| Label |
RSZB label |
RZB label |
CP label |
SZ label |
S label |
Name |
Level |
Index |
Genus |
Rank |
$\Q$-gonality |
Cusps |
$\Q$-cusps |
CM points |
Conductor |
Simple |
Squarefree |
Contains -1 |
Decomposition |
Models |
$j$-points |
Local obstruction |
$\operatorname{GL}_2(\mathbb{Z}/N\mathbb{Z})$-generators |
| 36.72.2-9.a.1.1 |
36.72.2.7 |
|
9A2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$2$ |
|
$3^{8}$ |
✓ |
✓ |
|
$2$ |
|
$1$ |
|
$\begin{bmatrix}8&3\\3&11\end{bmatrix}$, $\begin{bmatrix}16&3\\33&20\end{bmatrix}$, $\begin{bmatrix}20&27\\27&20\end{bmatrix}$ |
| 36.72.2-9.a.1.2 |
36.72.2.8 |
|
9A2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$2$ |
|
$3^{8}$ |
✓ |
✓ |
|
$2$ |
|
$1$ |
|
$\begin{bmatrix}4&21\\15&29\end{bmatrix}$, $\begin{bmatrix}5&30\\12&23\end{bmatrix}$, $\begin{bmatrix}35&33\\24&35\end{bmatrix}$ |
| 36.72.2-18.a.1.1 |
36.72.2.33 |
|
18F2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$1$ |
|
$2^{4}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}1&21\\21&2\end{bmatrix}$, $\begin{bmatrix}3&19\\23&30\end{bmatrix}$, $\begin{bmatrix}3&29\\7&30\end{bmatrix}$ |
| 36.72.2-18.a.1.2 |
36.72.2.36 |
|
18F2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$1$ |
|
$2^{4}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}10&33\\15&23\end{bmatrix}$, $\begin{bmatrix}21&17\\13&12\end{bmatrix}$, $\begin{bmatrix}24&17\\5&21\end{bmatrix}$ |
| 36.72.2-18.a.1.3 |
36.72.2.34 |
|
18F2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$1$ |
|
$2^{4}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}17&15\\15&16\end{bmatrix}$, $\begin{bmatrix}21&4\\28&15\end{bmatrix}$, $\begin{bmatrix}27&16\\10&27\end{bmatrix}$ |
| 36.72.2-18.a.1.4 |
36.72.2.35 |
|
18F2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$1$ |
|
$2^{4}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}9&5\\25&18\end{bmatrix}$, $\begin{bmatrix}16&15\\33&35\end{bmatrix}$, $\begin{bmatrix}29&0\\0&31\end{bmatrix}$ |
| 36.72.2.a.1 |
36.72.2.1 |
|
18N2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$6$ |
$3$ |
|
$2^{8}\cdot3^{4}$ |
✓ |
✓ |
✓ |
$2$ |
$3$ |
$1$ |
|
$\begin{bmatrix}1&27\\27&2\end{bmatrix}$, $\begin{bmatrix}14&35\\15&13\end{bmatrix}$, $\begin{bmatrix}17&9\\18&25\end{bmatrix}$, $\begin{bmatrix}35&0\\0&7\end{bmatrix}$ |
| 36.72.2-36.a.1.1 |
36.72.2.38 |
|
18F2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$1$ |
|
$2^{8}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}15&10\\7&3\end{bmatrix}$, $\begin{bmatrix}21&32\\1&15\end{bmatrix}$, $\begin{bmatrix}28&9\\21&28\end{bmatrix}$ |
| 36.72.2-36.a.1.2 |
36.72.2.37 |
|
18F2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$1$ |
|
