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

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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	Decomposition	Local obstruction	$\operatorname{GL}_2(\mathbb{Z}/N\mathbb{Z})$-generators
232.192.1-8.a.1.1	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}7&168\\188&173\end{bmatrix}$, $\begin{bmatrix}101&100\\148&187\end{bmatrix}$, $\begin{bmatrix}193&24\\88&27\end{bmatrix}$, $\begin{bmatrix}201&32\\228&33\end{bmatrix}$
232.192.1-8.a.1.2	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}61&84\\0&193\end{bmatrix}$, $\begin{bmatrix}103&0\\216&119\end{bmatrix}$, $\begin{bmatrix}127&168\\172&213\end{bmatrix}$, $\begin{bmatrix}141&204\\148&1\end{bmatrix}$
232.192.1-8.a.1.3	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}79&152\\156&127\end{bmatrix}$, $\begin{bmatrix}115&228\\152&37\end{bmatrix}$, $\begin{bmatrix}165&60\\176&33\end{bmatrix}$, $\begin{bmatrix}207&224\\76&197\end{bmatrix}$
232.192.1-8.a.1.4	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}11&76\\156&181\end{bmatrix}$, $\begin{bmatrix}33&16\\108&43\end{bmatrix}$, $\begin{bmatrix}93&4\\208&153\end{bmatrix}$, $\begin{bmatrix}173&204\\172&129\end{bmatrix}$
232.192.1-8.a.1.5	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}171&180\\120&167\end{bmatrix}$, $\begin{bmatrix}173&172\\68&139\end{bmatrix}$, $\begin{bmatrix}219&132\\180&223\end{bmatrix}$, $\begin{bmatrix}227&36\\116&141\end{bmatrix}$
232.192.1-8.a.1.6	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}21&204\\188&147\end{bmatrix}$, $\begin{bmatrix}57&8\\76&91\end{bmatrix}$, $\begin{bmatrix}115&52\\40&93\end{bmatrix}$, $\begin{bmatrix}141&100\\152&19\end{bmatrix}$
232.192.1-8.a.2.1	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}77&136\\60&31\end{bmatrix}$, $\begin{bmatrix}139&8\\48&225\end{bmatrix}$, $\begin{bmatrix}139&172\\176&13\end{bmatrix}$, $\begin{bmatrix}179&124\\20&173\end{bmatrix}$
232.192.1-8.a.2.2	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}17&92\\16&141\end{bmatrix}$, $\begin{bmatrix}93&108\\160&211\end{bmatrix}$, $\begin{bmatrix}117&44\\52&155\end{bmatrix}$, $\begin{bmatrix}175&120\\132&191\end{bmatrix}$
232.192.1-8.a.2.3	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}3&0\\84&1\end{bmatrix}$, $\begin{bmatrix}97&0\\204&17\end{bmatrix}$, $\begin{bmatrix}117&52\\180&179\end{bmatrix}$, $\begin{bmatrix}195&60\\76&109\end{bmatrix}$
232.192.1-8.a.2.4	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}83&148\\156&125\end{bmatrix}$, $\begin{bmatrix}107&28\\96&45\end{bmatrix}$, $\begin{bmatrix}127&64\\228&207\end{bmatrix}$, $\begin{bmatrix}203&24\\56&193\end{bmatrix}$
232.192.1-8.a.2.5	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}35&192\\144&89\end{bmatrix}$, $\begin{bmatrix}97&180\\140&13\end{bmatrix}$, $\begin{bmatrix}113&84\\56&93\end{bmatrix}$, $\begin{bmatrix}229&120\\180&87\end{bmatrix}$
232.192.1-8.a.2.6	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}35&124\\40&197\end{bmatrix}$, $\begin{bmatrix}151&80\\172&79\end{bmatrix}$, $\begin{bmatrix}175&96\\168&79\end{bmatrix}$, $\begin{bmatrix}195&112\\212&113\end{bmatrix}$
232.192.1-232.a.1.1	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}5&116\\140&187\end{bmatrix}$, $\begin{bmatrix}17&180\\116&35\end{bmatrix}$, $\begin{bmatrix}103&184\\176&173\end{bmatrix}$, $\begin{bmatrix}137&16\\180&73\end{bmatrix}$
232.192.1-232.a.1.2	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}1&224\\200&203\end{bmatrix}$, $\begin{bmatrix}107&8\\224&173\end{bmatrix}$, $\begin{bmatrix}177&204\\28&209\end{bmatrix}$, $\begin{bmatrix}225&8\\12&147\end{bmatrix}$
232.192.1-232.a.1.3	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}49&28\\168&99\end{bmatrix}$, $\begin{bmatrix}105&112\\200&139\end{bmatrix}$, $\begin{bmatrix}141&172\\112&139\end{bmatrix}$, $\begin{bmatrix}205&132\\140&1\end{bmatrix}$
232.192.1-232.a.1.4	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}43&120\\8&7\end{bmatrix}$, $\begin{bmatrix}43&224\\188&63\end{bmatrix}$, $\begin{bmatrix}61&108\\156&201\end{bmatrix}$, $\begin{bmatrix}159&152\\104&229\end{bmatrix}$
232.192.1-232.a.1.5	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}69&172\\16&153\end{bmatrix}$, $\begin{bmatrix}93&112\\64&209\end{bmatrix}$, $\begin{bmatrix}119&140\\100&69\end{bmatrix}$, $\begin{bmatrix}163&184\\200&21\end{bmatrix}$
232.192.1-232.a.1.6	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}47&76\\48&229\end{bmatrix}$, $\begin{bmatrix}57&144\\144&35\end{bmatrix}$, $\begin{bmatrix}123&208\\0&127\end{bmatrix}$, $\begin{bmatrix}147&224\\204&79\end{bmatrix}$
232.192.1-232.a.1.7	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}37&160\\108&163\end{bmatrix}$, $\begin{bmatrix}57&160\\188&67\end{bmatrix}$, $\begin{bmatrix}79&108\\228&87\end{bmatrix}$, $\begin{bmatrix}119&76\\176&7\end{bmatrix}$
232.192.1-232.a.1.8	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}163&144\\180&215\end{bmatrix}$, $\begin{bmatrix}175&176\\12&173\end{bmatrix}$, $\begin{bmatrix}197&192\\204&123\end{bmatrix}$, $\begin{bmatrix}205&100\\32&147\end{bmatrix}$
232.192.1-232.a.1.9	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}3&140\\128&143\end{bmatrix}$, $\begin{bmatrix}87&48\\184&205\end{bmatrix}$, $\begin{bmatrix}105&160\\28&43\end{bmatrix}$, $\begin{bmatrix}211&96\\168&95\end{bmatrix}$
232.192.1-232.a.1.10	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}81&116\\140&171\end{bmatrix}$, $\begin{bmatrix}119&84\\64&143\end{bmatrix}$, $\begin{bmatrix}129&40\\72&27\end{bmatrix}$, $\begin{bmatrix}147&16\\172&167\end{bmatrix}$
232.192.1-232.a.1.11	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}29&224\\36&115\end{bmatrix}$, $\begin{bmatrix}73&180\\212&171\end{bmatrix}$, $\begin{bmatrix}81&204\\228&17\end{bmatrix}$, $\begin{bmatrix}183&40\\188&181\end{bmatrix}$
232.192.1-232.a.1.12	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}91&92\\92&79\end{bmatrix}$, $\begin{bmatrix}103&172\\60&167\end{bmatrix}$, $\begin{bmatrix}139&192\\184&117\end{bmatrix}$, $\begin{bmatrix}149&140\\104&137\end{bmatrix}$
232.192.1-232.a.2.1	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}67&56\\192&85\end{bmatrix}$, $\begin{bmatrix}113&100\\80&161\end{bmatrix}$, $\begin{bmatrix}217&44\\48&21\end{bmatrix}$, $\begin{bmatrix}225&224\\196&197\end{bmatrix}$
232.192.1-232.a.2.2	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}9&112\\36&189\end{bmatrix}$, $\begin{bmatrix}19&196\\16&169\end{bmatrix}$, $\begin{bmatrix}109&104\\112&159\end{bmatrix}$, $\begin{bmatrix}129&56\\172&185\end{bmatrix}$
232.192.1-232.a.2.3	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}33&32\\24&149\end{bmatrix}$, $\begin{bmatrix}69&108\\16&147\end{bmatrix}$, $\begin{bmatrix}101&124\\92&179\end{bmatrix}$, $\begin{bmatrix}107&152\\112&25\end{bmatrix}$
232.192.1-232.a.2.4	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}13&132\\32&51\end{bmatrix}$, $\begin{bmatrix}49&164\\64&85\end{bmatrix}$, $\begin{bmatrix}137&60\\192&33\end{bmatrix}$, $\begin{bmatrix}189&200\\124&231\end{bmatrix}$
232.192.1-232.a.2.5	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}9&212\\120&165\end{bmatrix}$, $\begin{bmatrix}43&140\\176&161\end{bmatrix}$, $\begin{bmatrix}173&200\\28&151\end{bmatrix}$, $\begin{bmatrix}199&224\\224&115\end{bmatrix}$
232.192.1-232.a.2.6	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}1&212\\100&57\end{bmatrix}$, $\begin{bmatrix}23&124\\96&155\end{bmatrix}$, $\begin{bmatrix}29&44\\56&115\end{bmatrix}$, $\begin{bmatrix}177&24\\204&105\end{bmatrix}$
232.192.1-232.a.2.7	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}55&64\\196&155\end{bmatrix}$, $\begin{bmatrix}75&32\\208&69\end{bmatrix}$, $\begin{bmatrix}97&12\\24&65\end{bmatrix}$, $\begin{bmatrix}207&160\\216&187\end{bmatrix}$
232.192.1-232.a.2.8	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}25&116\\188&125\end{bmatrix}$, $\begin{bmatrix}55&64\\52&115\end{bmatrix}$, $\begin{bmatrix}143&132\\220&87\end{bmatrix}$, $\begin{bmatrix}221&52\\96&119\end{bmatrix}$
232.192.1-232.a.2.9	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}71&156\\120&187\end{bmatrix}$, $\begin{bmatrix}179&140\\80&73\end{bmatrix}$, $\begin{bmatrix}217&84\\44&29\end{bmatrix}$, $\begin{bmatrix}219&156\\56&69\end{bmatrix}$
232.192.1-232.a.2.10	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}5&188\\148&187\end{bmatrix}$, $\begin{bmatrix}7&100\\228&27\end{bmatrix}$, $\begin{bmatrix}57&104\\176&61\end{bmatrix}$, $\begin{bmatrix}93&104\\124&47\end{bmatrix}$
232.192.1-232.a.2.11	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}25&140\\20&125\end{bmatrix}$, $\begin{bmatrix}55&196\\164&119\end{bmatrix}$, $\begin{bmatrix}93&116\\172&79\end{bmatrix}$, $\begin{bmatrix}149&120\\204&55\end{bmatrix}$
232.192.1-232.a.2.12	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}15&84\\148&203\end{bmatrix}$, $\begin{bmatrix}27&156\\60&229\end{bmatrix}$, $\begin{bmatrix}129&108\\200&181\end{bmatrix}$, $\begin{bmatrix}217&200\\44&173\end{bmatrix}$
232.192.1-8.b.1.1	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}55&16\\204&13\end{bmatrix}$, $\begin{bmatrix}69&72\\144&75\end{bmatrix}$, $\begin{bmatrix}131&160\\44&61\end{bmatrix}$, $\begin{bmatrix}197&48\\180&153\end{bmatrix}$
232.192.1-8.b.1.2	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}49&184\\224&163\end{bmatrix}$, $\begin{bmatrix}91&224\\120&207\end{bmatrix}$, $\begin{bmatrix}119&16\\84&159\end{bmatrix}$, $\begin{bmatrix}161&8\\140&105\end{bmatrix}$
232.192.1-8.b.1.3	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}95&184\\68&111\end{bmatrix}$, $\begin{bmatrix}157&88\\176&209\end{bmatrix}$, $\begin{bmatrix}185&176\\44&89\end{bmatrix}$, $\begin{bmatrix}199&80\\156&21\end{bmatrix}$
232.192.1-8.b.1.4	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}105&32\\96&43\end{bmatrix}$, $\begin{bmatrix}155&176\\168&79\end{bmatrix}$, $\begin{bmatrix}201&208\\28&1\end{bmatrix}$, $\begin{bmatrix}221&136\\28&89\end{bmatrix}$
232.192.1-8.b.1.5	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}57&224\\132&171\end{bmatrix}$, $\begin{bmatrix}67&8\\196&15\end{bmatrix}$, $\begin{bmatrix}171&120\\132&213\end{bmatrix}$, $\begin{bmatrix}205&136\\196&177\end{bmatrix}$
232.192.1-8.b.1.6	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}81&16\\164&115\end{bmatrix}$, $\begin{bmatrix}87&176\\56&229\end{bmatrix}$, $\begin{bmatrix}189&112\\48&17\end{bmatrix}$, $\begin{bmatrix}199&144\\152&135\end{bmatrix}$
232.192.1-8.b.2.1	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}5&120\\40&47\end{bmatrix}$, $\begin{bmatrix}27&80\\200&45\end{bmatrix}$, $\begin{bmatrix}95&0\\204&23\end{bmatrix}$, $\begin{bmatrix}183&112\\128&207\end{bmatrix}$
232.192.1-8.b.2.2	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}33&64\\28&145\end{bmatrix}$, $\begin{bmatrix}101&168\\84&55\end{bmatrix}$, $\begin{bmatrix}171&56\\212&169\end{bmatrix}$, $\begin{bmatrix}211&168\\0&197\end{bmatrix}$
232.192.1-8.b.2.3	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}43&168\\52&141\end{bmatrix}$, $\begin{bmatrix}79&0\\196&223\end{bmatrix}$, $\begin{bmatrix}85&0\\136&95\end{bmatrix}$, $\begin{bmatrix}141&24\\36&227\end{bmatrix}$
232.192.1-8.b.2.4	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}89&192\\196&93\end{bmatrix}$, $\begin{bmatrix}99&8\\112&161\end{bmatrix}$, $\begin{bmatrix}181&168\\192&195\end{bmatrix}$, $\begin{bmatrix}217&128\\20&185\end{bmatrix}$
232.192.1-8.b.2.5	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}9&64\\44&141\end{bmatrix}$, $\begin{bmatrix}71&104\\104&67\end{bmatrix}$, $\begin{bmatrix}139&64\\168&157\end{bmatrix}$, $\begin{bmatrix}149&168\\28&191\end{bmatrix}$
232.192.1-8.b.2.6	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}99&56\\88&9\end{bmatrix}$, $\begin{bmatrix}189&0\\184&99\end{bmatrix}$, $\begin{bmatrix}193&0\\140&209\end{bmatrix}$, $\begin{bmatrix}227&200\\92&157\end{bmatrix}$
232.192.1-232.b.1.1	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}9&224\\148&185\end{bmatrix}$, $\begin{bmatrix}161&68\\12&123\end{bmatrix}$, $\begin{bmatrix}179&120\\148&79\end{bmatrix}$, $\begin{bmatrix}181&40\\80&83\end{bmatrix}$
232.192.1-232.b.1.2	8K1	$232$	$192$	$1$	$2 \le \gamma \le 96$	$16$	$0$	$?$	✓	✓	$1$	✓	$\begin{bmatrix}43&24\\180&77\end{bmatrix}$, $\begin{bmatrix}105&164\\168&107\end{bmatrix}$, $\begin{bmatrix}121&220\\44&177\end{bmatrix}$, $\begin{bmatrix}177&96\\96&131\end{bmatrix}$

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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.