Invariants
| Level: | $168$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8F1 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}29&76\\146&53\end{bmatrix}$, $\begin{bmatrix}57&4\\122&163\end{bmatrix}$, $\begin{bmatrix}61&4\\38&39\end{bmatrix}$, $\begin{bmatrix}117&76\\34&113\end{bmatrix}$, $\begin{bmatrix}125&76\\60&31\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 168.48.1.cy.1 for the level structure with $-I$) |
| Cyclic 168-isogeny field degree: | $64$ |
| Cyclic 168-torsion field degree: | $3072$ |
| Full 168-torsion field degree: | $1548288$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
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 | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.48.0-12.c.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 168.48.0-12.c.1.12 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 56.48.0-56.l.1.3 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 168.48.0-56.l.1.17 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 168.48.1-168.d.1.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.48.1-168.d.1.27 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 168.192.1-168.ic.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.ic.2.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.ie.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.ie.2.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.ig.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.ig.2.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.ii.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.ii.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.ik.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.ik.2.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.im.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.im.2.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.io.1.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.io.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.iq.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.iq.2.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.288.9-168.ku.1.19 | $168$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 168.384.9-168.go.1.35 | $168$ | $4$ | $4$ | $9$ | $?$ | not computed |