$2^{8}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}0&31\\17&9\end{bmatrix}$, $\begin{bmatrix}9&13\\26&33\end{bmatrix}$, $\begin{bmatrix}10&33\\21&35\end{bmatrix}$ |
| 36.72.2-36.a.1.3 |
36.72.2.40 |
|
18F2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$1$ |
|
$2^{8}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}19&27\\30&19\end{bmatrix}$, $\begin{bmatrix}26&21\\21&10\end{bmatrix}$, $\begin{bmatrix}33&26\\29&9\end{bmatrix}$ |
| 36.72.2-36.a.1.4 |
36.72.2.39 |
|
18F2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$1$ |
|
$2^{8}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}27&34\\31&3\end{bmatrix}$, $\begin{bmatrix}28&33\\33&26\end{bmatrix}$, $\begin{bmatrix}31&12\\6&23\end{bmatrix}$ |
| 36.72.2.a.2 |
36.72.2.5 |
|
18N2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$6$ |
$3$ |
|
$2^{8}\cdot3^{4}$ |
✓ |
✓ |
✓ |
$2$ |
$3$ |
$1$ |
|
$\begin{bmatrix}1&29\\12&31\end{bmatrix}$, $\begin{bmatrix}16&27\\9&1\end{bmatrix}$, $\begin{bmatrix}23&16\\30&31\end{bmatrix}$, $\begin{bmatrix}23&26\\3&23\end{bmatrix}$ |
| 36.72.2.b.1 |
36.72.2.3 |
|
18N2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$6$ |
$0$ |
|
$2^{8}\cdot3^{8}$ |
|
|
✓ |
$1^{2}$ |
$3$ |
$0$ |
✓ |
$\begin{bmatrix}11&8\\33&25\end{bmatrix}$, $\begin{bmatrix}17&19\\24&35\end{bmatrix}$, $\begin{bmatrix}23&25\\21&22\end{bmatrix}$, $\begin{bmatrix}28&15\\9&1\end{bmatrix}$ |
| 36.72.2-18.c.1.1 |
36.72.2.28 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}5&10\\24&13\end{bmatrix}$, $\begin{bmatrix}7&10\\6&17\end{bmatrix}$, $\begin{bmatrix}7&11\\12&5\end{bmatrix}$, $\begin{bmatrix}13&6\\0&23\end{bmatrix}$ |
| 36.72.2-18.c.1.2 |
36.72.2.10 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}11&26\\30&13\end{bmatrix}$, $\begin{bmatrix}13&29\\24&25\end{bmatrix}$, $\begin{bmatrix}31&21\\0&11\end{bmatrix}$, $\begin{bmatrix}35&17\\30&1\end{bmatrix}$ |
| 36.72.2-18.c.1.3 |
36.72.2.24 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}1&2\\12&35\end{bmatrix}$, $\begin{bmatrix}1&22\\30&19\end{bmatrix}$, $\begin{bmatrix}5&26\\30&7\end{bmatrix}$, $\begin{bmatrix}7&7\\24&23\end{bmatrix}$ |
| 36.72.2-18.c.1.4 |
36.72.2.26 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}5&3\\0&7\end{bmatrix}$, $\begin{bmatrix}19&0\\18&35\end{bmatrix}$, $\begin{bmatrix}23&9\\18&19\end{bmatrix}$, $\begin{bmatrix}25&1\\24&5\end{bmatrix}$ |
| 36.72.2-18.c.1.5 |
36.72.2.12 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}1&6\\0&7\end{bmatrix}$, $\begin{bmatrix}17&32\\6&35\end{bmatrix}$, $\begin{bmatrix}23&5\\6&29\end{bmatrix}$, $\begin{bmatrix}23&7\\24&31\end{bmatrix}$ |
| 36.72.2-18.c.1.6 |
36.72.2.22 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}1&33\\18&7\end{bmatrix}$, $\begin{bmatrix}17&16\\24&19\end{bmatrix}$, $\begin{bmatrix}19&15\\0&17\end{bmatrix}$, $\begin{bmatrix}23&12\\18&7\end{bmatrix}$ |
