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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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
84.24.0-3.a.1.1	3D0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}39&13\\52&45\end{bmatrix}$, $\begin{bmatrix}43&42\\27&19\end{bmatrix}$, $\begin{bmatrix}57&26\\2&27\end{bmatrix}$, $\begin{bmatrix}77&75\\60&23\end{bmatrix}$
84.24.0-3.a.1.2	3D0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}17&0\\42&53\end{bmatrix}$, $\begin{bmatrix}19&75\\45&70\end{bmatrix}$, $\begin{bmatrix}41&48\\75&83\end{bmatrix}$, $\begin{bmatrix}75&50\\80&45\end{bmatrix}$
84.24.0-4.a.1.1	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}5&36\\36&25\end{bmatrix}$, $\begin{bmatrix}21&46\\20&23\end{bmatrix}$, $\begin{bmatrix}61&8\\74&53\end{bmatrix}$, $\begin{bmatrix}63&62\\82&37\end{bmatrix}$
84.24.0-4.a.1.2	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}31&66\\20&49\end{bmatrix}$, $\begin{bmatrix}37&2\\12&11\end{bmatrix}$, $\begin{bmatrix}55&20\\4&15\end{bmatrix}$, $\begin{bmatrix}81&4\\10&61\end{bmatrix}$
84.24.0-6.a.1.1	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}12&35\\65&48\end{bmatrix}$, $\begin{bmatrix}23&36\\56&25\end{bmatrix}$, $\begin{bmatrix}45&46\\28&57\end{bmatrix}$, $\begin{bmatrix}57&10\\34&21\end{bmatrix}$, $\begin{bmatrix}69&8\\20&81\end{bmatrix}$
84.24.0-6.a.1.2	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}16&75\\7&20\end{bmatrix}$, $\begin{bmatrix}22&45\\63&76\end{bmatrix}$, $\begin{bmatrix}32&13\\65&54\end{bmatrix}$, $\begin{bmatrix}55&32\\66&71\end{bmatrix}$, $\begin{bmatrix}67&48\\42&67\end{bmatrix}$
84.24.0-6.a.1.3	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}15&4\\40&81\end{bmatrix}$, $\begin{bmatrix}18&65\\61&74\end{bmatrix}$, $\begin{bmatrix}62&15\\65&4\end{bmatrix}$, $\begin{bmatrix}62&69\\41&22\end{bmatrix}$, $\begin{bmatrix}72&47\\77&54\end{bmatrix}$
84.24.0-6.a.1.4	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}29&54\\8&25\end{bmatrix}$, $\begin{bmatrix}45&44\\82&41\end{bmatrix}$, $\begin{bmatrix}51&4\\68&79\end{bmatrix}$, $\begin{bmatrix}74&7\\33&34\end{bmatrix}$, $\begin{bmatrix}79&2\\76&57\end{bmatrix}$
84.24.0-6.a.1.5	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}25&62\\28&9\end{bmatrix}$, $\begin{bmatrix}30&13\\7&72\end{bmatrix}$, $\begin{bmatrix}42&25\\29&16\end{bmatrix}$, $\begin{bmatrix}80&31\\71&42\end{bmatrix}$, $\begin{bmatrix}82&59\\25&60\end{bmatrix}$
84.24.0-6.a.1.6	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}29&24\\60&17\end{bmatrix}$, $\begin{bmatrix}32&25\\39&82\end{bmatrix}$, $\begin{bmatrix}57&62\\40&35\end{bmatrix}$, $\begin{bmatrix}63&62\\52&11\end{bmatrix}$, $\begin{bmatrix}82&15\\57&64\end{bmatrix}$
84.24.0-6.a.1.7	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}16&81\\31&74\end{bmatrix}$, $\begin{bmatrix}44&31\\77&12\end{bmatrix}$, $\begin{bmatrix}50&67\\63&34\end{bmatrix}$, $\begin{bmatrix}79&20\\4&39\end{bmatrix}$, $\begin{bmatrix}79&38\\24&65\end{bmatrix}$
