Invariants
| Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot6^{4}\cdot8^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $2^{10}$ | ||
| 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: | 24AI7 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}49&36\\64&65\end{bmatrix}$, $\begin{bmatrix}85&56\\136&69\end{bmatrix}$, $\begin{bmatrix}99&52\\80&25\end{bmatrix}$, $\begin{bmatrix}119&90\\96&29\end{bmatrix}$, $\begin{bmatrix}133&36\\120&13\end{bmatrix}$, $\begin{bmatrix}155&160\\8&117\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 168.192.7.js.1 for the level structure with $-I$) |
| Cyclic 168-isogeny field degree: | $8$ |
| Cyclic 168-torsion field degree: | $384$ |
| Full 168-torsion field degree: | $387072$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known 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.cl.1.18 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 168.96.0-168.cy.1.7 | $168$ | $4$ | $4$ | $0$ | $?$ |
| 168.192.3-24.cl.1.29 | $168$ | $2$ | $2$ | $3$ | $?$ |
| 168.192.3-168.dx.1.1 | $168$ | $2$ | $2$ | $3$ | $?$ |
| 168.192.3-168.dx.1.17 | $168$ | $2$ | $2$ | $3$ | $?$ |
| 168.192.3-168.pj.1.25 | $168$ | $2$ | $2$ | $3$ | $?$ |
| 168.192.3-168.pj.1.40 | $168$ | $2$ | $2$ | $3$ | $?$ |