	not computed		$\begin{bmatrix}49&38\\200&43\end{bmatrix}$, $\begin{bmatrix}105&194\\144&151\end{bmatrix}$, $\begin{bmatrix}163&86\\224&137\end{bmatrix}$, $\begin{bmatrix}193&36\\192&185\end{bmatrix}$, $\begin{bmatrix}197&38\\192&167\end{bmatrix}$, $\begin{bmatrix}215&96\\204&107\end{bmatrix}$
232.48.0-232.b.1.1	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}109&206\\4&143\end{bmatrix}$, $\begin{bmatrix}133&46\\34&141\end{bmatrix}$, $\begin{bmatrix}185&156\\128&79\end{bmatrix}$
232.48.0-232.b.1.2	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}53&16\\176&43\end{bmatrix}$, $\begin{bmatrix}99&34\\50&85\end{bmatrix}$, $\begin{bmatrix}213&98\\124&143\end{bmatrix}$
232.48.0-232.b.1.3	4G0	$232$	$48$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?		not computed	?	$\begin{bmatrix}49&170\\158&207\end{bmatrix}$, $\begin{bmatrix}127&114\\204&59\end{bmatrix}$, $\begin{bmatrix}177&174\\140&227\end{bmatrix}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.