Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
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 | $2^{2}\cdot4^{3}$ | ||
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: | $\begin{bmatrix}71&24\\120&145\end{bmatrix}$, $\begin{bmatrix}71&48\\66&163\end{bmatrix}$, $\begin{bmatrix}73&160\\160&165\end{bmatrix}$, $\begin{bmatrix}135&164\\104&143\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.1.mi.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $3072$ |
Full 168-torsion field degree: | $774144$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 |
---|---|---|---|---|---|---|
24.96.0-24.r.1.15 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.96.0-56.j.2.10 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.96.0-56.j.2.6 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.q.1.5 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.q.1.17 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-24.r.1.3 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.co.2.9 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.co.2.31 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-168.ed.1.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ed.1.19 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eh.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eh.2.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ey.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ey.1.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |