Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{2}\cdot12^{8}\cdot24^{2}$ | Cusp orbits | $2^{6}\cdot4^{2}$ | ||
| 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: | 24AG7 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}5&48\\252&95\end{bmatrix}$, $\begin{bmatrix}9&200\\172&97\end{bmatrix}$, $\begin{bmatrix}41&252\\156&167\end{bmatrix}$, $\begin{bmatrix}133&12\\144&157\end{bmatrix}$, $\begin{bmatrix}179&120\\22&199\end{bmatrix}$, $\begin{bmatrix}243&16\\178&165\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.7.u.2 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $24$ |
| Cyclic 264-torsion field degree: | $1920$ |
| Full 264-torsion field degree: | $2534400$ |
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 |
|---|---|---|---|---|---|
| 12.192.3-12.e.1.5 | $12$ | $2$ | $2$ | $3$ | $0$ |
| 264.96.0-264.g.2.4 | $264$ | $4$ | $4$ | $0$ | $?$ |
| 264.192.3-12.e.1.22 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dv.1.65 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dv.1.94 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dw.2.11 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dw.2.124 | $264$ | $2$ | $2$ | $3$ | $?$ |