| 36.72.2-18.c.1.7 |
36.72.2.16 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}1&3\\0&29\end{bmatrix}$, $\begin{bmatrix}5&3\\18&35\end{bmatrix}$, $\begin{bmatrix}25&7\\30&25\end{bmatrix}$, $\begin{bmatrix}25&16\\24&17\end{bmatrix}$ |
| 36.72.2-18.c.1.8 |
36.72.2.18 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}5&31\\12&17\end{bmatrix}$, $\begin{bmatrix}11&32\\6&5\end{bmatrix}$, $\begin{bmatrix}13&14\\24&7\end{bmatrix}$, $\begin{bmatrix}23&30\\0&7\end{bmatrix}$ |
| 36.72.2-18.c.1.9 |
36.72.2.32 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}13&29\\24&7\end{bmatrix}$, $\begin{bmatrix}19&22\\6&35\end{bmatrix}$, $\begin{bmatrix}29&33\\0&5\end{bmatrix}$, $\begin{bmatrix}35&35\\12&19\end{bmatrix}$ |
| 36.72.2-18.c.1.10 |
36.72.2.14 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}1&5\\24&13\end{bmatrix}$, $\begin{bmatrix}11&2\\30&1\end{bmatrix}$, $\begin{bmatrix}11&14\\24&5\end{bmatrix}$, $\begin{bmatrix}35&20\\6&23\end{bmatrix}$ |
| 36.72.2-18.c.1.11 |
36.72.2.20 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}13&12\\0&23\end{bmatrix}$, $\begin{bmatrix}17&25\\24&7\end{bmatrix}$, $\begin{bmatrix}35&0\\18&19\end{bmatrix}$, $\begin{bmatrix}35&27\\0&5\end{bmatrix}$ |
| 36.72.2-18.c.1.12 |
36.72.2.30 |
|
18E2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
|
$3^{6}$ |
|
|
|
$1^{2}$ |
|
$1$ |
|
$\begin{bmatrix}17&24\\18&25\end{bmatrix}$, $\begin{bmatrix}29&27\\18&1\end{bmatrix}$, $\begin{bmatrix}31&1\\6&17\end{bmatrix}$, $\begin{bmatrix}35&31\\24&25\end{bmatrix}$ |
| 36.72.2.c.1 |
36.72.2.2 |
|
18N2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$6$ |
$3$ |
|
$2^{8}\cdot3^{6}$ |
✓ |
✓ |
✓ |
$2$ |
$3$ |
$1$ |
|
$\begin{bmatrix}14&13\\3&22\end{bmatrix}$, $\begin{bmatrix}23&7\\15&2\end{bmatrix}$, $\begin{bmatrix}31&14\\6&5\end{bmatrix}$ |
| 36.72.2.c.2 |
36.72.2.6 |
|
18N2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$6$ |
$3$ |
|
$2^{8}\cdot3^{6}$ |
✓ |
✓ |
✓ |
$2$ |
$3$ |
$1$ |
|
$\begin{bmatrix}7&17\\24&23\end{bmatrix}$, $\begin{bmatrix}17&26\\33&31\end{bmatrix}$, $\begin{bmatrix}29&34\\15&5\end{bmatrix}$ |
| 36.72.2-18.d.1.1 |
36.72.2.23 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}5&4\\30&19\end{bmatrix}$, $\begin{bmatrix}13&7\\30&17\end{bmatrix}$, $\begin{bmatrix}29&14\\30&29\end{bmatrix}$, $\begin{bmatrix}31&5\\12&1\end{bmatrix}$ |
| 36.72.2-18.d.1.2 |
36.72.2.27 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}1&25\\30&17\end{bmatrix}$, $\begin{bmatrix}11&20\\6&7\end{bmatrix}$, $\begin{bmatrix}17&8\\30&23\end{bmatrix}$, $\begin{bmatrix}25&18\\18&11\end{bmatrix}$ |
| 36.72.2-18.d.1.3 |
