Invariants
| Level: | $264$ | $\SL_2$-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: | $24$ (of which $4$ are rational) | Cusp widths | $2^{8}\cdot6^{8}\cdot8^{4}\cdot24^{4}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24Z5 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}31&168\\129&253\end{bmatrix}$, $\begin{bmatrix}85&216\\23&167\end{bmatrix}$, $\begin{bmatrix}145&156\\108&67\end{bmatrix}$, $\begin{bmatrix}241&120\\164&205\end{bmatrix}$, $\begin{bmatrix}247&120\\112&167\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.5.zo.2 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $12$ |
| Cyclic 264-torsion field degree: | $960$ |
| 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 |
|---|---|---|---|---|---|
| 24.192.1-24.dg.1.18 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 132.192.1-132.m.1.4 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-132.m.1.15 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-24.dg.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.rc.2.15 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.rc.2.24 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.3-264.kw.1.15 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.kw.1.20 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.lt.1.19 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.lt.1.48 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.pn.3.29 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.pn.3.44 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.pv.2.14 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.pv.2.24 | $264$ | $2$ | $2$ | $3$ | $?$ |