Invariants
| Level: | $168$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot4\cdot6\cdot12$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12F1 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}14&141\\159&92\end{bmatrix}$, $\begin{bmatrix}69&50\\70&149\end{bmatrix}$, $\begin{bmatrix}122&87\\65&10\end{bmatrix}$, $\begin{bmatrix}138&13\\109&54\end{bmatrix}$, $\begin{bmatrix}143&54\\2&79\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 168.24.1.hn.1 for the level structure with $-I$) |
| Cyclic 168-isogeny field degree: | $32$ |
| Cyclic 168-torsion field degree: | $1536$ |
| Full 168-torsion field degree: | $3096576$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
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 |
|---|---|---|---|---|---|---|
| 12.24.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 168.24.0-6.a.1.3 | $168$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 168.96.1-168.dg.1.14 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.gf.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.kf.1.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.kg.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.yu.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.yv.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.zd.1.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.ze.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.bkx.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.bky.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.bld.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.ble.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.blj.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.blk.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.blp.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.96.1-168.blq.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.144.3-168.dit.1.3 | $168$ | $3$ | $3$ | $3$ | $?$ | not computed |
| 168.384.13-168.pb.1.2 | $168$ | $8$ | $8$ | $13$ | $?$ | not computed |