Invariants
Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $8 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $6^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 14$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24D8 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}11&26\\92&37\end{bmatrix}$, $\begin{bmatrix}47&80\\68&145\end{bmatrix}$, $\begin{bmatrix}53&70\\16&157\end{bmatrix}$, $\begin{bmatrix}101&94\\8&149\end{bmatrix}$, $\begin{bmatrix}131&48\\36&29\end{bmatrix}$, $\begin{bmatrix}133&48\\24&113\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.144.8.pd.2 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $32$ |
Cyclic 168-torsion field degree: | $1536$ |
Full 168-torsion field degree: | $516096$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=47$, 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.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
168.144.4-168.bl.1.26 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-168.bl.1.70 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-24.ch.1.22 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-168.nr.1.22 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-168.nr.1.43 | $168$ | $2$ | $2$ | $4$ | $?$ |