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: | $\begin{bmatrix}43&48\\72&151\end{bmatrix}$, $\begin{bmatrix}69&110\\10&95\end{bmatrix}$, $\begin{bmatrix}76&105\\115&110\end{bmatrix}$, $\begin{bmatrix}78&119\\17&6\end{bmatrix}$, $\begin{bmatrix}158&135\\15&164\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.24.1.hm.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 |
---|---|---|---|---|---|---|
6.24.0-6.a.1.3 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.24.0-6.a.1.13 | $168$ | $2$ | $2$ | $0$ | $?$ | 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.dh.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.gg.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.jw.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.jx.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.yx.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.yy.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.za.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.zb.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bku.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bkv.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bla.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.blb.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.blg.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.blh.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.blm.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bln.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.144.3-168.diq.1.4 | $168$ | $3$ | $3$ | $3$ | $?$ | not computed |
168.384.13-168.pa.1.1 | $168$ | $8$ | $8$ | $13$ | $?$ | not computed |