Invariants
| Level: | $168$ | $\SL_2$-level: | $24$ | 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: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| 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: | 24G1 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}38&115\\29&24\end{bmatrix}$, $\begin{bmatrix}69&112\\148&141\end{bmatrix}$, $\begin{bmatrix}89&52\\50&159\end{bmatrix}$, $\begin{bmatrix}104&135\\167&124\end{bmatrix}$, $\begin{bmatrix}116&81\\83&58\end{bmatrix}$, $\begin{bmatrix}129&34\\70&45\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 168.48.1.zs.1 for the level structure with $-I$) |
| Cyclic 168-isogeny field degree: | $16$ |
| Cyclic 168-torsion field degree: | $768$ |
| Full 168-torsion field degree: | $1548288$ |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 3.8.0-3.a.1.1 | $3$ | $12$ | $12$ | $0$ | $0$ | full Jacobian |
| 56.12.0.y.1 | $56$ | $8$ | $4$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.48.0-12.g.1.10 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 168.48.0-12.g.1.16 | $168$ | $2$ | $2$ | $0$ | $?$ | 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.qz.1.32 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.qz.2.28 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.qz.3.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.qz.4.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.rb.1.26 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.rb.2.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.rb.3.28 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.rb.4.20 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.sj.1.30 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.sj.2.26 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.sj.3.20 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.sj.4.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.sl.1.28 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.sl.2.20 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.sl.3.26 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.1-168.sl.4.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 168.192.3-168.fe.1.12 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.fu.1.31 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.hg.1.40 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.hi.1.32 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.jk.1.31 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.jm.1.31 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.jw.1.31 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.jy.1.31 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.ls.1.32 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.lv.1.47 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.mj.1.16 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.mk.1.31 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.nc.1.32 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.nf.1.32 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.nl.1.32 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.nm.1.31 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.pu.1.5 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.pu.2.13 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.pu.3.7 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.pu.4.15 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.pw.1.3 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.pw.2.7 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.pw.3.13 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.pw.4.29 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.qs.1.7 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.qs.2.15 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.qs.3.5 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.qs.4.13 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.qu.1.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.qu.2.5 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.qu.3.15 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.192.3-168.qu.4.31 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 168.288.5-168.pc.1.2 | $168$ | $3$ | $3$ | $5$ | $?$ | not computed |