Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $9 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{4}\cdot8^{4}\cdot12^{4}\cdot24^{4}$ | Cusp orbits | $1^{4}\cdot2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 9$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AK9 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}13&150\\84&157\end{bmatrix}$, $\begin{bmatrix}89&112\\180&67\end{bmatrix}$, $\begin{bmatrix}107&232\\12&115\end{bmatrix}$, $\begin{bmatrix}113&226\\248&183\end{bmatrix}$, $\begin{bmatrix}115&186\\108&13\end{bmatrix}$, $\begin{bmatrix}245&216\\120&233\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.9.pt.4 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 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.192.3-24.bq.2.47 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 264.192.3-24.bq.2.31 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dz.4.100 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dz.4.119 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.5-264.l.2.12 | $264$ | $2$ | $2$ | $5$ | $?$ |
| 264.192.5-264.l.2.44 | $264$ | $2$ | $2$ | $5$ | $?$ |