Invariants
| Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $6^{4}\cdot12^{6}\cdot24^{2}$ | Cusp orbits | $2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24W7 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}1&154\\76&15\end{bmatrix}$, $\begin{bmatrix}35&24\\60&113\end{bmatrix}$, $\begin{bmatrix}49&86\\116&95\end{bmatrix}$, $\begin{bmatrix}77&132\\24&41\end{bmatrix}$, $\begin{bmatrix}79&34\\64&23\end{bmatrix}$, $\begin{bmatrix}109&164\\128&23\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 168.144.7.bak.2 for the level structure with $-I$) |
| Cyclic 168-isogeny field degree: | $64$ |
| Cyclic 168-torsion field degree: | $3072$ |
| Full 168-torsion field degree: | $516096$ |
Rational points
This modular curve has no $\Q_p$ points for $p=19$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.144.4-24.z.2.47 | $24$ | $2$ | $2$ | $4$ | $0$ |
| 168.144.3-168.cc.1.27 | $168$ | $2$ | $2$ | $3$ | $?$ |
| 168.144.3-168.cc.1.51 | $168$ | $2$ | $2$ | $3$ | $?$ |
| 168.144.4-24.z.2.50 | $168$ | $2$ | $2$ | $4$ | $?$ |
| 168.144.4-168.bm.2.47 | $168$ | $2$ | $2$ | $4$ | $?$ |
| 168.144.4-168.bm.2.89 | $168$ | $2$ | $2$ | $4$ | $?$ |