Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}25&28\\24&155\end{bmatrix}$, $\begin{bmatrix}111&92\\124&131\end{bmatrix}$, $\begin{bmatrix}137&160\\14&159\end{bmatrix}$, $\begin{bmatrix}143&164\\110&27\end{bmatrix}$, $\begin{bmatrix}161&40\\78&37\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 168.192.1-168.gm.1.1, 168.192.1-168.gm.1.2, 168.192.1-168.gm.1.3, 168.192.1-168.gm.1.4, 168.192.1-168.gm.1.5, 168.192.1-168.gm.1.6, 168.192.1-168.gm.1.7, 168.192.1-168.gm.1.8, 168.192.1-168.gm.1.9, 168.192.1-168.gm.1.10, 168.192.1-168.gm.1.11, 168.192.1-168.gm.1.12, 168.192.1-168.gm.1.13, 168.192.1-168.gm.1.14, 168.192.1-168.gm.1.15, 168.192.1-168.gm.1.16 |
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 |
---|---|---|---|---|---|---|
24.48.0.i.2 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.48.1.bi.2 | $56$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
168.48.0.g.1 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0.bo.1 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0.bs.1 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.1.bu.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.48.1.do.2 | $168$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.288.17.dyq.2 | $168$ | $3$ | $3$ | $17$ | $?$ | not computed |
168.384.17.blk.2 | $168$ | $4$ | $4$ | $17$ | $?$ | not computed |