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: | $\begin{bmatrix}9&40\\142&69\end{bmatrix}$, $\begin{bmatrix}55&128\\78&113\end{bmatrix}$, $\begin{bmatrix}59&104\\162&137\end{bmatrix}$, $\begin{bmatrix}137&16\\4&117\end{bmatrix}$, $\begin{bmatrix}141&68\\146&47\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.48.1.fb.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 |
---|---|---|---|---|---|---|
24.48.0-24.l.1.1 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.48.0-24.l.1.14 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
56.48.0-56.e.1.14 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.48.0-56.e.1.9 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.1-168.c.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.48.1-168.c.1.26 | $168$ | $2$ | $2$ | $1$ | $?$ | 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.mp.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mp.2.10 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mr.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mr.2.14 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mt.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mt.2.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mv.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mv.2.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mx.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mx.2.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mz.1.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mz.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.nb.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.nb.2.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.nd.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.nd.2.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.288.9-168.bap.1.25 | $168$ | $3$ | $3$ | $9$ | $?$ | not computed |
168.384.9-168.nt.1.41 | $168$ | $4$ | $4$ | $9$ | $?$ | not computed |