Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | Newform level: | $3136$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{6}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}39&68\\32&15\end{bmatrix}$, $\begin{bmatrix}41&20\\152&163\end{bmatrix}$, $\begin{bmatrix}97&4\\80&153\end{bmatrix}$, $\begin{bmatrix}97&72\\152&5\end{bmatrix}$, $\begin{bmatrix}129&128\\100&127\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.96.1.w.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $1536$ |
Full 168-torsion field degree: | $774144$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 3136.2.a.m |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.96.0-8.c.1.7 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.96.0-56.b.1.12 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-56.b.1.22 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-8.c.1.4 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-56.n.2.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-56.n.2.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
168.384.5-56.w.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.w.1.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.y.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.y.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.z.2.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.z.2.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.bb.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.bb.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hh.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hh.1.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hj.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hj.1.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hq.1.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hq.1.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ht.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ht.1.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |