Invariants
Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $6^{4}\cdot12^{6}\cdot24^{2}$ | Cusp orbits | $2^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24W7 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}35&94\\96&145\end{bmatrix}$, $\begin{bmatrix}69&80\\16&153\end{bmatrix}$, $\begin{bmatrix}91&38\\80&167\end{bmatrix}$, $\begin{bmatrix}139&68\\116&65\end{bmatrix}$, $\begin{bmatrix}139&128\\156&161\end{bmatrix}$, $\begin{bmatrix}143&108\\12&71\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.144.7.bba.2 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $3072$ |
Full 168-torsion field degree: | $516096$ |
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 |
---|---|---|---|---|---|
24.144.4-24.z.2.47 | $24$ | $2$ | $2$ | $4$ | $0$ |
168.144.3-168.cf.1.7 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.144.3-168.cf.1.51 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.144.4-24.z.2.17 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-168.bl.1.21 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-168.bl.1.35 | $168$ | $2$ | $2$ | $4$ | $?$ |