Invariants
Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $2^{8}\cdot6^{8}\cdot8^{4}\cdot24^{4}$ | Cusp orbits | $2^{2}\cdot4^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24Z5 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}25&84\\96&79\end{bmatrix}$, $\begin{bmatrix}55&12\\92&71\end{bmatrix}$, $\begin{bmatrix}115&36\\51&151\end{bmatrix}$, $\begin{bmatrix}157&144\\31&119\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.192.5.bba.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $16$ |
Cyclic 168-torsion field degree: | $768$ |
Full 168-torsion field degree: | $387072$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.192.1-24.dm.2.3 | $24$ | $2$ | $2$ | $1$ | $0$ |
168.192.1-24.dm.2.3 | $168$ | $2$ | $2$ | $1$ | $?$ |
168.192.1-168.rh.3.18 | $168$ | $2$ | $2$ | $1$ | $?$ |
168.192.1-168.rh.3.19 | $168$ | $2$ | $2$ | $1$ | $?$ |
168.192.1-168.rt.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ |
168.192.1-168.rt.1.25 | $168$ | $2$ | $2$ | $1$ | $?$ |
168.192.3-168.kv.1.2 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.192.3-168.kv.1.27 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.192.3-168.mp.1.9 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.192.3-168.mp.1.32 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.192.3-168.qc.2.6 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.192.3-168.qc.2.7 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.192.3-168.ql.2.2 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.192.3-168.ql.2.9 | $168$ | $2$ | $2$ | $3$ | $?$ |