84.24.0-6.a.1.8	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}9&20\\8&9\end{bmatrix}$, $\begin{bmatrix}9&28\\44&55\end{bmatrix}$, $\begin{bmatrix}18&79\\49&48\end{bmatrix}$, $\begin{bmatrix}21&38\\44&27\end{bmatrix}$, $\begin{bmatrix}25&72\\64&59\end{bmatrix}$
84.24.0-6.a.1.9	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}36&79\\11&34\end{bmatrix}$, $\begin{bmatrix}52&59\\63&32\end{bmatrix}$, $\begin{bmatrix}68&45\\63&38\end{bmatrix}$, $\begin{bmatrix}75&14\\40&71\end{bmatrix}$, $\begin{bmatrix}81&22\\10&45\end{bmatrix}$
84.24.0-6.a.1.10	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}14&13\\9&58\end{bmatrix}$, $\begin{bmatrix}35&48\\38&7\end{bmatrix}$, $\begin{bmatrix}36&31\\29&4\end{bmatrix}$, $\begin{bmatrix}56&25\\71&36\end{bmatrix}$, $\begin{bmatrix}80&31\\71&24\end{bmatrix}$
84.24.0-6.a.1.11	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}15&32\\32&33\end{bmatrix}$, $\begin{bmatrix}33&16\\34&69\end{bmatrix}$, $\begin{bmatrix}41&70\\56&27\end{bmatrix}$, $\begin{bmatrix}62&79\\69&28\end{bmatrix}$, $\begin{bmatrix}71&58\\2&21\end{bmatrix}$
84.24.0-6.a.1.12	6F0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}2&45\\35&82\end{bmatrix}$, $\begin{bmatrix}54&11\\47&12\end{bmatrix}$, $\begin{bmatrix}69&28\\68&79\end{bmatrix}$, $\begin{bmatrix}78&17\\67&80\end{bmatrix}$, $\begin{bmatrix}81&56\\34&83\end{bmatrix}$
84.24.0-12.a.1.1	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}7&24\\62&17\end{bmatrix}$, $\begin{bmatrix}11&28\\80&17\end{bmatrix}$, $\begin{bmatrix}21&38\\46&71\end{bmatrix}$, $\begin{bmatrix}79&50\\28&69\end{bmatrix}$
84.24.0-12.a.1.2	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}3&82\\58&7\end{bmatrix}$, $\begin{bmatrix}53&52\\82&75\end{bmatrix}$, $\begin{bmatrix}55&56\\74&69\end{bmatrix}$, $\begin{bmatrix}79&60\\56&29\end{bmatrix}$
84.24.0-12.a.1.3	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}11&48\\8&25\end{bmatrix}$, $\begin{bmatrix}19&6\\34&37\end{bmatrix}$, $\begin{bmatrix}39&8\\64&7\end{bmatrix}$, $\begin{bmatrix}81&28\\58&19\end{bmatrix}$
84.24.0-12.a.1.4	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}1&32\\28&55\end{bmatrix}$, $\begin{bmatrix}21&52\\58&75\end{bmatrix}$, $\begin{bmatrix}31&44\\44&35\end{bmatrix}$, $\begin{bmatrix}69&70\\56&59\end{bmatrix}$
84.24.0-28.a.1.1	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}11&72\\14&73\end{bmatrix}$, $\begin{bmatrix}41&22\\46&55\end{bmatrix}$, $\begin{bmatrix}49&24\\20&31\end{bmatrix}$, $\begin{bmatrix}65&38\\4&63\end{bmatrix}$
84.24.0-28.a.1.2	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}25&46\\58&33\end{bmatrix}$, $\begin{bmatrix}29&48\\78&77\end{bmatrix}$, $\begin{bmatrix}69&68\\68&19\end{bmatrix}$, $\begin{bmatrix}75&10\\16&45\end{bmatrix}$
84.24.0-28.a.1.3	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}33&16\\80&75\end{bmatrix}$, $\begin{bmatrix}57&10\\80&49\end{bmatrix}$, $\begin{bmatrix}75&14\\22&41\end{bmatrix}$, $\begin{bmatrix}77&6\\34&37\end{bmatrix}$
84.24.0-28.a.1.4	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}3&32\\80&59\end{bmatrix}$, $\begin{bmatrix}17&42\\72&47\end{bmatrix}$, $\begin{bmatrix}67&22\\34&41\end{bmatrix}$, $\begin{bmatrix}81&28\\64&47\end{bmatrix}$
