Invariants
| Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $288$ | ||||
| Genus: | $17 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $12^{8}\cdot24^{8}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 32$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 17$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24B17 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}55&128\\140&9\end{bmatrix}$, $\begin{bmatrix}65&0\\44&103\end{bmatrix}$, $\begin{bmatrix}83&44\\56&1\end{bmatrix}$, $\begin{bmatrix}91&138\\96&115\end{bmatrix}$, $\begin{bmatrix}139&70\\100&125\end{bmatrix}$, $\begin{bmatrix}149&98\\44&43\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 168-isogeny field degree: | $64$ |
| Cyclic 168-torsion field degree: | $1536$ |
| Full 168-torsion field degree: | $516096$ |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(3)$ | $3$ | $96$ | $96$ | $0$ | $0$ |
| 56.96.1.by.1 | $56$ | $3$ | $3$ | $1$ | $1$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.144.8.fd.1 | $24$ | $2$ | $2$ | $8$ | $1$ |
| 56.96.1.by.1 | $56$ | $3$ | $3$ | $1$ | $1$ |
| 168.144.8.bz.2 | $168$ | $2$ | $2$ | $8$ | $?$ |
| 168.144.8.cd.1 | $168$ | $2$ | $2$ | $8$ | $?$ |
| 168.144.8.ov.2 | $168$ | $2$ | $2$ | $8$ | $?$ |
| 168.144.9.sh.1 | $168$ | $2$ | $2$ | $9$ | $?$ |
| 168.144.9.sl.2 | $168$ | $2$ | $2$ | $9$ | $?$ |
| 168.144.9.bbc.1 | $168$ | $2$ | $2$ | $9$ | $?$ |