36.72.2.9 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}13&5\\24&29\end{bmatrix}$, $\begin{bmatrix}13&30\\0&11\end{bmatrix}$, $\begin{bmatrix}17&9\\18&5\end{bmatrix}$, $\begin{bmatrix}35&11\\30&5\end{bmatrix}$ |
| 36.72.2-18.d.1.4 |
36.72.2.17 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}17&30\\18&35\end{bmatrix}$, $\begin{bmatrix}19&18\\18&11\end{bmatrix}$, $\begin{bmatrix}35&7\\24&23\end{bmatrix}$, $\begin{bmatrix}35&8\\30&23\end{bmatrix}$ |
| 36.72.2-18.d.1.5 |
36.72.2.31 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}5&9\\0&1\end{bmatrix}$, $\begin{bmatrix}17&20\\12&23\end{bmatrix}$, $\begin{bmatrix}23&13\\30&13\end{bmatrix}$, $\begin{bmatrix}29&31\\24&29\end{bmatrix}$ |
| 36.72.2-18.d.1.6 |
36.72.2.15 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}11&3\\0&1\end{bmatrix}$, $\begin{bmatrix}11&7\\6&29\end{bmatrix}$, $\begin{bmatrix}13&4\\12&5\end{bmatrix}$, $\begin{bmatrix}25&3\\0&17\end{bmatrix}$ |
| 36.72.2-18.d.1.7 |
36.72.2.21 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}25&30\\18&31\end{bmatrix}$, $\begin{bmatrix}29&9\\0&25\end{bmatrix}$, $\begin{bmatrix}31&19\\6&25\end{bmatrix}$, $\begin{bmatrix}31&21\\0&17\end{bmatrix}$ |
| 36.72.2-18.d.1.8 |
36.72.2.25 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}5&9\\18&25\end{bmatrix}$, $\begin{bmatrix}5&35\\12&11\end{bmatrix}$, $\begin{bmatrix}11&34\\24&5\end{bmatrix}$, $\begin{bmatrix}25&24\\18&25\end{bmatrix}$ |
| 36.72.2-18.d.1.9 |
36.72.2.11 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}11&24\\0&19\end{bmatrix}$, $\begin{bmatrix}13&32\\6&11\end{bmatrix}$, $\begin{bmatrix}31&1\\30&11\end{bmatrix}$, $\begin{bmatrix}35&22\\12&25\end{bmatrix}$ |
| 36.72.2-18.d.1.10 |
36.72.2.19 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}7&19\\6&25\end{bmatrix}$, $\begin{bmatrix}11&8\\6&7\end{bmatrix}$, $\begin{bmatrix}23&25\\12&1\end{bmatrix}$, $\begin{bmatrix}31&26\\24&11\end{bmatrix}$ |
| 36.72.2-18.d.1.11 |
36.72.2.29 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}11&25\\30&31\end{bmatrix}$, $\begin{bmatrix}11&27\\18&17\end{bmatrix}$, $\begin{bmatrix}13&1\\30&11\end{bmatrix}$, $\begin{bmatrix}31&5\\24&11\end{bmatrix}$ |
| 36.72.2-18.d.1.12 |
36.72.2.13 |
|
18D2 |
|
|
|
$36$ |
$72$ |
$2$ |
$0$ |
$2$ |
$4$ |
$4$ |
✓ |
$2^{2}\cdot3^{6}$ |
|
✓ |
|
$1^{2}$ |
|
$3$ |
|
$\begin{bmatrix}7&31\\12&5\end{bmatrix}$, $\begin{bmatrix}13&31\\30&35\end{bmatrix}$, $\begin{bmatrix}17&3\\18&1\end{bmatrix}$, $\begin{bmatrix}17&23\\12&23\end{bmatrix}$ |
| 36.72.2.d.1 |
36.72.2.4 |
|
18N2 |
|
|
|
$36$ |
$72$ |
$2$ |
$2$ |
$2$ |
$6$ |
$0$ |
✓ |
$2^{8}\cdot3^{8}$ |
|
|
✓ |
$1^{2}$ |
$3$ |
$0$ |
|
$\begin{bmatrix}11&25\\12&7\end{bmatrix}$, $\begin{bmatrix}17&1\\15&8\end{bmatrix}$, $\begin{bmatrix}32&35\\3&32\end{bmatrix}$ |
