Invariants
| Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $4^{2}\cdot8^{2}\cdot12^{2}\cdot24^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24H5 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}17&76\\92&45\end{bmatrix}$, $\begin{bmatrix}77&79\\68&111\end{bmatrix}$, $\begin{bmatrix}87&158\\124&95\end{bmatrix}$, $\begin{bmatrix}149&30\\44&145\end{bmatrix}$, $\begin{bmatrix}155&157\\152&117\end{bmatrix}$, $\begin{bmatrix}165&74\\80&141\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 168.96.5.bw.1 for the level structure with $-I$) |
| Cyclic 168-isogeny field degree: | $16$ |
| Cyclic 168-torsion field degree: | $768$ |
| Full 168-torsion field degree: | $774144$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.96.1-12.h.1.23 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 168.96.1-12.h.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.