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: | 8G1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}59&84\\112&127\end{bmatrix}$, $\begin{bmatrix}97&4\\64&93\end{bmatrix}$, $\begin{bmatrix}137&98\\112&93\end{bmatrix}$, $\begin{bmatrix}139&76\\108&89\end{bmatrix}$, $\begin{bmatrix}143&52\\32&65\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.48.1.ch.2 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 |
---|---|---|---|---|---|---|
24.48.1-24.d.1.11 | $24$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
168.48.1-24.d.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
56.48.0-56.i.1.6 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.48.0-56.i.1.29 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.u.1.31 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.u.1.63 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
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.bv.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ci.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.fl.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.fn.1.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.he.2.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.hg.2.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.hu.2.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.hw.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.jq.2.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.js.2.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.kg.2.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ki.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ks.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ku.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.lc.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ld.1.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.288.9-168.ip.2.32 | $168$ | $3$ | $3$ | $9$ | $?$ | not computed |
168.384.9-168.fs.2.30 | $168$ | $4$ | $4$ | $9$ | $?$ | not computed |