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: | $\begin{bmatrix}8&153\\57&158\end{bmatrix}$, $\begin{bmatrix}29&6\\60&155\end{bmatrix}$, $\begin{bmatrix}95&154\\144&1\end{bmatrix}$, $\begin{bmatrix}117&58\\70&135\end{bmatrix}$, $\begin{bmatrix}158&145\\45&64\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.24.1.hk.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.1.5 | $168$ | $2$ | $2$ | $0$ | $?$ | 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.dj.1.14 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.gi.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.jz.1.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ka.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.zj.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.zk.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.zm.1.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.zn.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bad.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bae.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bag.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bah.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bap.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.baq.1.11 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bas.1.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bat.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.144.3-168.cwd.1.11 | $168$ | $3$ | $3$ | $3$ | $?$ | not computed |
168.384.13-168.oy.1.2 | $168$ | $8$ | $8$ | $13$ | $?$ | not computed |