Invariants
| Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $9 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{4}\cdot8^{4}\cdot12^{4}\cdot24^{4}$ | Cusp orbits | $1^{4}\cdot2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 9$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AH9 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}3&130\\40&153\end{bmatrix}$, $\begin{bmatrix}29&28\\8&159\end{bmatrix}$, $\begin{bmatrix}35&132\\68&31\end{bmatrix}$, $\begin{bmatrix}37&138\\12&7\end{bmatrix}$, $\begin{bmatrix}127&150\\40&143\end{bmatrix}$, $\begin{bmatrix}145&78\\4&167\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 168.192.9.kp.2 for the level structure with $-I$) |
| Cyclic 168-isogeny field degree: | $16$ |
| Cyclic 168-torsion field degree: | $768$ |
| Full 168-torsion field degree: | $387072$ |
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 |
|---|---|---|---|---|---|
| 24.192.3-24.bq.2.47 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 168.96.1-168.ef.2.18 | $168$ | $4$ | $4$ | $1$ | $?$ |
| 168.192.3-24.bq.2.38 | $168$ | $2$ | $2$ | $3$ | $?$ |
| 168.192.3-168.dw.2.3 | $168$ | $2$ | $2$ | $3$ | $?$ |
| 168.192.3-168.dw.2.88 | $168$ | $2$ | $2$ | $3$ | $?$ |
| 168.192.5-168.h.1.23 | $168$ | $2$ | $2$ | $5$ | $?$ |
| 168.192.5-168.h.1.78 | $168$ | $2$ | $2$ | $5$ | $?$ |