Invariants
| Level: | $264$ | $\SL_2$-level: | $66$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $13 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot6^{2}\cdot22^{2}\cdot66^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 24$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 13$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 66A13 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}5&168\\101&169\end{bmatrix}$, $\begin{bmatrix}142&39\\51&121\end{bmatrix}$, $\begin{bmatrix}180&239\\203&111\end{bmatrix}$, $\begin{bmatrix}209&85\\224&183\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.13.ct.3 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 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 |
|---|---|---|---|---|---|
| 132.192.7-132.b.1.5 | $132$ | $2$ | $2$ | $7$ | $?$ |
| 264.192.5-264.qz.4.9 | $264$ | $2$ | $2$ | $5$ | $?$ |
| 264.192.5-264.qz.4.19 | $264$ | $2$ | $2$ | $5$ | $?$ |
| 264.192.7-132.b.1.16 | $264$ | $2$ | $2$ | $7$ | $?$ |
| 264.192.7-264.l.4.2 | $264$ | $2$ | $2$ | $7$ | $?$ |
| 264.192.7-264.l.4.25 | $264$ | $2$ | $2$ | $7$ | $?$ |