84.24.0.a.1	4G0	$84$	$24$	$0$	$2$	$6$	$0$	$?$	?	?	✓	not computed	✓	$\begin{bmatrix}35&30\\12&61\end{bmatrix}$, $\begin{bmatrix}41&16\\12&13\end{bmatrix}$, $\begin{bmatrix}73&54\\8&19\end{bmatrix}$, $\begin{bmatrix}79&12\\62&55\end{bmatrix}$
84.24.0-84.a.1.1	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}1&70\\60&47\end{bmatrix}$, $\begin{bmatrix}17&66\\52&37\end{bmatrix}$, $\begin{bmatrix}33&80\\20&49\end{bmatrix}$, $\begin{bmatrix}61&70\\82&65\end{bmatrix}$
84.24.0-84.a.1.2	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}29&34\\26&47\end{bmatrix}$, $\begin{bmatrix}35&30\\36&59\end{bmatrix}$, $\begin{bmatrix}55&46\\20&21\end{bmatrix}$, $\begin{bmatrix}77&50\\44&3\end{bmatrix}$
84.24.0-84.a.1.3	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}5&30\\66&59\end{bmatrix}$, $\begin{bmatrix}41&44\\50&25\end{bmatrix}$, $\begin{bmatrix}47&36\\40&17\end{bmatrix}$, $\begin{bmatrix}53&68\\16&35\end{bmatrix}$
84.24.0-84.a.1.4	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}7&68\\60&53\end{bmatrix}$, $\begin{bmatrix}11&64\\6&17\end{bmatrix}$, $\begin{bmatrix}35&4\\16&61\end{bmatrix}$, $\begin{bmatrix}55&34\\12&65\end{bmatrix}$
84.24.0-84.a.1.5	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}11&54\\48&35\end{bmatrix}$, $\begin{bmatrix}47&14\\10&47\end{bmatrix}$, $\begin{bmatrix}71&8\\82&27\end{bmatrix}$, $\begin{bmatrix}77&32\\62&63\end{bmatrix}$
84.24.0-84.a.1.6	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}5&62\\40&59\end{bmatrix}$, $\begin{bmatrix}13&50\\72&43\end{bmatrix}$, $\begin{bmatrix}21&62\\44&1\end{bmatrix}$, $\begin{bmatrix}71&46\\42&47\end{bmatrix}$
84.24.0-84.a.1.7	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}5&52\\36&73\end{bmatrix}$, $\begin{bmatrix}29&30\\58&77\end{bmatrix}$, $\begin{bmatrix}43&70\\4&59\end{bmatrix}$, $\begin{bmatrix}71&32\\76&69\end{bmatrix}$
84.24.0-84.a.1.8	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}7&6\\82&17\end{bmatrix}$, $\begin{bmatrix}7&48\\80&49\end{bmatrix}$, $\begin{bmatrix}29&12\\16&19\end{bmatrix}$, $\begin{bmatrix}75&62\\20&43\end{bmatrix}$
84.24.0-4.b.1.1	4E0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}21&64\\20&19\end{bmatrix}$, $\begin{bmatrix}55&16\\36&13\end{bmatrix}$, $\begin{bmatrix}75&52\\2&27\end{bmatrix}$, $\begin{bmatrix}81&4\\52&27\end{bmatrix}$
84.24.0-4.b.1.2	4E0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}1&20\\64&61\end{bmatrix}$, $\begin{bmatrix}7&4\\2&49\end{bmatrix}$, $\begin{bmatrix}47&52\\48&83\end{bmatrix}$, $\begin{bmatrix}73&76\\0&55\end{bmatrix}$
84.24.0-4.b.1.3	4E0	$84$	$24$	$0$	$1$	$4$	$4$	$?$	?	?		not computed		$\begin{bmatrix}7&16\\34&27\end{bmatrix}$, $\begin{bmatrix}15&16\\2&35\end{bmatrix}$, $\begin{bmatrix}55&52\\80&67\end{bmatrix}$, $\begin{bmatrix}81&56\\64&27\end{bmatrix}$
84.24.0-12.b.1.1	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}7&82\\66&59\end{bmatrix}$, $\begin{bmatrix}23&30\\36&55\end{bmatrix}$, $\begin{bmatrix}57&34\\28&39\end{bmatrix}$, $\begin{bmatrix}59&22\\26&41\end{bmatrix}$
84.24.0-12.b.1.2	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}29&72\\0&83\end{bmatrix}$, $\begin{bmatrix}65&82\\56&11\end{bmatrix}$, $\begin{bmatrix}71&42\\26&79\end{bmatrix}$, $\begin{bmatrix}75&20\\64&75\end{bmatrix}$
84.24.0-12.b.1.3	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}21&10\\82&29\end{bmatrix}$, $\begin{bmatrix}51&74\\50&67\end{bmatrix}$, $\begin{bmatrix}73&34\\30&35\end{bmatrix}$, $\begin{bmatrix}77&10\\8&29\end{bmatrix}$
84.24.0-12.b.1.4	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}9&40\\14&83\end{bmatrix}$, $\begin{bmatrix}43&46\\0&11\end{bmatrix}$, $\begin{bmatrix}55&40\\48&55\end{bmatrix}$, $\begin{bmatrix}69&76\\44&43\end{bmatrix}$
84.24.0-28.b.1.1	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}17&2\\4&69\end{bmatrix}$, $\begin{bmatrix}35&66\\40&43\end{bmatrix}$, $\begin{bmatrix}57&46\\74&15\end{bmatrix}$, $\begin{bmatrix}79&80\\14&51\end{bmatrix}$
84.24.0-28.b.1.2	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}21&74\\32&45\end{bmatrix}$, $\begin{bmatrix}23&66\\62&61\end{bmatrix}$, $\begin{bmatrix}59&76\\64&75\end{bmatrix}$, $\begin{bmatrix}79&62\\18&43\end{bmatrix}$
84.24.0-28.b.1.3	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}19&74\\78&77\end{bmatrix}$, $\begin{bmatrix}37&2\\52&79\end{bmatrix}$, $\begin{bmatrix}49&60\\66&5\end{bmatrix}$, $\begin{bmatrix}61&58\\82&45\end{bmatrix}$
84.24.0-28.b.1.4	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}23&48\\74&77\end{bmatrix}$, $\begin{bmatrix}29&48\\74&49\end{bmatrix}$, $\begin{bmatrix}55&40\\14&27\end{bmatrix}$, $\begin{bmatrix}71&82\\74&11\end{bmatrix}$
84.24.0.b.1	4G0	$84$	$24$	$0$	$1 \le \gamma \le 2$	$6$	$0$	$?$	?	?	✓	not computed	?	$\begin{bmatrix}1&2\\40&49\end{bmatrix}$, $\begin{bmatrix}13&42\\32&1\end{bmatrix}$, $\begin{bmatrix}47&66\\4&55\end{bmatrix}$, $\begin{bmatrix}47&66\\66&29\end{bmatrix}$
84.24.0-84.b.1.1	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}21&52\\44&31\end{bmatrix}$, $\begin{bmatrix}45&74\\26&21\end{bmatrix}$, $\begin{bmatrix}65&26\\74&43\end{bmatrix}$, $\begin{bmatrix}65&80\\62&55\end{bmatrix}$
84.24.0-84.b.1.2	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}5&30\\80&49\end{bmatrix}$, $\begin{bmatrix}11&64\\22&57\end{bmatrix}$, $\begin{bmatrix}21&34\\58&51\end{bmatrix}$, $\begin{bmatrix}49&18\\76&23\end{bmatrix}$
84.24.0-84.b.1.3	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}5&18\\12&73\end{bmatrix}$, $\begin{bmatrix}23&58\\42&47\end{bmatrix}$, $\begin{bmatrix}51&82\\20&11\end{bmatrix}$, $\begin{bmatrix}63&2\\68&77\end{bmatrix}$
84.24.0-84.b.1.4	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}19&54\\72&25\end{bmatrix}$, $\begin{bmatrix}55&58\\30&61\end{bmatrix}$, $\begin{bmatrix}67&44\\80&81\end{bmatrix}$, $\begin{bmatrix}73&40\\26&49\end{bmatrix}$
84.24.0-84.b.1.5	4E0	$84$	$24$	$0$	$1$	$4$	$2$	$?$	?	?		not computed		$\begin{bmatrix}17&42\\72&31\end{bmatrix}$, $\begin{bmatrix}57&14\\20&65\end{bmatrix}$, $\begin{bmatrix}61&70\\40&53\end{bmatrix}$, $\begin{bmatrix}79&80\\62&63\end{bmatrix}$

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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.