Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | 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 | $4^{2}\cdot8^{2}$ | 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: | 8B1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}23&4\\4&7\end{bmatrix}$, $\begin{bmatrix}73&100\\160&35\end{bmatrix}$, $\begin{bmatrix}141&44\\152&55\end{bmatrix}$, $\begin{bmatrix}145&110\\120&31\end{bmatrix}$, $\begin{bmatrix}153&158\\80&21\end{bmatrix}$, $\begin{bmatrix}167&58\\68&47\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.24.1.c.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
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 |
---|---|---|---|---|---|---|
8.24.0-4.b.1.5 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
84.24.0-4.b.1.2 | $84$ | $2$ | $2$ | $0$ | $?$ | 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.o.2.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.o.2.30 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.v.1.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.v.1.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.da.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.da.1.26 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dd.1.12 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dd.1.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ds.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ds.1.24 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ds.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ds.2.29 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dt.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dt.1.31 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dt.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dt.2.14 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.du.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.du.1.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.du.2.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.du.2.16 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dv.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dv.1.23 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dv.2.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dv.2.23 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dw.1.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dw.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dw.2.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dw.2.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dx.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dx.1.24 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dx.2.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dx.2.21 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dy.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dy.1.31 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dy.2.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dy.2.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dz.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dz.1.24 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dz.2.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dz.2.27 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fb.1.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fb.1.20 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fc.1.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fc.1.32 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fp.1.10 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fp.1.20 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fq.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fq.1.28 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.144.5-168.g.1.8 | $168$ | $3$ | $3$ | $5$ | $?$ | not computed |
168.192.5-168.g.1.11 | $168$ | $4$ | $4$ | $5$ | $?$ | not computed |
168.384.13-168.g.1.55 | $168$ | $8$ | $8$ | $13$ | $?$ | not computed |