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: | $24$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot3^{4}\cdot4^{2}\cdot6^{2}\cdot8^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $2^{4}\cdot4^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AA5 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}2&183\\25&136\end{bmatrix}$, $\begin{bmatrix}34&79\\189&68\end{bmatrix}$, $\begin{bmatrix}145&258\\204&175\end{bmatrix}$, $\begin{bmatrix}203&150\\22&235\end{bmatrix}$, $\begin{bmatrix}226&49\\221&30\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.5.bfj.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $12$ |
| Cyclic 264-torsion field degree: | $480$ |
| 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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.48.0-8.ba.1.1 | $8$ | $8$ | $8$ | $0$ | $0$ |
| 33.8.0-3.a.1.1 | $33$ | $48$ | $48$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.192.3-24.gf.2.3 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 264.192.1-264.se.1.8 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.se.1.15 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.3-24.gf.2.14 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.pg.2.19 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.pg.2.59 | $264$ | $2$ | $2$ | $3$ | $?$ |