Invariants
| Level: | $168$ | $\SL_2$-level: | $8$ | Newform level: | $3136$ | ||
| Index: | $192$ | $\PSL_2$-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 | $2^{4}\cdot4^{2}$ | ||
| 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: | $\begin{bmatrix}49&76\\128&133\end{bmatrix}$, $\begin{bmatrix}55&36\\94&19\end{bmatrix}$, $\begin{bmatrix}127&80\\130&105\end{bmatrix}$, $\begin{bmatrix}143&52\\12&155\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 56.96.1.by.1 for the level structure with $-I$) |
| Cyclic 168-isogeny field degree: | $64$ |
| Cyclic 168-torsion field degree: | $1536$ |
| Full 168-torsion field degree: | $774144$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 3136.2.a.m |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.96.0-8.i.1.2 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 168.96.0-8.i.1.8 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 168.96.0-56.i.2.3 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 168.96.0-56.i.2.9 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 168.96.0-56.j.1.2 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 168.96.0-56.j.1.9 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 168.96.0-56.x.1.3 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 168.96.0-56.x.1.13 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 168.96.1-56.bi.1.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-56.bi.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-56.bj.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-56.bj.2.11 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-56.bs.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-56.bs.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |