Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-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 | $4^{2}$ | ||
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: | $\begin{bmatrix}33&142\\92&67\end{bmatrix}$, $\begin{bmatrix}47&148\\71&125\end{bmatrix}$, $\begin{bmatrix}145&84\\26&149\end{bmatrix}$, $\begin{bmatrix}165&44\\79&159\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 168-isogeny field degree: | $128$ |
Cyclic 168-torsion field degree: | $6144$ |
Full 168-torsion field degree: | $3096576$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.24.1.cv.1 | $24$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
56.24.0.by.1 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.24.0.ga.1 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.24.0.iv.1 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.24.0.kj.1 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.24.1.dt.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.24.1.fx.1 | $168$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.144.9.kev.1 | $168$ | $3$ | $3$ | $9$ | $?$ | not computed |
168.192.9.cfj.1 | $168$ | $4$ | $4$ | $9$ | $?$ | not computed |