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: | $\begin{bmatrix}59&164\\38&13\end{bmatrix}$, $\begin{bmatrix}83&60\\84&137\end{bmatrix}$, $\begin{bmatrix}83&72\\14&29\end{bmatrix}$, $\begin{bmatrix}155&76\\98&143\end{bmatrix}$, $\begin{bmatrix}155&136\\68&41\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.48.1.v.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $1536$ |
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 |
---|---|---|---|---|---|---|
8.48.0-8.c.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.48.0-8.c.1.6 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.x.1.1 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.x.1.28 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.1-168.c.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.48.1-168.c.1.29 | $168$ | $2$ | $2$ | $1$ | $?$ | 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.dt.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.dt.2.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.dv.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.dv.2.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.dx.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.dx.2.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.dz.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.dz.2.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.eb.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.eb.2.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ed.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ed.2.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ef.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ef.2.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.eh.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.eh.2.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.288.9-168.eb.1.10 | $168$ | $3$ | $3$ | $9$ | $?$ | not computed |
168.384.9-168.cm.1.2 | $168$ | $4$ | $4$ | $9$ | $?$ | not computed |